Models and methodologies for simulating mobile ad-hoc networks
SimMechanics帮助文件
• Getting Started• Introducing SimMechanics Software• Product OverviewProduct DefinitionMechanical Simulation and Physical Modeling• Related ProductsRequired ProductsOther Related Products• Running a Demo ModelWhat the Demo RepresentsViewing a Mechanical Drawing of the ConveyorWhat the Demo IllustratesOpening the ModelRunning the ModelModifying the ModelVisualizing and Animating the Model• What You Can Do with SimMechanics SoftwareAbout SimMechanics SoftwareModeling Mechanical SystemsBodies, Coordinate Systems, Joints, and Constraints Sensors, Actuators, Friction, and Force ElementsSimulating and Analyzing Mechanical MotionVisualizing and Animating ModelsFor More Information• Learning MoreUsing the MATLAB Help System for Documentation and Demos Finding Special SimMechanics Help• Modeling, Simulating, and Visualizing Simple Machines• Introducing the SimMechanics Block LibrariesAbout the SimMechanics Block LibraryAccessing the LibrariesUsing the Libraries• Essential Steps to Building and Running a Mechanical Model About Machine Modeling and SimulationEssential Steps to Build a ModelEssential Steps to Configure and Run a Model• Modeling and Simulating a Simple MachineModeling the Simple PendulumOpening the SimMechanics Block LibraryThe World Coordinate System and GravityConfiguring the GroundConfiguring the BodyConfiguring the JointAdding a Sensor and Starting the Simulation• Visualizing a Simple MachineVisualizing and Animating the Simple PendulumStarting VisualizationSelecting a Body GeometryDisplaying the PendulumModeling and Visualizing More Complex Machines• Modeling and Simulating a Closed-Loop Machine Modeling the Four Bar MechanismViewing a Mechanical Drawing of the Four Bar Mechanism Counting the Degrees of FreedomConfiguring the Mechanical EnvironmentSetting Up the Block DiagramConfiguring the Ground and JointsConfiguring the BodiesSensing Motion and Running the ModelFor More About the Four Bar Mechanism• Representing Motion• Kinematics and Machine Motion StateAbout KinematicsDegrees of FreedomThe State of MotionHome, Initial, and Assembled ConfigurationsFor More Information• Representations of Body MotionAbout Body MotionMachine Geometry and MotionReference Frames and Coordinate SystemsRelating Coordinate Systems in Relative Motion Observing Body Motion in Different Coordinate Systems Representing Body Translations and Rotations• Representations of Body OrientationAbout Body Orientation RepresentationsAxis-Angle RepresentationQuaternion RepresentationRotation Matrix RepresentationEuler Angle RepresentationConverting Rotation RepresentationsConverting the Angular Velocity• Orienting a Body and Its Coordinate SystemsAbout the Body Orientation ExamplesSetting Up the Test BodyRotating the Body and Its CG CS Relative to World Rotating the Body Relative to Its Center of Gravity Creating and Rotating Body Coordinate SystemsReferences• User's Guide• Reference• Blocks• FunctionsExamples• Release NotesGetting StartedIf you have limited Simulink® and/or mechanical simulation experience, you will especiallyUser's GuideThese chapters compose the SimMechanics™ User's Guide. They introduce you to SimMechanics software, help you to build simple models, and explain the general steps to modeling and simulating mechanical systems. They also present SimMechanics tools and methods for analyzing mechanical motion.Modeling Mechanical Systems How to represent machines with block diagramsRunning Mechanical Models How to set up and run your simulation, generate and use code,and troubleshoot simulation errorsAnalyzing Motion Advanced methods for analyzing motionMotion, Control, and Real-Time Simulation Advanced controls and code generation applications, based on the Stewart platformStewart Platform as SimMechanics Plant in Simulink Control ModelModeling Mechanical SystemsSimMechanics software gives you a complete set of block libraries for modeling machine parts and connecting them into a Simulink® block diagram.●Representing Machines with Models●Modeling Grounds and Bodies●Modeling Degrees of Freedom●Constraining and Driving Degrees of Freedom●Cutting Machine Diagram Loops●Applying Motions and Forces●Sensing Motions and Forces●Adding Internal Forces●Combining One- and Three-Dimensional Mechanical Elements●Validating Mechanical ModelsConsult Representing Motion to review body kinematics. If you need more information on rigid body mechanics, consult the physics and engineering literature, beginning with the Bibliography. Classic engineering mechanics texts include Goodman and Warner [2], [3] and Meriam [8]. The books of Goldstein [1] and José and Saletan [5] are more theoretically oriented.Running Mechanical ModelsSimMechanics software gives you multiple ways to simulate and analyze machine motion in the Simulink environment. Running a mechanical simulation is similar to running a simulation of any other type of Simulink model. It entails setting various simulation options, starting the simulation, interpreting results, and dealing with simulation errors. See the Simulink documentation for a general discussion of these topics. This chapter focuses on aspects of simulation specific to SimMechanics models.●Configuring SimMechanics Models in Simulink●Configuring Methods of Solution●Starting Visualization and Simulation●How SimMechanics Software Works●Troubleshooting Simulation Errors●Improving Performance●Generating Code●Limitations●ReferenceAnalyzing MotionSimMechanics analysis modes allow you to study machine motion beyond the simple forward dynamics integration of forces. This chapter explains how to specify machine motion, then deduce the necessary forces and torques, with the Inverse Dynamics and Kinematic analysis modes. You can also specify a machine steady state and analyze perturbations about any machine trajectory by trimming and linearizing your model, respectively.●Mechanical Dynamics●Finding Forces from Motions●Trimming Mechanical Models●Linearizing Mechanical ModelsThe Motion, Control, and Real-Time Simulation chapter covers more sophisticated motion analysis and control design techniques applied to more complex systems.Motion, Control, and Real-Time SimulationSimMechanics software and Simulink form a powerful basis for advanced controls applications:trimming and linearizing motion, analyzing and designing controllers, generating code from the plant and controller models, and simulating controller and plant on dedicated hardware. This chapter is a connected set of case studies illustrating these methods. As its example system, the studies use the Stewart platform, a moderately complex, six degree-of-freedom positioning system.●About the Stewart Platform Case Studies●About the Stewart Platform●Modeling the Stewart Platform●Trimming and Linearizing Through Inverse Dynamics●About Controllers and Plants●Analyzing Controllers●Designing and Improving Controllers●Generating and Simulating with Code●Simulating with Hardware in the Loop●ReferencesBefore attempting these intricate case studies, you should understand the simpler motion analysis concepts, methods, and results of Analyzing Motion.Translating a CAD Stewart Platform in the Importing Mechanical Models chapter presents a related example, converting a Stewart platform computer-aided design assembly into a SimMechanics model.Introducing Visualization and AnimationYou can visualize your model's bodies using the SimMechanics visualization window. This overview explains the essentials of starting visualization and choosing body colors and geometries.●About SimMechanics Visualization●About Body Color and Geometry●Hierarchy of Body, Machine, and Model Visualization SettingsGetting Started with the Visualization WindowThe SimMechanics visualization window allows you to control how you view your model's bodies in both static display and dynamic simulation-based animation. It also allows you to record animations.●Introducing the SimMechanics Visualization Window●Controlling Body and Body Component Display●Adjusting the Camera View●Communicating with the Model from the Visualization Window●Controlling Simulation from the Visualization Window●Controlling Animation●Recording Animation●SimMechanics Visualization Menus and Their ControlsCustomizing Visualization and AnimationYou can customize the colors and geometries of visualized bodies in the SimMechanics visualization window. Choice of colors is intrinsic to visualization. Specifying a custom body geometry requires an external graphics file for each customized body.As an alternative to the visualization window, you can also visualize your mechanical system with virtual reality.●About Custom SimMechanics Visualization●Customizing Visualized Body Colors●Customizing Visualized Body Geometries●Visualizing with a Virtual Reality Client●ReferenceImporting Mechanical ModelsUsing SimMechanics software with computer-aided design (CAD) extends your mechanical modeling and simulation capabilities, allowing you to create SimMechanics models from CAD assemblies. This chapter covers what you need to get started with CAD translation. It assumes some familiarity with SimMechanics modeling, as explained in the SimMechanics Getting Started Guide and SimMechanics User's Guide.●Introducing Mechanical Import●Generating New Models from Physical Modeling XML●Working with Generated Models●Updating Generated Models Using Physical Modeling XML●Controlling Model Update at the Block Level●Troubleshooting Imported and Updated ModelsComputer-Aided Design TranslationThese case studies illustrate how to translate mechanical systems defined externally, as computer-aided design (CAD) assemblies, into mechanical models.●About the CAD Translation Case Studies●Translating a CAD Part into a Body●Translating CAD Constraints into Joints●Updating and Retranslating a CAD Pendulum●Translating a CAD Robot Arm●Translating a CAD Stewart Platform。
英文翻译
A Facial Aging Simulation Method Using flaccidity deformation criteriaAlexandre Cruz Berg Lutheran University of Brazil.Dept Computer ScienceRua Miguel Tostes, 101. 92420-280 Canoas, RS, Brazil berg@ulbra.tche.br Francisco José Perales LopezUniversitat les Illes Balears.Dept Mathmatics InformaticsCtra Valldemossa, km 7,5E-07071 Palma MallorcaSpainpaco.perales@uib.esManuel GonzálezUniversitat les Illes Balears.Dept Mathmatics InformaticsCtra Valldemossa, km 7,5E-07071 Palma MallorcaSpainmanuel.gonzales@uib.esAbstractDue to the fact that the aging human face encompasses skull bones, facial muscles, and tissues, we render it using the effects of flaccidity through the observation of family groups categorized by sex, race and age. Considering that patterns of aging are consistent, facial ptosis becomes manifest toward the end of the fourth decade. In order to simulate facial aging according to these patterns, we used surfaces with control points so that it was possible to represent the effect of aging through flaccidity. The main use of these surfaces is to simulate flaccidity and aging consequently.1.IntroductionThe synthesis of realistic virtual views remains one of the central research topics in computer graphics. The range of applications encompasses many fields, including: visual interfaces for communications, integrated environments of virtual reality, as well as visual effects commonly used in film production.The ultimate goal of the research on realistic rendering is to display a scene on a screen so that it appears as if the object exists behind the screen. This description, however, is somewhat ambiguous and doesn't provide a quality measure for synthesized images. Certain areas, such as plastic surgery, need this quality evaluation on synthesized faces to make sure how the patient look like and more often how the patient will look like in the future. Instead, in computer graphics and computer vision communities, considerable effort has been put forthto synthesize the virtual view of real or imaginary scenes so that they look like the real scenes.Much work that plastic surgeons put in this fieldis to retard aging process but aging is an inevitable process. Age changes cause major variations in the appearance of human faces [1]. Some aspects of aging are uncontrollable and are based on hereditary factors; others are somewhat controllable, resulting from many social factors including lifestyle, among others [2].1.1.Related WorkMany works about aging human faces have been done. We can list some related work in the simulation of facial skin deformation [3].One approach is based on geometric models, physically based models and biomechanical models using either a particle system or a continuous system.Many geometrical models have been developed, such as parametric model [4] and geometric operators [5]. The finite element method is also employed for more accurate calculation of skin deformation, especially for potential medical applications such as plastic surgery [6]. Overall, those works simulate wrinkles but none of them have used flaccidity as causing creases and aging consequently.In this work is presented this effort in aging virtual human faces, by addressing the synthesis of new facial images of subjects for a given target age.We present a scheme that uses aging function to perform this synthesis thru flaccidity. This scheme enforces perceptually realistic images by preserving the identity of the subject. The main difference between our model and the previous ones is that we simulate increase of fat and muscular mass diminish causing flaccidity as one responsible element for the sprouting of lines and aging human face.In the next section will plan to present the methodology. Also in section 3, we introduce the measurements procedure, defining structural alterations of the face. In section 4, we present a visual facial model. We describe age simulation thrua deformation approach in section 5. In the last section we conclude the main results and future work.2.MethodologyA methodology to model the aging of human face allows us to recover the face aging process. This methodology consists of: 1) defining the variations of certain face regions, where the aging process is perceptible; 2) measuring the variations of those regions for a period of time in a group of people and finally 3) making up a model through the measurements based on personal features.That could be used as a standard to a whole group in order to design aging curves to the facial regions defined.¦njjjpVM2.1Mathematical Background and AnalysisHuman society values beauty and youth. It is well known that the aging process is influenced by several parameters such: feeding, weight, stress level, race, religious factors, genetics, etc. Finding a standard set of characteristics that could possibly emulate and represent the aging process is a difficult proposition.This standard set was obtained through a mathematical analysis of some face measurements in a specific group of people, whose photographs in different ages were available [7]. To each person in the group, there were, at least, four digitized photographs. The oldest of them was taken as a standard to the most recent one. Hence, some face alterations were attained through the passing of time for the same person.The diversity of the generated data has led to the designing of a mathematical model, which enabled the acquiring of a behavior pattern to all persons of the same group, as the form of a curve defined over the domain [0,1] in general, in order to define over any interval [0,Į] for an individual face. The unknown points Įi are found using the blossoming principle [8] to form the control polygon of that face.The first step consisted in the selection of the group to be studied. Proposing the assessment of the face aging characteristics it will be necessary to have a photographic follow-up along time for a group of people, in which their face alterations were measurable.The database used in this work consisted of files of patients who were submitted to plastic surgery at Medical Center Praia do Guaíba, located in Porto Alegre, Brazil.3.MeasurementsAccording to anatomic principles [9] the vectors of aging can be described aswhich alter the position and appearance of key anatomic structures of the face as can be shown in figure 1 which compares a Caucasian mother age 66 (left side) with her Caucasian daughters, ages 37 (right above) and 33 (right below) respectively.Figure 1 - Observation of family groupsTherefore, basic anatomic and surgical principles must be applied when planning rejuvenative facial surgery and treating specific problems concomitantwith the aging process.4.Visual Facial ModelThe fact that human face has an especially irregular format and interior components (bones, muscles and fabrics) to possess a complex structure and deformations of different face characteristics of person to person, becomes the modeling of the face a difficult task. The modeling carried through in the present work was based on the model, where the mesh of polygons corresponds to an elastic mesh, simulating the dermis of the face. The deformations in this mesh, necessary to simulate the aging curves, are obtained through the displacement of the vertexes, considering x(t) as a planar curve, which is located within the (u,v ) unit square. So, we can cover the square with a regular grid of points b i,j =[i/m,j/n]T ; i=0,...,m; j=0,...,n. leading to every point (u,v ) asfrom the linear precision property of Bernstein polynomials. Using comparisons with parents we can distort the grid of b i,j into a grid b'i,j , the point (u,v )will be mapped to a point (u',v') asIn order to construct our 3D mesh we introduce the patch byAs the displacements of the vertexes conform to the certain measures gotten through curves of aging and no type of movement in the face is carried through, the parameters of this modeling had been based on the conformation parameter.4.1Textures mappingIn most cases the result gotten in the modeling of the face becomes a little artificial. Using textures mapping can solve this problem. This technique allows an extraordinary increase in the realism of the shaped images and consists of applying on the shaped object, existing textures of the real images of the object.In this case, to do the mapping of an extracted texture of a real image, it is necessary that the textureaccurately correspond to the model 3D of that is made use [9].The detected feature points are used for automatic texture mapping. The main idea of texture mapping is that we get an image by combining two orthogonal pictures in a proper way and then give correct texture coordinates of every point on a head.To give a proper coordinate on a combined image for every point on a head, we first project an individualized 3D head onto three planes, the front (x, y), the left (y, z) and the right (y, z) planes. With the information of feature lines, which are used for image merging, we decide on which plane a 3D-head point on is projected.The projected points on one of three planes arethen transferred to one of feature points spaces suchas the front and the side in 2D. Then they are transferred to the image space and finally to the combined image space.The result of the texture mapping (figure 2) is excellent when it is desired to simulate some alteration of the face that does not involve a type of expression, as neutral. The picture pose must be the same that the 3D scanned data.¦¦¦ mi nj lk n j m i lk k j i w B v B u B b w v u 000,,)()()(')',','(¦¦ m i nj n jmij i v B u B b v u 00,)()(),(¦¦ m i nj n j m i j i v B u B b v u 00,)()(')','(¦¦¦ mi nj lk n j m i lk k j i w B v B u B b w v u 000,,)()()(')',','(Figure 2 - Image shaped with texturemapping5.Age SimulationThis method involves the deformation of a face starting with control segments that define the edges of the faces, as¦¦¦ mi nj lk n j m i lk k j i w B v B u B b w v u 000,,)()()(')',','(Those segments are defined in the original face and their positions are changed to a target face. From those new positions the new position of each vertex in the face is determined.The definition of edges in the face is a fundamental step, since in that phase the applied aging curves are selected. Hence, the face is divided in influencing regions according to their principal edges and characteristics.Considering the face morphology and the modeling of the face aging developed [10], the face was divided in six basic regions (figure 3).The frontal region (1) is limited by the eyelids and the forehead control lines. The distance between these limits enlarges with forward aging.The orbitary region (2) is one of the most important aging parameters because a great number of wrinkles appears and the palpebral pouch increases [11]. In nasal region (3) is observed an enlargement of its contour.The orolabial region (4) is defined by 2 horizontal control segments bounding the upper and lower lips and other 2 segments that define the nasogenian fold. Figure 3 - Regions considering the agingparametersThe lips become thinner and the nasogenian fold deeper and larger. The mental region (5) have 8 control segments that define the low limit of the face and descend with aging. In ear curve (6) is observed an enlargement of its size. The choice of feature lines was based in the characteristic age points in figure 6.The target face is obtained from the aging curves applied to the source face, i.e., with the new control segment position, each vertex of the new image has its position defined by the corresponding vertex in the target face. This final face corresponds to the face in the new age, which was obtained through the application of the numerical modeling of the frontal face aging.The definition of the straight-line segment will control the aging process, leading to a series of tests until the visual result was adequate to the results obtained from the aging curves. The extremes of the segments are interpolated according to the previously defined curves, obtained by piecewise bilinear interpolation [12].Horizontal and vertical orienting auxiliary lines were defined to characterize the extreme points of the control segments (figure 4). Some points, that delimit the control segments, are marked from the intersection of the auxiliary lines with the contour of the face, eyebrow, superior part of the head and the eyes. Others are directly defined without the use of auxiliary lines, such as: eyelid hollow, eyebrow edges, subnasion, mouth, nasolabial wrinkle andnose sides.Figure 4 - Points of the control segmentsOnce the control segments characterize the target image, the following step of the aging process can be undertaken, corresponding to the transformations of the original points to the new positions in the target image. The transformations applied to the segments are given by the aging curves, presented in section 4.In the present work the target segments are calculated by polynomial interpolations, based on parametric curves [12].5.1Deformation approachThe common goal of deformation models is to regulate deformations of a geometric model by providing smoothness constraints. In our age simulation approach, a mesh-independent deformation model is proposed. First, connected piece-wise 3D parametric volumes are generated automatically from a given face mesh according to facial feature points.These volumes cover most regions of a face that can be deformed. Then, by moving the control pointsof each volume, face mesh is deformed. By using non-parallel volumes [13], irregular 3D manifolds are formed. As a result, smaller number of deformvolumes are necessary and the number of freedom incontrol points are reduced. Moreover, based on facialfeature points, this model is mesh independent,which means that it can be easily adopted to deformany face model.After this mesh is constructed, for each vertex on the mesh, it needs to be determined which particularparametric volume it belongs to and what valueparameters are. Then, moving control points ofparametric volumes in 3D will cause smooth facialdeformations, generating facial aging throughflaccidity, automatically through the use of the agingparameters. This deformation is written in matricesas , where V is the nodal displacements offace mesh, B is the mapping matrix composed ofBernstein polynomials, and E is the displacementvector of parametric volume control nodes.BE V Given a quadrilateral mesh of points m i,j ,, we define acontinuous aged surface via a parametricinterpolation of the discretely sampled similaritiespoints. The aged position is defined via abicubic polynomial interpolation of the form with d m,n chosen to satisfy the known normal and continuity conditions at the sample points x i,j .>@>M N j i ,...,1,...,1),(u @@>@>1,,1,),,( j j v i i u v u x ¦3,,),(n m n m n m v u d v u x An interactive tool is programmed to manipulate control points E to achieve aged expressions making possible to simulate aging through age ranges. Basic aged expression units are orbicularis oculi, cheek, eyebrow, eyelid, region of chin, and neck [14]. In general, for each segment, there is an associated transformation, whose behavior can be observed by curves. The only segments that do not suffer any transformation are the contour of the eyes and the superior side of the head.5.2Deformation approachThe developed program also performs shape transformations according to the created aging curves, not including any quantification over the alterations made in texture and skin and hair color. Firstly, in the input model the subjects are required to perform different ages, as previouslymentioned, the first frame needs to be approximately frontal view and with no expression.Secondly, in the facial model initialization, from the first frame, facial features points are extracted manually. The 3D fitting algorithm [15] is then applied to warp the generic model for the person whose face is used. The warping process and from facial feature points and their norms, parametric volumes are automatically generated.Finally, aging field works to relieve the drifting problem in template matching algorithm, templates from the previous frame and templates from the initial frame are applied in order to combine the aging sequence. Our experiments show that this approach is very effective. Despite interest has been put in presenting a friendly user interface, we have to keep in mind that the software system is research oriented. In this kind of applications an important point is the flexibility to add and remove test facilities. 6.Results The presented results in the following figuresrefer to the emulations made on the frontalphotographs, principal focus of this paper, with theobjective to apply the developed program to otherpersons outside the analyzed group. The comparisonswith other photographs of the tested persons dependon their quality and on the position in which theywere taken. An assessment was made of the new positions, of the control segments. It consisted in: after aging a face, from the first age to the second one, through the use of polynomial interpolation of the control segments in the models in the young age, the new positions are then compared with the ones in the model of a relative of older age (figure 5). The processed faces were qualitatively compared with theperson’s photograph at the same age. Figure 5 - Synthetic young age model,region-marked model and aged modelAlso the eyelid hollow, very subtle falling of the eyebrow, thinning of the lips with the enlarging of the nasion and the superior part of the lip, enlargingof the front and changing in the nasolabial wrinkle.7.ConclusionsModelling biological phenomena is a great deal of work, especially when the biggest part of the information about the subject involves only qualitative data. Thus, this research developed had has a challenge in the designing of a model to represent the face aging from qualitative data.Due to its multi-disciplinary character, the developed methodology to model and emulate the face aging involved the study of several other related fields, such as medicine, computing, statistics and mathematics.The possibilities opened by the presented method and some further research on this field can lead to new proposals of enhancing the current techniques of plastic face surgery. It is possible to suggest the ideal age to perform face lifting. Once the most affected aging regions are known and how this process occurs over time. Also missing persons can be recognized based on old photographs using this technique. AcknowledgementsThe project TIN2004-07926 of Spanish Government have subsidized this work.8. References[1] Burt, D. M. et al., Perc. age in adult Caucasianmale faces, in Proc. R. Soc., 259, pp 137-143,1995.[2] Berg, A C. Aging of Orbicularis Muscle inVirtual Human Faces. IEEE 7th InternationalConference on Information Visualization, London, UK, 2003a.[3] Beier , T., S. Neely, Feature-based imagemetamorphosis, In Computer Graphics (Proc.SIGGRAPH), pp. 35-42, 1992.[4] Parke, F. I. P arametrized Models for FacialAnimation, IEEE Computer & Graphics Applications, Nov. 1982.[5] Waters, K.; A Muscle Model for Animating ThreeDimensional Facial Expression. Proc SIGGRAPH'87,Computer Graphics, Vol. 21, Nº4, United States, 1987. [6] Koch, R.M. et alia.. Simulation Facial SurgeryUsing Finite Element Models, Proceedings of SIGGRAPH'96, Computer Graphics, 1996.[7] Kurihara, Tsuneya; Kiyoshi Arai, ATransformation Method for Modeling and Animation of the Human Face from Photographs, Computer Animatio n, Springer-Verlag Tokyo, pp.45-58, 1991.[8] Kent, J., W. Carlson , R. Parent, ShapeTransformation for Polygon Objects, In Computer Graphics (Proc. SIGGRAPH), pp. 47-54, 1992. [9] Sorensen, P., Morphing Magic, in ComputerGraphics World, January 1992.[10]Pitanguy, I., Quintaes, G. de A., Cavalcanti, M.A., Leite, L. A. de S., Anatomia doEnvelhecimento da Face, in Revista Brasileira deCirurgia, Vol 67, 1977.[11]Pitanguy, I., F. R. Leta, D. Pamplona, H. I.Weber, Defining and measuring ageing parameters, in Applied Mathematics and Computation , 1996.[12]Fisher, J.; Lowther, J.; Ching-Kuang S. Curveand Surface Interpolation and Approximation: Knowledge Unit and Software Tool. ITiCSE’04,Leeds, UK June 28–30, 2004.[13]Lerios, A. et al., Feature-Based VolumeMetamorphosis, in SIGGRAPH 95 - Proceedings,pp 449-456, ACM Press, N.Y, 1995.[14]Berg, A C. Facial Aging in a VirtualEnvironment. Memória de Investigación, UIB, Spain, 2003b.[15]Hall, V., Morphing in 2-D and 3-D, in Dr.Dobb's Journal, July 1993.。
Mathematical Modelling and Numerical Analysis Will be set by the publisher Modelisation Mat
c EDP Sciences, SMAI 1999
2
PAVEL BEL K AND MITCHELL LUSKIN
In general, the analysis of stability is more di cult for transformations with N = 4 such as the tetragonal to monoclinic transformations studied in this paper and N = 6 since the additional wells give the crystal more freedom to deform without the cost of additional energy. In fact, we show here that there are special lattice constants for which the simply laminated microstructure for the tetragonal to monoclinic transformation is not stable. The stability theory can also be used to analyze laminates with varying volume fraction 24 and conforming and nonconforming nite element approximations 25, 27 . We also note that the stability theory was used to analyze the microstructure in ferromagnetic crystals 29 . Related results on the numerical analysis of nonconvex variational problems can be found, for example, in 7 12,14 16,18,19,22,26,30 33 . We give an analysis in this paper of the stability of a laminated microstructure with in nitesimal length scale that oscillates between two compatible variants. We show that for any other deformation satisfying the same boundary conditions as the laminate, we can bound the pertubation of the volume fractions of the variants by the pertubation of the bulk energy. This implies that the volume fractions of the variants for a deformation are close to the volume fractions of the laminate if the bulk energy of the deformation is close to the bulk energy of the laminate. This concept of stability can be applied directly to obtain results on the convergence of nite element approximations and guarantees that any nite element solution with su ciently small bulk energy gives reliable approximations of the stable quantities such as volume fraction. In Section 2, we describe the geometrically nonlinear theory of martensite. We refer the reader to 2,3 and to the introductory article 28 for a more detailed discussion of the geometrically nonlinear theory of martensite. We review the results given in 34, 35 on the transformation strains and possible interfaces for tetragonal to monoclinic transformations corresponding to the shearing of the square and rectangular faces, and we then give the transformation strain and possible interfaces corresponding to the shearing of the plane orthogonal to a diagonal in the square base. In Section 3, we give the main results of this paper which give bounds on the volume fraction of the crystal in which the deformation gradient is in energy wells that are not used in the laminate. These estimates are used in Section 4 to establish a series of error bounds in terms of the elastic energy of deformations for the L2 approximation of the directional derivative of the limiting macroscopic deformation in any direction tangential to the parallel layers of the laminate, for the L2 approximation of the limiting macroscopic deformation, for the approximation of volume fractions of the participating martensitic variants, and for the approximation of nonlinear integrals of deformation gradients. Finally, in Section 5 we give an application of the stability theory to the nite element approximation of the simply laminated microstructure.
simultaneous equation method
Simultaneous Equation MethodIntroductionIn mathematics, simultaneous equations play a crucial role in solving real-world problems and modeling various phenomena. The simultaneous equation method is a powerful technique used to find solutions for a system of equations. This method involves solving multiple equations together to determine the values of unknown variables. In this article, we will explore the simultaneous equation method in detail and discuss its applications.Understanding Simultaneous EquationsDefinitionSimultaneous equations, also known as a system of equations, are a set of equations that share the same variables. The solutions of these equations simultaneously satisfy each equation in the system. The general form of simultaneous equations can be written as:a1x + b1y = c1a2x + b2y = c2Here, x and y are the variables, while a1, a2, b1, b2, c1, and c2 are constants.Types of Simultaneous EquationsSimultaneous equations can be classified into three types based on the number of solutions they have:1.Consistent Equations: These equations have a unique solution,meaning there is a specific set of values for the variables thatsatisfy all the equations in the system.2.Inconsistent Equations: This type of system has no solution. Theequations are contradictory and cannot be satisfied simultaneously.3.Dependent Equations: In this case, the system has infinitely manysolutions. The equations are dependent on each other and represent the same line or plane in geometric terms.To solve simultaneous equations, we employ various methods, with the simultaneous equation method being one of the most commonly used techniques.The Simultaneous Equation MethodThe simultaneous equation method involves manipulating and combining the given equations to eliminate one variable at a time. By eliminating one variable, we can reduce the system to a single equation with one variable, making it easier to find the solution.ProcedureThe general procedure for solving simultaneous equations using the simultaneous equation method is as follows:1.Identify the unknow n variables. Let’s assume we have n variables.2.Write down the given equations.3.Choose two equations and eliminate one variable by employingsuitable techniques such as substitution or elimination.4.Repeat step 3 until you have a single equation with one variable.5.Solve the single equation to determine the value of the variable.6.Substitute the found value back into the other equations to obtainthe values of the remaining variables.7.Verify the solution by substituting the found values into all theoriginal equations. The values should satisfy each equation.If the system is inconsistent or dependent, the simultaneous equation method will also lead to appropriate conclusions.Applications of Simultaneous Equation MethodThe simultaneous equation method finds applications in numerous fields, including:EngineeringSimultaneous equations are widely used in engineering to model and solve various problems. Engineers employ this method to determine unknown quantities in electrical circuits, structural analysis, fluid mechanics, and many other fields.EconomicsIn economics, simultaneous equations help analyze the relationship between different economic variables. These equations assist in studying market equilibrium, economic growth, and other economic phenomena.PhysicsSimultaneous equations are a fundamental tool in physics for solving complex problems involving multiple variables. They are used in areas such as classical mechanics, electromagnetism, and quantum mechanics.OptimizationThe simultaneous equation method is utilized in optimization techniques to find the optimal solution of a system subject to certain constraints. This is applicable in operations research, logistics, and resource allocation problems.ConclusionThe simultaneous equation method is an essential mathematical technique for solving systems of equations. By employing this method, we can find the values of unknown variables and understand the relationships between different equations. The applications of this method span across various fields, making it a valuable tool in problem-solving and modeling real-world situations. So, the simultaneous equation method continues to be akey topic in mathematics and its practical applications in diverse disciplines.。
数模德尔菲法的英文名称
数模德尔菲法的英文名称《The Delphi Method in Numerical Modeling》The Delphi Method is a widely used research technique that is particularly valuable in the field of numerical modeling. This method involves obtaining input from a panel of experts to reach consensus on a particular topic or issue. The process typically involves multiple rounds of questionnaires and feedback, and is designed to distill the collective wisdom of the experts involved.In the context of numerical modeling, the Delphi Method can be a powerful tool for gathering insights from experts in various fields such as mathematics, computer science, and engineering. This input can be used to refine and improve the mathematical and computational models used to simulate complex systems and phenomena. By leveraging the knowledge and experience of a diverse group of experts, the Delphi Method can help ensure that the numerical models developed are accurate, reliable, and practical.The application of the Delphi Method in numerical modeling can lead to more robust and effective models, which in turn can have far-reaching implications in fields such as weather forecasting, structural engineering, and fluid dynamics. By leveraging the collective intelligence of a panel of experts, researchers and practitioners can gain valuable insights into the intricacies of the systems they are modeling, and develop more accurate and insightful predictions.In conclusion, the Delphi Method in numerical modeling holds great promise for improving the quality and reliability of mathematical and computational models. By harnessing the wisdom and expertise of a diverse group of experts, researchers and practitioners can develop more accurate and practical models that have the potential to revolutionize the way we understand and interact with the world around us.。
科技英语交流(第2版)Lecture 5 How to write Methods
Basic components
Generalization or introduction Materials or subjects Methods or procedures Data analysis
The experimental apparatus for...is shown in Fig.2.
5.4.3 Typical expressions of equipment and apparatus
The experimental system was based on a ... A fine wire screen is installed at the ... Example: The experimental system was composed of
vehicles 3. Decoupling PF dynamic model
… 4. Case study
…
3. Organization-related data selection
3.1 Fixed and dynamic keywords sources
3.2 Known accounts sources 3.3 Org keyusers sources 3.4 Two-class SUM
5.3 Specific analyses: generalization and introduction
This part is a general introduction of the principal activity, sometimes presenting the purpose of the research. For example, “In this letter we present the first systematic study on the electrical and magnetic effects of hole compensation.” It also introduces some background information related to the methods or the author’s hypothesis to the research. Study the example on page 87-89.
建模与仿真技术.
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建 模 与 仿 真 技 . 术使用菜单拟合Origin 直接使用菜单回 归 的 菜 单 命 令 在 【 Analysis】菜单下,有 线性回归、多项式拟合、 指数拟合以及 S 曲线拟合 等。【 Analysis】菜单下 的拟合的菜单命令如图 81 所示,其具体拟合的函 数见表 1 。采用菜单拟合 时,必须使要拟合的数据 被 激 活 , 而 后 在 【 Analysis】菜单下选择 相应拟合类型进行拟合。
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建 模 与 仿 真 技 . 术
安装数字化插件
• 在 Origin 网页的文件交换目录中下载 Digitize.OPK, 运 行 Origin7.0, 从 Windows 文 件 管 理 器 将 Digitize.OPK 拖曳到 Origin7.0 的工作空间,此时完 成安装,在 Origin7.0 的工作空间里可以看到一个 Digitize按钮,如图所示。
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三种拟合工具对话框
建 模 与 仿 真 技 . 术
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建 模 与 仿 真 技 . 术
S曲线拟合工具举例
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Geometric Modeling
Geometric ModelingGeometric modeling is a crucial aspect of computer graphics and design, allowing for the creation of complex shapes and structures in virtual environments. It involves the representation of objects using mathematical equations and algorithms to accurately depict their form and appearance. This process isessential for various applications, such as animation, simulation, and virtual reality, where realistic and detailed visuals are required to enhance user experiences. One of the primary benefits of geometric modeling is its ability to accurately represent real-world objects and environments in a digital format. By using mathematical formulas to define shapes, sizes, and positions of various elements, designers can create highly detailed and realistic 3D models thatclosely resemble their physical counterparts. This level of precision is essential for applications such as architectural design, where accurate representations of buildings and structures are necessary for planning and visualization purposes. Furthermore, geometric modeling allows for the manipulation and transformation of objects in virtual space, enabling designers to explore different design options and variations without the need for physical prototypes. This flexibility is particularly useful in industries such as product design and manufacturing, where rapid prototyping and iterative design processes are common. By using geometric modeling techniques, designers can quickly modify and refine their designs, saving time and resources in the product development cycle. In addition to its practical applications, geometric modeling also plays a significant role in artistic and creative endeavors, such as digital sculpting and character design. Artists and animators use geometric modeling tools to create visually stunning and expressive characters and environments, bringing their creative visions to life in virtual space. The ability to manipulate shapes, textures, and colors with precisionallows artists to push the boundaries of imagination and create captivatingvisuals that captivate audiences. Despite its many advantages, geometric modeling also presents challenges and limitations that designers must overcome. One common issue is the complexity of mathematical equations and algorithms required to accurately represent and manipulate 3D objects. Designers need to have a strong understanding of geometry, trigonometry, and calculus to effectively use geometricmodeling tools, which can be daunting for those without a background in mathematics. Another challenge is the computational intensity of geometric modeling processes, which can be resource-intensive and time-consuming, especially when dealing with large and complex models. Designers often face performance bottlenecks and long processing times when working with high-resolution textures, intricate details, and intricate simulations, which can hinder workflow efficiency and productivity. In conclusion, geometric modeling is a powerful and versatile tool that enables designers and artists to create realistic, detailed, andvisually stunning 3D models for a wide range of applications. From architectural design and product development to digital art and animation, geometric modeling plays a crucial role in shaping the virtual world around us. While it presents challenges and limitations, the benefits of geometric modeling far outweigh the drawbacks, making it an essential tool for anyone working in the field of computer graphics and design.。
《非傅里叶热传导模型的H~1-Galerkin混合连续时空有限元方法》范文
《非傅里叶热传导模型的H~1-Galerkin混合连续时空有限元方法》篇一非傅里叶热传导模型的H^1-Galerkin混合连续时空有限元方法一、引言在科学与工程计算中,热传导现象是一个基本而重要的研究课题。
传统的傅里叶热传导模型虽然能解释许多热传导现象,但在某些极端或复杂环境下,如纳米材料、微尺度系统以及高频率变化的热流环境中,其模型不再适用。
因此,非傅里叶热传导模型逐渐成为研究的热点。
为了更准确地模拟和解决这些复杂问题,本文提出了一种基于H^1-Galerkin混合连续时空有限元方法(H^1-Galerkin Hybrid Continuous Space-Time Finite Element Method)来研究非傅里叶热传导模型。
二、非傅里叶热传导模型非傅里叶热传导模型是在传统的傅里叶热传导模型基础上发展起来的,它考虑了热波传播的延迟效应和热流的不连续性。
在非傅里叶热传导模型中,温度的变化不仅取决于温度梯度,还与热流的传播速度和方向有关。
这使得我们能够更准确地模拟和分析复杂的热传导现象。
三、H^1-Galerkin混合连续时空有限元方法H^1-Galerkin混合连续时空有限元方法是一种有效的数值求解方法,它结合了时空有限元和混合有限元的特点,能够在连续时间和空间上求解偏微分方程。
这种方法可以处理复杂的几何形状和非线性问题,适用于求解非傅里叶热传导模型。
在H^1-Galerkin混合连续时空有限元方法中,我们将空间和时间看作一个统一的维度,采用有限元方法对时间进行离散化处理。
在每个时间步长内,通过求解Galerkin方程来获得温度的近似解。
同时,我们使用混合有限元的方法来处理未知的边界条件和源项。
四、应用H^1-Galerkin混合连续时空有限元方法求解非傅里叶热传导模型在应用H^1-Galerkin混合连续时空有限元方法求解非傅里叶热传导模型时,我们首先将求解区域划分为一系列的子区域(即有限元),然后在每个子区域内进行离散化处理。
板结构特性分析
實驗力學研究室
Beam Coordinate System
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Stress Recovery in Beams
Tensile and compressive stress is calculated for the entire beam, but reported bending stress and stress from torsion will depend on your choice of stress recovery points.
3Dsimulation and modeling
• Beam simulation • Symmetry or anti-symmetry • Plate or shell models • Solid models
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實驗力學研究室
Plane Stress Modeling
The definition of plane stress requires that the behavior of interest occurs in such a manner that there is no stress component normal to the plane of action. This means that one of the three principal stresses is zero.
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實驗力學研究室
Cyclic Symmetry
Cyclic symmetry is a more specialized condition where features that are repeated about an axis can be modeled by a single instance of that feature.
Model Parameters for Simulating Fate and Transport
Review Paper/Model Parameters for Simulating Fate and Transport of On-Site Wastewater Nutrientsby John E.McCray 1,2,4,Shiloh L.Kirkland 2,Robert L.Siegrist 3,and Geoffrey D.Thyne 2AbstractThis paper presents a critical review of model-input parameters for transport of on-site wastewater treatment system (OWS)pollutants.Approximately 25%of the U.S.population relies on soil-based OWS for effective treat-ment and protection of public health and environmental quality.Mathematical models are useful tools for under-standing and predicting the transport and fate of wastewater pollutants and for addressing water-budget issues related to wastewater reclamation from site to watershed scales.However,input parameters for models that simu-late fate and transport of OWS pollutants are not readily obtained.The purpose of this analysis is to illustrate an objective,statistically supported method for choosing model-input parameters related to nitrogen (N)and phos-phorus (P).Data were gathered from existing studies reported in the literature.Cumulative frequency distributions (CFDs)are provided for OWS effluent concentrations of N and P,nitrification and denitrification rates,and linear sorption isotherm constants for P.When CFDs are not presented,ranges and median values are provided.Median values for model-input parameters are as follows:total N concentration (44mg/L),nitrate-N (0.2mg/L),ammo-nium (60mg/L),phosphate-P (9mg/L),organic N (14mg/L),zero-order nitrification rate (264mg/L/d),first-order nitrification (2.9/d),first-order dentrification (0.025/d),maximum soil capacity for P uptake (237mg/kg),linear sorption isotherm constant for P (15.1L/kg),and OWS effluent flow rates (260L/person/d).IntroductionThe standard of practice for wastewater management in the United States and many developed countries has evolved to include large,centralized wastewater treat-ment plants fed by networks of sewer pipes that connect to individual wastewater generators.However,many sit-uations exist where this practice is neither cost effective nor sustainable due to a variety of factors.Examples include areas that are sparsely populated,have uneven ter-rain,and have limited water and energy supplies (Siegrist 2001).Furthermore,centralized treatment of wastewater can incur additional problems associated with leaking sewers and the possibility of treatment plant failure,bothresulting in untreated raw sewage being discharged directly into the subsurface or surface water.Thus,on-site wastewater treatment systems (OWS)are considered a feasible and economical wastewater treatment alternative to centralized systems rather than a temporary wastewater disposal method while centralized sewers and wastewater treatment plants are being constructed.Approximately 25%of the U.S.population is served by OWS,and this proportion is growing (U.S.EPA 1997).Conventional OWS comprise four basic components:a wastewater source,a pretreatment unit (septic tank),an effluent delivery system that includes a subsurface infiltration gallery,and a soil absorption field (or leach field)(see Figure 1).In this paper,we focus on OWS that use septic tanks,where the wastewater source may be an individual residence,business,or a small cluster of homes or businesses.Wastewater generated on-site is collected from the source and piped to a nearby pretreatment unit,commonly called a septic tank.Pretreatment processes in this unit include sedimentation of solids and floatation of oils and greases,as well as anaerobic digestion.Effluent from this tank is then periodically discharged by gravity or via pumping to the subsurface through an effluent1HydrogeologyProgram,Colorado School of Mines,Golden,CO 804012Department of Geology and Geological Engineering,Colorado School of Mines,Golden,CO 804013Environmental Science and Engineering Division,Colorado School of Mines,Golden,CO 804014Corresponding author:(303)273-3490;fax (303)273-3413;jmccray@Received April 2003,accepted December 2003.Copyright ª2005National Ground WaterAssociation.628Vol.43,No.4—GROUND WATER—July–August 2005(pages 628–639)delivery system.This effluent delivery system usually comprises a series of perforated pipes within a number of subsurface trenches or a single subsurface bed.The effluent from the delivery system infiltrates into the soil absorption field where it percolates through the vadose zone down to the ground water zone.During per-colation through the vadose zone,the effluent receives advanced treatment through pollutant sorption,precipita-tion,transformation,filtration,chemical degradation,and biodegradation.However,conditions in the subsurface such as a high water table,thin soil layer,or shallow frac-tured or karst bedrock may exist,and contaminants such as nutrients and pathogens may not be treated thoroughly before recharge into the underlying ground water.In addition,contaminants reaching the ground water may then exfiltrate to nearby surface water through base flow or seepage and runoff,thereby contributing to the con-taminant load in those surface water.Clearly,OWS are possible contributors to surface-water contaminant load-ing.With the increasing emphasis on watershed manage-ment and non–point source control,there is a need to develop quantitative approaches to assess OWS pollutant fate and transport.In many rural and urban fringe areas,the OWS density is increasing as clusters or subdivisions of homes are being built with OWS.In these settings,the need ex-ists for a quantitative method of evaluating on-site system performance and predicting potential cumulative effects of OWS on public health and environmental quality. Understanding the cumulative effects of these systems is critical for determining the probability of adverse effects on nearby drinking water supply wells that may be as lit-tle as30m from the wastewater infiltration system.Site-level fate and transport relationships are also needed to account for OWS inputs when determining potential impacts on sensitive surface water and allocating total daily maximum loads(TMDLs)in watersheds.Wastewater discharged into the subsurface from OWS includes biological constituents such as pathogenic virus and bacteria,chemical constituents such as nutrients and metals,and physical constituents such as suspended and dissolved solids(Crites and Tchobanoglous1998).The scope of this paper is limited to the macronutrients nitrogen(N)and phosphorus(P)from OWS,as they result in the most common adverse impacts on environ-mental plementary research is currently under way at the Colorado School of Mines to assess the site-scale and cumulative effects of pathogenic virus and bacteria(Van Cuyk et al.2001),as well as clogging zone genesis at the wastewater infiltrative surface(e.g.,Beach and McCray2003;Beach et al.2005).Humans generate~13.3g N per capita per day (Crites and Tchobanoglous1998).Assuming an average density of2.4people/household and1house/0.405ha (1house/acre lot),the annual N loading rate from a sub-division is potentially2880kg/km2/year.In some areas, the housing density is much greater.This value compares to N-loading rates of~600to1200kg/km2/year from atmospheric deposition(Howarth et al.1996)and ~10,000to20,000kg/km2/year from fertilizer applied to row crop agriculture(Keeney1986).Because of the large amount of fertilizer used in agriculture and the large amounts of nutrients deposited by animals in large live-stock farms,agriculture’s impact is potentially much greater than the impact of on-site systems overall in areas where agricultural production is dominant.However,in nonagricultural areas,OWS can be a significant con-tributor to ground water and potentially to surface water nitrogen loadings.Humans generate~3.28g P per capita per day in domestic wastewater(Crites and Tchobanoglous1998). Annual P loading rates from OWS depend on several fac-tors but primarily on OWS density(Gold and Sims2000). Assuming the same population density as in the previous example with N,the annual P loading rate from a sub-division is potentially710kg/km2/year.This compares to P loadings of<100kg/km2/year from atmospheric deposi-tion,~490kg/km2/year from maintenance fertilization of lawns,and~990to14,800kg/km2/year as fertilizer or manure in agricultural production systems(Gold and Sims2000).MethodologyData related to OWS nutrient concentrations in septic tank effluent(STE)and nutrient transport and transfor-mation parameters were collected from studies published in the literature.These data are presented in detail in Kirkland(2001).Summary tables of compiled data, including the median,range,and number of data gathered for each OWS parameter,are presented in this paper. These data were used to create cumulative frequency dis-tribution(CFD)diagrams.CFD diagrams may be used to estimate the percentage of a population whose measured values exceed or fall short of a particular level.CFD dia-grams were created for STE concentrations of N and P, nitrification rates,denitrification rates,and linear sorption isotherm constants for P.While P is known to precipitate as well as sorb,particularly under suitable electro-chemical conditions,too few data were found in literature sources to include P precipitation parameters using the CFD methodology.The cumulative frequencyas Figure1.Schematic of a conventional OWS delivery system.J.E.McCray et al.GROUND WATER43,no.4:628–639629a percentage is presented on the vertical axis of the CFD diagrams,and the associated STE concentration or the nutrient transformation rate constant is presented on the horizontal axis.Data points represent values obtained or calculated from data gathered from literature sources. Trend lines are presented as solid lines.For this paper, median values and other percentile values that were ob-tained from the CFD plots are derived from the trend lines or interpolated between particular data points.The data used to construct these CFD diagrams were obtained from numerous literature sources.These sources used various experimental methodologies and data-reporting styles.For example,some studies report an average value of many samples collected in one study.In other studies,only one parameter value is reported.In other studies,only a range of measured values was given. For this latter type of report,the median value was used for inclusion into the CFD.If multiple data were given for a single site(e.g.,different sampling times),the value re-ported or calculated as the median of the data was used.In the literature,nitrogen species in STE were not consistently reported as N concentrations(i.e.,NH4-N, NO3-N).However,in this study,all nitrate concentrations are reported as N equivalent concentrations based on molecular weight ratios.In some cases,total Kjeldahl nitrogen(TKN)was reported in lieu of total N(TN). Because nitrates and nitrites generally comprise a negligi-ble fraction of TN in STE,TKN was assumed to be a sat-isfactory estimate for TN.Nitrogen and denitrification rates were reported in varying units.Sometimes a zero-order rate was reported(e.g.,mg N/kg soil/d),which was converted to first-order rate constant unit(1/d)using the reported soil properties.When necessary,a soil particle density of2.65g/cm3and a porosity of40%was assumed for this conversion.Reported STE phosphorus concentrations were some-times ambiguous.While phosphate concentrations were generally reported as total phosphorus(TP)or phosphate-phosphorus(PO4-P),concentrations were also reported as PO432,and P.The notation PO4-P represents the phos-phorus concentration due only to phosphate.It was often unclear whether values reported as P represented PO4-P or TP.Because85%to90%of TP in STE consists of phosphate(Wilhelm et al.1994;Correll1998;Willman et al.1981),all concentrations reported simply as P,with no explanation,were assumed to represent PO4-P con-centrations in this study.To obtain consistent phosphorus concentration parameters,PO432and TP concentrations are converted to PO4-P concentrations.When TP is reported,the PO4-P concentration is assumed to equal 0.85TP.Reported phosphate(as PO432)concentrations are converted to PO4-P concentrations(as P)based on molecular weight ratios.PO4-P concentrations(or the concentration of PO432as P)in STE are less than the concentrations of PO432by a factor of2.55.Results and DiscussionNitrogen Concentrations in STECommon forms of inorganic nitrogen associated with wastewater include ammonium(NH41),nitrate(NO32), nitrite(NO22),and nitrogen gas(N2).Nitrogen present in fresh wastewater is contained primarily in protein-rich matter and urea.Decomposition by bacteria readily changes organic N to ammonium in the septic tank (Crites and Tchobanoglous1998).Approximately75%to 85%of the TKN(organic N plus ammonium)consists of NH41in STE(Kirkland2001).Table1summarizes the data collected in this study,as well as average values re-ported by the Onsite Wastewater Treatment Systems Manual(U.S.EPA2002).Data from Anderson et al. (1994)were the source of the nitrate and phosphate data reported by U.S.EPA(2002).Nitrogen concentrations in STE vary depending on the wastewater generation and water use at the source,Table1Summary of N and P Concentrations in STE1,2,3PollutantConcentration(mg/L)Median RangeNumberof DataAverage Value fromU.S.EPA(2002)TN(mg N/L)52or68412to4531844.25 Organic N(mg N/L)149.4to156—6 Ammonium(mg N/L)5817to17837—6 Nitrate(mg N/L)0.20to1.94330.04 Phosphate(mg P/L)9.0 1.2to21.8358.671N and P data sources:Kirkland(2001);Robertson et al.(1998);Robertson and Blowes(1995);Wilhelm et al.(1996,1994);Robertson and Cherry(1992);Sherman and Anderson(1991);SSWMP(1978);Harkin et al.(1979);Brown et al.(1977);Robertson et al.(1991);Reneau et al.(1989);Cogger et al.(1988);Whelan(1988);Crites(1985);Willman et al.(1981);Kristiansen(1981);U.S.EPA(2002);Viraraghavan and Warnock(1976);Magdoff et al.(1974);Otis et al.(1973);Walker et al.(1973);Ronayne et al.(1982);Ayres Associates(1993,1996);Otis(1978).2N data sources:Converse(1999);DeSimone and Howes(1998);Harman et al.(1996);Bowne(1982);Pell and Nyberg(1989).3P data sources:Fischer(1999);Ptacek(1998);Zanini et al.(1998);Harman et al.(1996);Robertson(1995);Nagpal(1986);Reneau(1979);Lance(1977);Reneau and Pettry(1976).4Three lowest values by Crites(1985)are omitted,see text.5NH4plus organic N(n=11).6Not reported.7Total P(n=11).630J.E.McCray et al.GROUND WATER43,no.4:628–639especially over time due to changing water-use practices. Keeney(1986)reported that the TN concentration of typi-cal effluent from a septic tank ranges from50to70mg N/L,~75%as ammonium and25%as organic nitrogen. Crites and Tchobanoglous(1998)reported similar values, with organic nitrogen in STE ranging from20to40mg N/L and NH4-N ranging from30to50mg N/L.U.S.EPA (2002)cites ranges of40to100mg/L for TN and0.01to 0.16mg/L for nitrate-N for typical residential wastewater. These specific data from the EPA study could not be ob-tained.Therefore,our STE nutrient pollutant concen-trations provide an independent evaluation using more data.However,the average value of each constituent from this EPA study(Table1)is included as one data point for our analysis.In addition,the U.S.EPA(2002)evaluation does not present the data in a CFD as is done in this study.These CFD diagrams are very useful for planning, design,and modeling,as will be discussed in more detail later.As shown in Table1,our recent compilation of data relating to STE concentrations from operating OWS range from17to178mg N/L for ammonium and9.5to 15mg N/L for organic N.Nitrate-N concentrations are much lower,as is expected since nitrification would not transform ammonium to nitrate in the anaerobic con-ditions of the septic tank.Surprisingly,the range and median of NH3concentrations reported in the literature are larger than the TN concentrations.This occurs because the STE concentration data for these two species were generally derived from different sources.In particu-lar,3of the18TN values(reported by Crites1985)were very low(between12and18mg/L)compared to the other TN values.If these lowest values are omitted,the median value for TN is67.5,which is somewhat higher than the median for NH41.Figure2illustrates a CFD diagram for NH4-N con-centrations in residential STE based on our data compila-tion.CFD diagrams were not created for NO3-N or NO22N because STE concentrations are generally negli-gible and are thus not generally reported in detail.Data for organic N were not sufficient to construct a CFD.Due to nitrification in the vadose zone,OWS can generate NO3-N concentrations at the water table from25 to80mg N/L in most situations,even though NO3-N con-centrations in STE are usually<2mg N/L(Gold et al. 1999).Conversely,NH4-N concentrations at the water table are most often low,if any NH4-N reaches the water table at all(Robertson et al.1998).The U.S.EPA drink-ing water standard for NO3-N is10mg N/L(U.S.EPA 2000).The European Union ground water standard for NO3-N is11.3mg/L(usually reported as an NO3concen-tration of50mg/L).Considering that many residences serviced by OWS also draw their water from on-site drinking water wells,N contributions from OWS may have local ground water impacts in some areas,as well as potential impacts on ground water and surface water load-ings in the watershed.Dilution may play a part in reducing nitrogen con-centrations in the short term.Ground water will normally provide some dilution,but mixing is not always efficient and plumes of higher concentrations will exist(Converse 1999).In a study of two ground water nitrate plumes in sand aquifers(Cambridge and Muskoka sites in cen-tral Canada)that originated from wastewater sources, Robertson et al.(1991)found very low transverse and longitudinal dispersivity leading to well-defined nitrate plumes in ground water.Furthermore,even though nitrogen concentrations may be reduced through dilution,mass loadings are not.As the density and areal extent of unsewered development grows,the dilution capacity of undeveloped lands is diminished(Gold et al.1999). Therefore,dilution as the primary means of reducing nitro-gen concentrations is not always a practical long-term solution.To assess these problems in a more rigorous fashion,mathematical models may be used.Other trans-port parameters for nitrogen,such as degradation rates,are also necessary,and are discussed in detail subsequently. Nitrogen Transport and TransformationProcesses affecting the fate and transport of N from OWS include nitrification and denitrification.Nitrification is the process whereby ammonium(NH41),the primary constituent in STE,is converted to nitrite(NO22)and then to nitrate(NO32).However,the conversion to nitrite is so rapid that we can assume that nitrification occurs in a single step(NH41to NO32).Nitrification has been described using zero-order(Equation1a or Equation1b) and first-order(Equation2)reactions.During denitrifica-tion,nitrate is converted to gaseous diatomic nitrogen (N2).Denitrification rates are typically described using first-order reactions(Equation3).Reaction rate constants reported in literature sources are summarized in Table2.@ðNO3Þ@t¼2@ðNH4Þ@t¼lð1aÞ2@ðNH4Þ@t¼l9¼l M NH4ð1bÞ@ðNO3Þ@t¼2@ðNH4Þ@t¼k1ðNH4Þð2Þ@ðNO3Þ@t¼2k2ðNO3Þð3Þwhere the parentheses indicate molar concentrations of the enclosed chemical species(mol/L),k1and k2are Figure2.CFD for NH4-N concentrations in domestic STE.J.E.McCray et al.GROUND WATER43,no.4:628–639631first-order rate constants (per day),l is the zero-order rate constant reported on a molar basis (mol/L/d),l 9is the zero-order rate constant reported on an ammonium mass basis (mg/L/d),and M NH 4is the molecular weight of ammonium (18,000mg/L).Table 2presents a very wide range of reaction rates for nitrification.This is due to the fact that reported nitri-fication or denitrification rates for OWS were sparse,and because rates were also tabulated from studies of nitrifi-cation in natural soil,and not specifically OWS.With the wide range of values reported,selecting a single value for a nitrification rate is difficult.Field observations of on-site systems have shown that very little,if any,ammo-nium reaches the ground water below an OWS infiltration trench.This observation should be taken into account when evaluating the adequacy of a nitrification rate to be used in modeling efforts.Figure 3is a CFD of first-order nitrification rates summarized from literature sources.Due to the large variability in the limited literature data,nitrification rates cannot currently be distinguished by soil type.Denitrification is possible both at anaerobic micro-sites in the vadose zone and in anaerobic ground water when a source of carbon is present and available.How-ever,while many studies have been performed on nitrateremoval in the subsurface via denitrification,it is stillneither well understood nor well quantified.First-order denitrification rates vary widely in literature sources.No zero-order rates were found in the literature to describe denitrification.The first-order reaction rates for denitrifi-cation summarized in Table 2are presented in a CFD in Figure 4.Due to the large variability in literature data,denitrification rates could not be segregated by soil type.Phosphorus Concentrations in STEPhosphorus in domestic wastewater is derived gener-ally from human waste and synthetic detergents,although modern detergents contain minimal P.Concentrations of P in STE will vary according to the type of source,vol-ume of wastewater generated,and the extent of synthetic detergent use.Concentrations of P normally found in OWS effluent (1to 22mg P/L)much exceed the lower P concentrations (0.01to 0.10mg P/L)that have been observed to stimulate algal growth in aquatic environ-ments (Gold and Sims 2000).The majority of P in waste-water is in the form of soluble orthophosphate (PO 432).The orthophosphate form is considered the most haz-ardous in the environment due to its abundance and the availability for biological metabolism without further breakdown.P in organic molecules and polyphosphates is hydrolyzed to PO 432in the septic tank (Wilhelm et al.1994),contributing to the high percentage of TP as ortho-phosphate (PO 4)in STE.Orthophosphate equaling 85%of TP in STE is often reported to be a typical value,although ranges from 76%to >95%have been measured (e.g.,Magdoff et al.1974;Wilhelm et al.1994;Correll 1998;Willman et al.1981).Table 1summarizes P concentrations in STE reported in various literature sources (Kirkland 2001).The PO 4-P concentrations reported in Table 1are consistent with val-ues reported by the U.S.EPA (2002)of 5to 17mg TP/L.However,the design manual does not present the fre-quency distribution of reported P concentrations in STE.Figure 5presents a CFD diagram for P concentrations in domestic STE created from data summarized in Table 1.Increasing public awareness in the 1960s of the adverse effects of P overenrichment of surface water led to vari-ous actions by political units,detergent manufacturers,and consumers to limit the use of phosphate in detergents (Hem 1992).Phosphate detergent bans went into effect inTable 2Summary of Nitrification and Denitrification RatesReported in Literature Sources 1Process/Reaction OrderMedianRangeNumber of DataNitrification—zeroorder,l 9(mg/L/d)264156to 14647Nitrification—first order,k 1(per day) 2.90.0768to 211.219Denitrification—first order,k 2(per day)0.0250.004to 2.27531Genget al.(1996);Cho (1971);Ling and El-Kadi (1998);Yamaguchi et al.(1996);Starr et al.(1974);Starr and Gillham (1993);Misra et al.(1974);Ardakani et al.(1974a,1974b);Lind (1983);Slater and Capone (1987);Anderson (1998);Trudell et al.(1986);Smith and Duff (1988);Bengtsson and Annadotter (1989);Francis et al.(1989);Obenhuber and Lowrance (1991);Smith et al.(1991);Ekpete and Cornfield (1965);Christensen et al.(1989);Bradley et al.(1992);Tesoriero et al.(2000);Smith et al.(1996);Lawrence and Foster (1986);Korom (1992);Hiscock(1991).Figure 3.CFD for first-order nitrificationrate.Figure 4.CFD for first-order denitrification rate.632J.E.McCray et al.GROUND WATER 43,no.4:628–639the mid-to late1980s in many states.An overall decreas-ing temporal trend in STE phosphate concentrations in available STE data from the1970s to the present was observed in the data collected for this study.Based on data collected in papers published in1970to1980,the range of reported PO4-P concentrations for this decade was5.5to21.8mg/L,with an average of13.1mg/L.In the1980s,the reported range was 2.1to20.6mg/L, with an average of11.1mg/L.Finally,in the1990s,the reported range was1.2to14.2mg/L,with an average of 8.4mg/L.Phosphorus Transport and TransformationMost OWS rely on chemical processes such as sorp-tion and precipitation during vadose zone percolation to prevent P from entering the ground water and eventually discharging to surface water.The effectiveness of soils and underlying aquifer materials in attenuating P move-ment to subsurface and surface water depends upon a number of factors including the soil chemical and phys-ical properties,the chemical properties and loading rate of the wastewater,site hydrology,proximity of the site to surface water,and the design and management of the OWS(Robertson et al.1998;Gold and Sims2000). Mechanisms for P transformation related to OWS have not been fully elucidated,although Robertson(1995)pro-vides a good review of what is known about P trans-formation mechanisms.Sorption of P in soils is well documented and is often thought to be associated with metal-oxide minerals that can possess a positive surface charge at typical pH ranges,allowing sorption of the anionic phosphate.Some researchers have suggested a two-stage attenuation process with an initial reversible reaction representing sorption,and an irreversible reac-tion that causes loss of P from the aqueous phase,which is sometimes considered to represent precipitation of sparingly soluble phosphate minerals(Robertson1995). Several phosphate minerals have been suggested as con-trols on phosphate in natural water.Most of these mineral phases involve iron,although calcium and aluminum may also be important(Robertson and Blowes1995).Sorption has been described in many ways.Kirkland (2001)summarizes linear and nonlinear(Freundlich and Langmuir)P sorption isotherms reported in numerous literature sources.P sorption isotherms could not be sepa-rated specifically by soil type,with the exception of max-imum sorption capacity,which was often reported in studies where no isotherm was measured.The first isotherm to be discussed is the linear iso-therm.The low concentration of P found below an OWS infiltrative surface is often in the linear range of reported nonlinear isotherms.In addition,the data available are often insufficient to justify a more sophisticated ap-proach;thus,the linear sorption isotherm is the most widely used in hydrologic models(Drever1997).A lin-ear isotherm is represented by the equation:S¼K D Cð4Þwhere S is the mass of solute sorbed per unit dry weight of solid(mg/kg),C is the concentration of the solute in solution in equilibrium with the mass of solute sorbed onto the solid(mg/L),and K D is linear distribution coeffi-cient(L/kg).K D values were obtained directly from those reported in literature sources or calculated from reported or as-sumed aquifer porosity and bulk density properties of the soil material and the reported retardation factor using the following equation:R f¼11q b/K Dð5Þwhere q b is the dry bulk density of the aquifer solids (g/cm3)and u is the aquifer porosity(dimensionless). Retardation factors reported in studies were generally ob-tained from wastewater–derived plumes in saturated zones.Sorption parameters for unsaturated soil were not generally specified in the literature.However,the K D is theoretically independent of the water content,provided the soil in the unsaturated and saturated zones are similar.A major limitation of the linear sorption isotherm is that it does not limit the amount of solute that can be sorbed onto the solid.This assumption is clearly not physically realistic as there must be an upper limit of the amount of solute that can be sorbed to a given solid particle.How-ever,this assumption is often appropriate because low aqueous concentrations in ground water may not supply enough chemicals to saturate sorption sites,particularly for noncontinuous plumes.The Freundlich sorption isotherm is a more general description of sorption and may be described by the gen-eral equation:S¼KC Nð6Þwhere K and N are empirical constants.Freundlich iso-therms are nonlinear and usually obtained through empir-ical fits to experimental data.As with the linear isotherm, a major limitation of the Freundlich isotherm is that there is no upper limit to the amount of solute that could be sorbed for N>1.However,for N<1,an asymptotic limit may be approached.For N=1,the Freundlich isotherm reduces to the linear sorption isotherm where K=K D.The Langmuir sorption isotherm is a more complex sorption isotherm.The Langmuir sorption isotherm incor-porates the assumption that a finite number ofsorption Figure5.CFD for PO4-P concentrations in STE.J.E.McCray et al.GROUND WATER43,no.4:628–639633。
simulation modelling practice
simulation modelling practiceSimulation modelling is a crucial tool in the field of science and engineering. It allows us to investigate complex systems and predict their behaviour in response to various inputs and conditions. This article will guide you through the process of simulation modelling, from its basicprinciples to practical applications.1. Introduction to Simulation ModellingSimulation modelling is the process of representing real-world systems using mathematical models. These models allow us to investigate systems that are too complex or expensiveto be fully studied using traditional methods. Simulation models are created using mathematical equations, functions, and algorithms that represent the interactions and relationships between the system's components.2. Building a Basic Simulation ModelTo begin, you will need to identify the key elements that make up your system and define their interactions. Next, you will need to create mathematical equations that represent these interactions. These equations should be as simple as possible while still capturing the essential aspects of the system's behaviour.Once you have your equations, you can use simulation software to create a model. Popular simulation softwareincludes MATLAB, Simulink, and Arena. These software packages allow you to input your equations and see how the system will respond to different inputs and conditions.3. Choosing a Simulation Software PackageWhen choosing a simulation software package, consider your specific needs and resources. Each package has its own strengths and limitations, so it's important to select one that best fits your project. Some packages are more suitable for simulating large-scale systems, while others may bebetter for quickly prototyping small-scale systems.4. Practical Applications of Simulation ModellingSimulation modelling is used in a wide range of fields, including engineering, finance, healthcare, and more. Here are some practical applications:* Engineering: Simulation modelling is commonly used in the automotive, aerospace, and manufacturing industries to design and test systems such as engines, vehicles, and manufacturing processes.* Finance: Simulation modelling is used by financial institutions to assess the impact of market conditions on investment portfolios and interest rates.* Healthcare: Simulation modelling is used to plan and manage healthcare resources, predict disease trends, and evaluate the effectiveness of treatment methods.* Education: Simulation modelling is an excellent toolfor teaching students about complex systems and how they interact with each other. It helps students develop critical thinking skills and problem-solving techniques.5. Case Studies and ExamplesTo illustrate the practical use of simulation modelling, we will take a look at two case studies: an aircraft engine simulation and a healthcare resource management simulation.Aircraft Engine Simulation: In this scenario, a simulation model is used to assess the performance ofdifferent engine designs under various flight conditions. The model helps engineers identify design flaws and improve efficiency.Healthcare Resource Management Simulation: This simulation model helps healthcare providers plan their resources based on anticipated patient demand. The model can also be used to evaluate different treatment methods and identify optimal resource allocation strategies.6. ConclusionSimulation modelling is a powerful tool that allows us to investigate complex systems and make informed decisions about how to best manage them. By following these steps, you can create your own simulation models and apply them to real-world problems. Remember, it's always important to keep anopen mind and be willing to adapt your approach based on the specific needs of your project.。
基于大数据的数学建模方法融入高职数学教学实践探究
基于大数据的数学建模方法融入高职数学教学实践探究王英(甘肃财贸职业学院 甘肃兰州 730207)摘要:“数学建模”是指利用计算机将现实生活中遇到的实际问题用一定的数学方法表示出来,并在计算机上进行模拟运算。
通过对现实生活中问题的分析和抽象,得到“数学模型”,再用模型来解决实际问题。
它融合了自然科学与社会科学,利用数学工具建立问题模型,通过计算机计算、分析、归纳和总结得出结论并提出解决问题的办法。
文章利用大数据技术和学习分析技术,设计了高职数学的精准教学模式,以云班课为平台,构建了数学建模方法融入高职数学教学模式。
关键词:大数据 数学建模 高职数学 实践环节 应用能力中图分类号:G712;O141.4-4文献标识码:A 文章编号:1672-3791(2023)13-0187-04Exploration on the Integration of the Mathematical Modeling Method Based on Big Data into Higher VocationalMathematics Teaching PracticeWANG Ying(Gansu Finance and Trade Professional College, Lanzhou, Gansu Province, 730207 China)Abstract: "Mathematical modeling" refers to using computers to express practical problems encountered in real life in certain mathematical methods, and performing simulation operations on computers. Through the analysis and abstraction of the problems in real life, a "mathematical model" is obtained, and then the model is used to solve practical problems. It integrates natural science and social science, uses mathematical tools to establish problem models, and draws conclusions and proposes solutions to problems through computer calculation, analysis, induction and summary. This article uses big data technology and learning analysis technology to design an accurate teaching model for higher vocational mathematics, and constructs a mode of integrating the mathematical modeling method into higher vocational mathematics teaching with Mosoteach as the platform.Key Words: Big data; Mathematical modeling; Higher vocational mathematics; Practice; Application ability近年来,随着高职教育招生规模的扩大和招生途径的多样化,学生基础参差不齐,学习行为分化的现象越来越突出,这些给高职数学教学带来了新的困难和挑战。
常用研究生课程翻译
立体化学 Stereochemistry
高等发光分析 Advanced Luminescence Analysis
激光光谱分析 Laser Spectroscopy Analysis
现代传感技术 Modern Sensor Technology
数学模型与计算机模拟 Mathematical Models and Computer Simulations
计算物理谱方法 Spectral Method in Computational Physics
蒙特卡罗方法在统计物理中的应用 Applications of the Monte Carlo Method
生物与化学传感技术 Biosensors & Chemical Sensors
现代分析化学研究方法 Research Methods of Modern Analytical Chemistry
神经生物学 Neurobiology
动物遗传工程 Animal Genetic Engineering
linear
Hyperbolic Conservation Laws
粘性守恒律解的稳定性 Stability of Solutions for Viscous Conservation
Laws
微分方程数值解 Numerical Methods for Differential Equations
物理光学与光电子技术实验 Experiments for Physical Optics and Op
toelectronic Technology
Shear_Strengthening_of_Reinforced_Concrete_(RC)_wi
Z. Lv, M. N. Wangids Can Mobilize Oil Remaining after Water-Flood by Force Parallel to the Oil-Water Interface. SPE Asia Pacific Improved Oil Recovery Conference, Kuala Lum-pur, 8-9 October 2001, SPE-72123-MS. https:///10.2118/72123-MS[2]Southwick, J.G., Shell Development Co. and Manke, C.W. (1988) Molecular Degra-dation, Injectivity, and Elastic Properties of Polymer Solutions. SPE Reservoir En-gineering,3, 1193-1201. https:///10.2118/15652-PA[3]Marshall, R.J. and Metzner, A.B. (1967) Flow of Viseoelastic Fluids through PorousMedia. Industrial & Engineering Chemistry Fundamentals, 6, 393-400.https:///10.2118/1687-MS[4]Hass, R. and Durst, F. (1981) Viscoelastic Flow of Dilute Polymer Solutions in Reg-ularly Packed Beds. Rheologica Acta, 21, 566-571.https:///10.1007/BF01534349[5]Han, X.-Q. (1988) Viscoelastic Coefficient of Polymer Molecules Trapped in PorousMedia. Journal of Southwest Petroleum Institute, 10, 54-59.[6]Mohammad (1992) Quantification and Optimization of Viscoelastic Effects of Po-lymer Solutions for Enhanced oil Recovery. SPE Journal, 24, 2731-2757.[7]Cao, R.-Y. and Cheng, L.-S. (2007) A Mathematical Model for Viscoelastic PolymerSolution Seepage. Journal of Xi’an Petroleum University (Natural Science Edition),22, 107-109.[8]Wang, X.-H. and Zhao, G.-P. (1998) Shear Rate of Power-Law Fluid in Porous Me-dia. Xinjiang Petroleum Geology, 19, 312-314.[9]Yan, F. (2016) Properties and Demulsification Laws of Crude Oil Emulsions in Hy-drophobically A ssociating Polymer Flooding System. A cta Petrolei Sinica (Petro-leum Processing Section), 32, 546-552.[10]Zhang, J.-H. and Yan, F. (2014) Relationship between Structure of Polyether and theDemulsification of Fractured Emulsion. Acta Petrolei Sinica (Petroleum ProcessingSection), 30, 548-554.World Journal of Engineering and Technology, 2023, 11, 281-292 Array https:///journal/wjetISSN Online: 2331-4249ISSN Print: 2331-4222Shear Strengthening of Reinforced Concrete (RC) with FRP Sheets Using Different GuidelinesBashir H. OsmanCivil Engineering Department, College of Engineering, University of Sinnar, Sinnar, Sudan/licenses/by/4.0/and mechanical strengths of structures repair or rehabilitation ([1][2][3]).Over the last two decades, many researches were carried out on the streng-thening of RC beams using FRP composites using different methods such as ex-ternally strengthening, near-surface mounted (NSM) strengthening, and em-bedded section (internal strengthening) ([4][5][6][7][8]). Furthermore, someB. H. Osmanstudies [9] [10] [11] [12] investigate the flexural behavior of pre-damaged rein-forced concrete (RC) beams repaired by using grids and engineered cementi-tious composite (ECC) and carbon fiber reinforced polymer (CFRP) under sus-tained load. Their results showed that most of the beams failed by debonding. Furthermore, the proposed repairing technique was effective in enhancing the flexural stiffness and bearing capacity of pre-damaged RC beams. Moreover, they proposed a mathematical model to calculate the flexural capacities of the repaired beams and the results were in accordance with excremental results. Six RC beams strengthened with CFRP sheets under static and fatigue loading were studied by Min, et al. [13] to show the failure mechanism. The results showed that acceleration the fatigue failure of the specimens is due to coupling of stresses between accumulated fatigue damage in the steel reinforcement and fa-tigue debonding of the CFRP plate. Jia, J., et al. [14] used the novel models of Extreme Learning Machine (ELM) in co-operation with Particle Swarm Opti-mization (PSO), Teaching-Learning based Optimization (TLBO), and gray wolf optimizer (GWO) to investigate the debonding strength of FRP. The results pre-dicted from ELM-GWO showed the best performance compared with ELM-PSO and ELM-TLBO.2. Material Properties and Codes of Practice Used in This StudyBased on this study, a prediction model was proposed by considering all common parameters that influence the ultimate shear capacity of a strengthened beam in-cluding concrete strength (c f ′), effective height of the beam (d ), FRP thickness (t f ), and strengthening configuration (completely wrapped, U-jacketing, and side bonding). The obtained results were compared with that recommended design guide given by different guidelines ([13] [14] [15] [16] [17]). Beam geometry andmaterials properties were illustrated in Figure 1 and Table 1, respectively.Figure 1. Geometrical details of proposed RC beams.Table 1. The properties of materials used in this study.y f yv f f w c F ′ f E f S f d fu εfu f b46025010035223,500503000.0183000120B. H. Osman3. FE Model DescriptionNumerical ModelingA finite element analysis (FEA ) by using A NSYS [18] computer program was used to analysis the reinforced concrete beams. SOLID65 element, was used to model the concrete as this element is capable of modeling cracking in tension and crushing in compression. An eight nodes three degrees of freedom at each node: translations of the nodes in x, y, and z-directions used to define the ele-ment.Steel reinforcement was modeled using link 8 element and which consists of two nodes with three degrees of freedom in each node. The FE model for the re-bar was assumed to be a bilinear isotropic, elastic-perfectly plastic material, and identical in tension and compression. Solid element with an eight-node, solid 45, was used to simulate the plates in the supports and the loading points. This ele-ment has defined with eight nodes of three degrees of freedom at each node translation in the nodal y -, x -, and z -directions.FRP sheet was modeled using Shell41 element. This element allows for differ-ent material layers with different orientations and orthotropic material proper-ties in each layer. Since the FRP materials considered as orthotropic materials, they showed different properties in each direction. The relationship betweenxy v and yx v is illustrated in Equations (1) and (2) ([15] [18] [19]):22212Positive y zzzxy yz xz xy yz xz xyxx E E E E v v v v v v E E E E−−−−=(1) ()or ,and 221x yz yy xy xzyzyxxy x y xy xxyz E E E E E G G G v v E E v E E v ====+++ (2)In this study, Poisson’s ratios of: 0.22, 0.22 and 0.30 are used for xy v , xz v ,and yz v , respectively, which are widely used in the related published literature based on this subject. Contact elements TARGE170 and CONTA174 are used to model the contact between concrete and FRP. To study the contact between two elements, the surface of one element is considered as a contact surface (e.g. FRP) and the other body surface considered as a target surface (e.g. concrete). The contact and target pair concepts has been widely used in finite element models. As used in this study, the FRP was considered as the contact surface which is as-sociated with the deformable body; the concrete was considered as the target surface which must be the rigid surface [20].4. Comparison of Different Method with Design GuidelinesFollowing the previous discussion on the behavior of FRP shear-strengthened beams, it is of interest to see how the measured shear capacity compares with the predictions from available design guidelines. Three design guidelines are consi-dered in this study which compared with A merican Concrete Institute (A CI)(2008) such as Traintafillou and Anton 2000, carolin and taljsten 2005 and Zhi-B. H. Osmanchao and cheng 2005. The equations used in this part of this study related with below guides:4.1. ACI EquationSimplified method: the above equation is not so simple to use as a design equa-tion, the ACI code permits use of below equation:c w Vd =(3)For beams with shear reinforcement, the ACI consider nominal shear strength,n V as flow:nc s V V V =+ (4) Which c V = shear strength of concrete; s V = shear strength of shear rein-forcement. Shear strength for inclined stirrup at an angle α with horizontal sug-gested as:()sin cos v yv s A f dV sαα+=(5)Which v A , yv f are area of shear reinforcement in distance s and is the yieldstrength of shear reinforcement respectively.When α = 90˚ (vertical stirups are used) the above equation reduces tov yv s A f d V s=, but s s V V ∅≥ (6)The nominal shear strength of an FRP-strengthened concrete member can be determined by adding the contribution of the FRP external shear reinforcement to the contributions from the reinforcing steel (stirrups, ties, or spirals) and the concrete. A n additional reduction factor f ψ is applied to the contribution of the FRP system.()n c s f f V V V V ϕϕψ=++ (7)The reduction factor f ψ of 0.85 is recommended for the three-sided FRP U-wrap or two-opposite-sides strengthening schemes. Insufficient experimental data exist to perform a reliability analysis for fully-wrapped sections; however, there should be less variability with this strengthening scheme as it is less bond independent, and therefore, the reduction factor f ψ of 0.95 is recommended. Figure 2 illustrates the dimensional variables used in shear-strengthening calcu-lations for FRP laminates. The contribution of the FRP system to shear strength of a member is based on the fiber orientation and an assumed crack pattern. The shear strength provided by the FRP reinforcement can be determined by calcu-lating the force resulting from the tensile stress in the FRP across the assumed crack. The shear contribution of the FRP shear reinforcement is then given by:()sin cos f fv fe fv f V A f d s αα=+ (8)where: 2fv f fA nt w =B. H. OsmanFigure 2. Illustration of the dimensional variables used in shear-strengthening calculations for repair, retrofit, or strengthening using FRP laminates.For reinforced concrete column and beam members completely wrapped by FRP0.0040.75fe fu εε=≤ FRP systems that do not enclose the entire section (two- and three-sidedwraps) have been observed to delaminate from the concrete before the loss of aggregate interlock of the section. For this reason, bond stresses have been ana-lyzed to determine the usefulness of these systems and the effective strain level that can be achieved. The effective strain is calculated using a bond-reduction coefficient v κ applicable to shear: 0.004fe v fu εκε=≤, The bond-reduction coefficient can be computed from:12119000.75v e fu K k k L ε=≤ The active bond length Le is the length over which the majority of the bondstress is maintained. This length is given by:()0.5823300e f f f L n t E = The bond-reduction coefficient also relies on two modification factors, k 1 and k 2, that account for the concrete strength and the type of wrapping scheme used, respectively. Expressions for these modification factors are given in:23127c f k ′ =, 1for U warps 2for two sides bondedfv efv yve yv d L d k d L d− =−4.2. Traintafillou and Anton 2000 Equation for FRP Contribution()()0.3220.17for full warp 2f f f ffe c f ffu f f f f fe ffw t b s f E V w t E d s ρερεε===∗∗B. H. Osman()230.04310.56230.72e for three or two sides or 0.00065ff f f c fe fu c fef fa E f d f E ρεεερ−Γ== Γ= (9) 4.3. Carolin and Taljsten 2005 Equation()cos sin ,0.6,,,fcrf f f fe cr f f f fecr V E t r z r b s ηεθαεηεηεε===== (10) 4.4. Zhichao and Cheng 2005 Equation()()()()()())0.748820.58232,1.4871or0.5(2)/ 1.21622which is smal 880.7780.004l2f f f f fe ff fe fuf f f f f f c f f f f c ff ffu fV w t E d s R w t bs E f E E R f w E t d R R εεερρρρε−======−+ (11)4.5. Zhichao and Cheng 2005()()()())()0.50.5822,60.0042,2fff f fe ff cc c ffffu ffe fu ffffV wt E d V f b d Rf w E t d R p w t b sεεεε=∗∗∗∗=∗∗=∗∗∗∗=∗=∗∗ (12)5. Results and DiscussionThe main goal for this work is to study the influence of fiber reinforcement po-lymer (FRP) on shear behavior of RC beams with various guidelines. The pur-pose was also to study the strength parameters such as, FRP thickness, beam depth and concrete strength at ultimate load.5.1. FRP ThicknessTable 2 shows the effect of FRP thickness on the shear strength, which plotted in Figure 3.Table 2 and Figure 3 show that the FRP thickness has a grater effects on con-crete strength, the results predicted from Carolin equation showed under esti-mation compared with those from FE program. Furthermore, the ACI guideline showed acceptable differences compared with the other guidelines when com-pared with FE.5.2. Effect of Concrete StrengthTable 3 shows the effect of FRP thickness on the shear strength, which plotted in Figure 4.B. H. Osman5.3. Effect of Beam DepthFigure 3. Effect of FRP thickness on beams strength using different con-figurations (a) Full warp (b) U-warp (c) 2 sides warp.B. H. OsmanTable 2. Effect of FRP thickness on the strength.Full U Side t f0.08 0.1 0.2 0.08 0.1 0.2 0.08 0.1 0.2 Numerical 179.22 201.34 270 115 119.6 131.54 100 108.13 122.15 ACI 150.94 174.59 239.99 86.52 90.43 104.99 79.4 83.589 98.8666 Traintaf. 76.35197 87.15745 141.1848 66.83981 75.26725 117.4044Carolin 43.85954 46.54191 59.95377Zhichao 114.8425 122.8709 153.1969Table 3. Effect of concrete strength on shear strength.Full U Side Strength 40 30 20 40 30 20 40 30 20 Numerical 165.2 160.3 154.6 108.5 89.4 77.32 93.67 85.08 69.5 ACI 154.83 146.764 137.195 93.2211 79.393 63.371 85.467 72.993 58.485 Traintaf. 78.63943 73.89438 68.26588 69.12727 64.38222 58.75372Carolin 46.147 41.40195 35.77345Zhichao 124.7377 104.4046 81.31203Table 4. Effect of beam depth on shear strength.Full U SideDepth 250 280 320 250 280 320 250 280 320 Numerical 150.1 163.5 185.4 82 98.5 108.34 76.25 91 107.3 ACI 134.77 150.94 172.51 76.49 86.52 99.894 69.397 79.43 92.8 Traintaf. 68.1714 76.35197 87.25939 59.6784 66.83981 76.38835Carolin 40.30989 43.85954 48.5924B. H. Osmantions (a) Full warp (b) U-warp (c) 2 sides warp.6. ConclusionsBased on the results of analysis using A NSYS software and different design guidelines on reinforced concrete RC beams strengthened with fiber reinforce-ment polymer (FRP) and reported in literature the following conclusions are: 1) The use of FRP strengthening has greater effect in the stiffness of the con-crete.2) The finite element models were able to accurately predict the load capaci-ties for the simulated RC beams. This confirms the validity of the developed FE models and reliability of the FE simulation.3) For the FRP shear contribution, the ACI equation is believed to be the most appropriate for practical design. However, for the fully wrapped scheme, the ACI method appears to predict the FRP shear contribution with a relatively high discrepancy.4) The ACI model predicted the ultimate capacity of RC beams based on the beam geometry and concrete compressive strength without considering the ef-B. H. Osman fect of the longitudinal reinforcement.5) The theoretical prediction of ultimate shear strength on the basis of me-thods used in this study gives results over estimate compared with the other de-sign guidelines values in most of the beams.6) Use ACI assumptions because it gives results with more reliable safety fac-tors than other theorems according to results on the previous literature of RC beams in case of using analytical theorems in RC beams analysis. Conflicts of InterestThe author declares no conflicts of interest regarding the publication of this pa-per.References[1]Barnes, R.A. and Mays, G.C. (1999) Fatigue Performance of Concrete BeamsStrengthened with CFRP Plates. Journal of Composites for Construction, 3, 63-72.https:///10.1061/(ASCE)1090-0268(1999)3:2(63)[2]Aboutaha, R.S. (2002) Ductility of CFRP Strengthened Concrete Flexural Members.In: Wendichansky, D. and Paumarada-O’Neill, L.F., Eds., Rehabilitating and Re-pairing the Buildings and Bridges of Americas: Hemispheric Workshop on Future Directions, ASCE, Reston. https:///10.1061/40613(272)1[3]Danraka, M.N., Mahmod, H.M., Oluwatosin, O.K.J. and Student, P. (2017) Streng-thening of Reinforced Concrete Beams Using FRP Technique: A Review. Interna-tional Journal of Engineering Science, 7, 13199-13213.[4]Uji, K. (1992) Improving Shear Capacity of Existing Reinforced Concrete Membersby Applying Carbon Fiber Sheets. Transactions of the Japan Concrete Institute, 14, 253-266.[5]Triantafillou, T.C. (1998) Shear Strengthening of Reinforced Concrete Beams UsingEpoxy-Bonded FRP Composites. ACI Structural Journal, 95, 107-115.https:///10.14359/531[6]Khalifa, A., Gold, W.J., Nanni, A. and A ziz, A. (1998) Contribution of ExternallyBonded FRP to Shear Capacity of RC Flexural Members. Journal of Composites for Construction, 2, 195-203. https:///10.1061/(ASCE)1090-0268(1998)2:4(195) [7]Yang, Z.J., Chen, J.F. and Proverbs, D. (2003) Finite Element Modelling of ConcreteCover Separation Failure in FRP Plated RC Beams. Construction and Building Ma-terials, 17, 3-13. https:///10.1016/S0950-0618(02)00090-9[8]Galal, K. and Mofidi, A. (2010) Shear Strengthening of RC T-Beams Using Me-chanically Anchored Unbonded Dry Carbon Fibre Sheets. Journal of Performance of Constructed Facilities, 24, 31-39.https:///10.1061/(ASCE)CF.1943-5509.0000067[9]Yan, Y., Lu, Y., Zhao, Q. and Li, S. (2023) Flexural Behavior of Pre-Damaged andRepaired Reinforced Concrete Beams with Carbon Fiber Reinforced Polymer Grid and Engineered Cementitious Composite. Engineering Structures, 277, Article ID: 115390. https:///10.1016/j.engstruct.2022.115390[10]Min, X., Zhang, J., Li, X., Wang, C., Tu, Y., Sas, G. and Elfgren, L. (2022) An Expe-rimental Study on Fatigue Debonding Growth of RC Beams Strengthened with Pre-stressed CFRP Plates. Engineering Structures, 273, Article ID: 115081.https:///10.1016/j.engstruct.2022.115081。
粘弹性功能梯度有限元法使用对应原理
Viscoelastic Functionally Graded Finite-Element MethodUsing Correspondence PrincipleEshan V.Dave,S.M.ASCE1;Glaucio H.Paulino,Ph.D.,M.ASCE2;andWilliam G.Buttlar,Ph.D.,P.E.,A.M.ASCE3Abstract:Capability to effectively discretize a problem domain makes thefinite-element method an attractive simulation technique for modeling complicated boundary value problems such as asphalt concrete pavements with material non-homogeneities.Specialized “graded elements”have been shown to provide an efficient and accurate tool for the simulation of functionally graded materials.Most of the previous research on numerical simulation of functionally graded materials has been limited to elastic material behavior.Thus,the current work focuses onfinite-element analysis of functionally graded viscoelastic materials.The analysis is performed using the elastic-viscoelastic correspondence principle,and viscoelastic material gradation is accounted for within the elements by means of the generalized iso-parametric formulation.This paper emphasizes viscoelastic behavior of asphalt concrete pavements and several examples, ranging from verification problems tofield scale applications,are presented to demonstrate the features of the present approach.DOI:10.1061/͑ASCE͒MT.1943-5533.0000006CE Database subject headings:Viscoelasticity;Asphalt pavements;Concrete pavements;Finite-element method.Author keywords:Viscoelasticity;Functionally graded materials;Asphalt pavements;Finite-element method;Correspondence principle.IntroductionFunctionally Graded Materials͑FGMs͒are characterized by spa-tially varied microstructures created by nonuniform distributionsof the reinforcement phase with different properties,sizes andshapes,as well as,by interchanging the role of reinforcement andmatrix materials in a continuous manner͑Suresh and Mortensen1998͒.They are usually engineered to produce property gradientsaimed at optimizing structural response under different types ofloading conditions͑thermal,mechanical,electrical,optical,etc.͒͑Cavalcante et al.2007͒.These property gradients are produced in several ways,for example by gradual variation of the content ofone phase͑ceramic͒relative to another͑metallic͒,as used in ther-mal barrier coatings,or by using a sufficiently large number ofconstituent phases with different properties͑Miyamoto et al.1999͒.Designer viscoelastic FGMs͑VFGMs͒can be tailored tomeet design requirements such as viscoelastic columns subjectedto axial and thermal loads͑Hilton2005͒.Recently,Muliana ͑2009͒presented a micromechanical model for thermoviscoelastic behavior of FGMs.Apart from engineered or tailored FGMs,several civil engi-neering materials naturally exhibit graded material properties. Silva et al.͑2006͒have studied and simulated bamboo,which is a naturally occurring graded material.Apart from natural occur-rence,a variety of materials and structures exhibit nonhomoge-neous material distribution and constitutive property gradations as an outcome of manufacturing or construction practices,aging, different amount of exposure to deteriorating agents,etc.Asphalt concrete pavements are one such example,whereby aging and temperature variation yield continuously graded nonhomogeneous constitutive properties.The aging and temperature induced prop-erty gradients have been well documented by several researchers in thefield of asphalt pavements͑Garrick1995;Mirza and Witc-zak1996;Apeagyei2006;Chiasson et al.2008͒.The current state-of-the-art in viscoelastic simulation of asphalt pavements is limited to either ignoring non-homogeneous property gradients ͑Kim and Buttlar2002;Saad et al.2006;Baek and Al-Qadi2006; Dave et al.2007͒or considering them through a layered ap-proach,for instance,the model used in the American Association of State Highway and Transportation Officials͑AASHTO͒Mechanistic Empirical Pavement Design Guide͑MEPDG͒͑ARA Inc.,EC.2002͒.Significant loss of accuracy from the use of the layered approach for elastic analysis of asphalt pavements has been demonstrated͑Buttlar et al.2006͒.Extensive research has been carried out to efficiently and ac-curately simulate functionally graded materials.For example, Cavalcante et al.͑2007͒,Zhang and Paulino͑2007͒,Arciniega and Reddy͑2007͒,and Song and Paulino͑2006͒have all reported onfinite-element simulations of FGMs.However,most of the previous research has been limited to elastic material behavior.A variety of civil engineering materials such as polymers,asphalt concrete,Portland cement concrete,etc.,exhibit significant rate and history effects.Accurate simulation of these types of materi-als necessitates the use of viscoelastic constitutive models.1Postdoctoral Research Associate,Dept.of Civil and EnvironmentalEngineering,Univ.of Illinois at Urbana-Champaign,Urbana,IL61801͑corresponding author͒.2Donald Biggar Willett Professor of Engineering,Dept.of Civil andEnvironmental Engineering,Univ.of Illinois at Urbana-Champaign,Ur-bana,IL61801.3Professor and Narbey Khachaturian Faculty Scholar,Dept.of Civiland Environmental Engineering,Univ.of Illinois at Urbana-Champaign,Urbana,IL61801.Note.This manuscript was submitted on April17,2009;approved onOctober15,2009;published online on February5,2010.Discussion pe-riod open until June1,2011;separate discussions must be submitted forindividual papers.This paper is part of the Journal of Materials in CivilEngineering,V ol.23,No.1,January1,2011.©ASCE,ISSN0899-1561/2011/1-39–48/$25.00.JOURNAL OF MATERIALS IN CIVIL ENGINEERING©ASCE/JANUARY2011/39The current work presents afinite element͑FE͒formulation tailored for analysis of viscoelastic FGMs and in particular,as-phalt concrete.Paulino and Jin͑2001͒have explored the elastic-viscoelastic correspondence principle͑CP͒in the context of FGMs.The CP-based formulation has been used in the current study in conjunction with the generalized iso-parametric formu-lation͑GIF͒by Kim and Paulino͑2002͒.This paper presents the details of thefinite-element formulation,verification,and an as-phalt pavement simulation example.Apart from simulation of as-phalt pavements,the present approach could also be used for analysis of other engineering systems that exhibit graded vis-coelastic behavior.Examples of such systems include metals and metal composites at high temperatures͑Billotte et al.2006;Koric and Thomas2008͒;polymeric and plastic based systems that un-dergo oxidative and/or ultraviolet hardening͑Hollaender et al. 1995;Hale et al.1997͒and gradedfiber reinforced cement and concrete structures.Other application areas for the graded vis-coelastic analysis include accurate simulation of the interfaces between viscoelastic materials such as the layer interface between different asphalt concrete lifts or simulations of viscoelastic glu-ing compounds used in the manufacture of layered composites ͑Diab and Wu2007͒.Functionally Graded Viscoelastic Finite-Element MethodThis section describes the formulation for the analysis of vis-coelastic functionally graded problems using FE framework and the elastic-viscoelastic CP.The initial portion of this section es-tablishes the basic viscoelastic constitutive relationships and the CP.The subsequent section provides the FE formulation using the GIF.Viscoelastic Constitutive RelationsThe basic stress-strain relationships for viscoelastic materials have been presented by,among other writers,Hilton͑1964͒and Christensen͑1982͒.The constitutive relationship for quasi-static, linear viscoelastic isotropic materials is given asij͑x,t͒=2͵tЈ=−ϱtЈ=t G͓x,͑t͒−͑tЈ͔͒ͫij͑x,tЈ͒−13␦ijkkͬdtЈ+͵tЈ=−ϱtЈ=t K͓x,͑t͒−͑tЈ͔͒␦ijkk dtЈ͑1͒whereij=stresses;ij=strains at any location x.The parameters G and K=shear and bulk relaxation moduli;␦ij=Kronecker delta; and tЈ=integration variable.Subscripts͑i,j,k,l=1,2,3͒follow Einstein’s summation convention.The reduced timeis related to real time t and temperature T through the time-temperature super-position principle͑t͒=͵0t a͓T͑tЈ͔͒dtЈ͑2͒For a nonhomogeneous viscoelastic body in quasi-static condi-tion,assume a boundary value problem with displacement u i on volume⍀u,traction P i on surface⍀and body force F i,the equilibrium and strain-displacement relationships͑for small de-formations͒are as shown in Eq.͑3͒ij,j+F i=0,ij=12͑u i,j+u j,i͒͑3͒respectively,where,u i=displacement and͑•͒,j=ץ͑•͒/ץx j.CP and Its Application to FGMsThe CP allows a viscoelastic solution to be readily obtained by simple substitution into an existing elastic solution,such as a beam in bending,etc.The concept of equivalency between trans-formed viscoelastic and elastic boundary value problems can be found in Read͑1950͒.This technique been extensively used by researchers to analyze variety of nonhomogeneous viscoelastic problems including,but not limited to,beam theory͑Hilton and Piechocki1962͒,finite-element analysis͑Hilton and Yi1993͒, and boundary element analysis͑Sladek et al.2006͒.The CP can be more clearly explained by means of an ex-ample.For a simple one-dimensional͑1D͒problem,the stress-strain relationship for viscoelastic material is given by convolution integral shown in Eq.͑4͒.͑t͒=͵0t E͑t−tЈ͒ץ͑tЈ͒ץtЈdtЈ͑4͒If one is interested in solving for the stress and material properties and imposed strain conditions are known,using the elastic-viscoelastic correspondence principle the convolution integral can be reduced to the following relationship using an integral trans-form such as the Laplace transform:˜͑s͒=sE˜͑s͒˜͑s͒͑5͒Notice that the above functional form is similar to that of the elastic problem,thus the analytical solution available for elastic problems can be directly applied to the viscoelastic problem.The transformed stress quantity,˜͑s͒is solved with known E˜͑s͒and ˜͑s͒.Inverse transformation of˜͑s͒provides the stress͑t͒.Mukherjee and Paulino͑2003͒have demonstrated limitations on the use of the correspondence principle in the context of func-tionally graded͑and nonhomogenous͒viscoelastic boundary value problems.Their work establishes the limitation on the func-tional form of the constitutive properties for successful and proper use of the CP.Using correspondence principle,one obtains the Laplace trans-form of the stress-strain relationship described in Eq.͑1͒as ˜ij͑x,s͒=2G˜͓x,˜͑s͔͒˜ij͑x,s͒+K˜͓x,˜͑s͔͒␦ij˜kk͑x,s͒͑6͒where s=transformation variable and the symbol tilde͑ϳ͒on top of the variables represents transformed variable.The Laplace transform of any function f͑t͒is given byL͓f͑t͔͒=f˜͑s͒=͵0ϱf͑t͒Exp͓−st͔dt͑7͒Equilibrium͓Eq.͑3͔͒for the boundary value problem in the trans-formed form becomes˜,j͑x,s͒=2G˜͑x,s͒˜,j d͑x,s͒+2G˜,j͑x,s͒˜d͑x,s͒+K˜͑x,s͒˜,j͑x,s͒+K˜,j͑x,s͒˜͑x,s͒͑8͒where superscript d indicates the deviatoric component of the quantities.Notice that the transformed equilibrium equation for a nonho-mogeneous viscoelastic problem has identical form as an elastic40/JOURNAL OF MATERIALS IN CIVIL ENGINEERING©ASCE/JANUARY2011nonhomogeneous boundary value problem.This forms the basis for using CP-based FEM for solving graded viscoelastic problems such as asphalt concrete pavements.The basic FE framework for solving elastic problems can be readily used through the use of CP,which makes it an attractive alternative when compared to more involved time integration schemes.However,note that due to the inapplicability of the CP for problems involving the use of the time-temperature superposition principle,the present analysis is applicable to problems with nontransient thermal conditions.In the context of pavement analysis,this makes the present proce-dure applicable to simulation of traffic ͑tire ͒loading conditions for given aging levels.The present approach is not well-suited for thermal-cracking simulations,which require simulation of con-tinuously changing and nonuniform temperature conditions.FE FormulationThe variational principle for quasi-static linear viscoelastic mate-rials under isothermal conditions can be found in Gurtin ͑1963͒.Taylor et al.͑1970͒extended it for thermoviscoelastic boundary value problem͟=͵⍀u͵t Ј=−ϱt Ј=t ͵t Љ=−ϱt Љ=t −t Ј12C ijkl ͓x ,ijkl ͑t −t Љ͒−ijklЈ͑t Ј͔͒ϫץij ͑x ,t Ј͒ץt Јץkl ͑x ,t Љ͒ץt Љdt Јdt Љd ⍀u−͵⍀u͵t Ј=−ϱt Ј=t ͵t Љ=−ϱt Љ=t −t ЈC ijkl ͓x ,ijkl ͑t −t Љ͒−ijklЈ͑t Ј͔͒ϫץij ء͑x ,t Ј͒ץt Јץkl ء͑x ,t Љ͒ץt Љdt Јdt Љd ⍀u −͵⍀͵t Љ=−ϱt Љ=tP i ͑x ,t −t Љ͒ץu i ͑x ,t Љ͒ץt Љdt Љd ⍀=0͑9͒where ⍀u =volume of a body;⍀=surface on which tractions P iare prescribed;u i =displacements;C ijkl =space and time depen-dent material constitutive properties;ij =mechanical strains and ij ء=thermal strains;while ijkl =reduced time related to real time t and temperature T through time-temperature superposition prin-ciple of Eq.͑2͒.The first variation provides the basis for the FE formulation␦͟=͵⍀u ͵t Ј=−ϱt Ј=t ͵t Љ=−ϱt Љ=t −t ЈͭC ijkl ͓x ,ijkl ͑t −t Љ͒−ijklЈ͑t Ј͔͒ץץt Ј͑ij ͑x ,t Ј͒−ij ء͑x ,t Ј͒͒ץ␦kl ͑x ,t Љ͒ץt Љͮdt Јdt Љd ⍀u−͵⍀͵t Љ=−ϱt Љ=tP i ͑x ,t −t Љ͒ץ␦u i ͑x ,t Љ͒ץt Љdt Љd ⍀=0͑10͒The element displacement vector u i is related to nodal displace-ment degrees of freedom q j through the shape functions N iju i ͑x ,t ͒=N ij ͑x ͒q j ͑t ͒͑11͒Differentiation of Eq.͑11͒yields the relationship between strain i and nodal displacements q i through derivatives of shape func-tions B iji ͑x ,t ͒=B ij ͑x ͒q j ͑t ͒͑12͒Eqs.͑10͒–͑12͒provide the equilibrium equation for each finite element͵tk ij ͓x ,͑t ͒−͑t Ј͔͒ץq j ͑t Ј͒ץt Јdt Ј=f i ͑x ,t ͒+f i th ͑x ,t ͒͑13͒where k ij =element stiffness matrix;f i =mechanical force vector;and f i th =thermal force vector,which are described as follows:k ij ͑x ,t ͒=͵⍀uB ik T ͑x ͒C kl ͓x ,͑t ͔͒B lj ͑x ͒d ⍀u ͑14͒f i ͑x ,t ͒=͵⍀N ij ͑x ͒P j ͑x ,t ͒d ⍀͑15͒f i th ͑x ,t ͒=͵⍀u͵−ϱtB ik ͑x ͒C kl ͓x ,͑t ͒−͑t Ј͔͒ץl ء͑x ,t Ј͒ץt Јdt Јd ⍀u͑16͒l ء͑x ,t ͒=␣͑x ͒⌬T ͑x ,t ͒͑17͒where ␣=coefficient of thermal expansion and ⌬T =temperaturechange with respect to initial conditions.On assembly of the individual finite element contributions for the given problem domain,the global equilibrium equation can be obtained as͵tK ij ͓x ,͑t ͒−͑t Ј͔͒ץU j ͑t Ј͒ץt Јdt Ј=F i ͑x ,t ͒+F i th ͑x ,t ͒͑18͒where K ij =global stiffness matrix;U i =global displacement vec-tor;and F i and F i th =global mechanical and thermal force vectors respectively.The solution to the problem requires solving the con-volution shown above to determine nodal displacements.Hilton and Yi ͑1993͒have used the CP-based procedure for implementing the FE formulation.However,the previous re-search efforts were limited to use of conventional finite elements,while in the current paper graded finite elements have been used to efficiently and accurately capture the effects of material non-homogeneities.Graded elements have benefit over conventional elements in context of simulating non-homogeneous isotropic and orthotropic materials ͑Paulino and Kim 2007͒.Kim and Paulino ͑2002͒proposed graded elements with the GIF,where the consti-tutive material properties are sampled at each nodal point and interpolated back to the Gauss-quadrature points ͑Gaussian inte-gration points ͒using isoparametric shape functions.This type of formulation allows for capturing the material nonhomogeneities within the elements unlike conventional elements which are ho-mogeneous in nature.The material properties,such as shear modulus,are interpolated asG Int.Point =͚i =1mG i N i ͑19͒where N i =shape functions;G i =shear modulus corresponding tonode i ;and m =number of nodal points in the element.JOURNAL OF MATERIALS IN CIVIL ENGINEERING ©ASCE /JANUARY 2011/41A series of weak patch tests for the graded elements have been previously established ͑Paulino and Kim 2007͒.This work dem-onstrated the existence of two length scales:͑1͒length scale as-sociated with element size,and ͑2͒length scale associated with material nonhomogeneity.Consideration of both length scales is necessary in order to ensure convergence.Other uses of graded elements include evaluation of stress-intensity factors in FGMs under mode I thermomechanical loading ͑Walters et al.2004͒,and dynamic analysis of graded beams ͑Zhang and Paulino 2007͒,which also illustrated the use of graded elements for simulation of interface between different material layers.In a recent study ͑Silva et al.2007͒graded elements were extended for multiphys-ics applications.Using the elastic-viscoelastic CP,the functionally graded vis-coelastic finite element problem could be deduced to have a func-tional form similar to that of elastic place transform of the global equilibrium shown in Eq.͑18͒isK ˜ij ͑x ,s ͒U ˜j ͑s ͒=F ˜i ͑x ,s ͒+F ˜i th ͑x ,s ͒͑20͒Notice that the Laplace transform of hereditary integral ͓Eq.͑18͔͒led to an algebraic relationship ͓Eq.͑23͔͒,this is major benefit of using CP as the direct integration for solving hereditary integrals will have significant computational cost.As discussed in a previ-ous section,the applicability of correspondence principle for vis-coelastic FGMs imposes limitations on the functional form of constitutive model.With this knowledge,it is possible to further customize the FE formulation for the generalized Maxwell model.Material constitutive properties for generalized Maxwell model is given asC ij ͑x ,t ͒=͚h =1n͓C ij ͑x ͔͒h Exp ͫ−t ͑ij ͒hͬ͑no sum ͒͑21͒where ͑C ij ͒h =elastic contributions ͑spring coefficients ͒;͑ij ͒h=viscous contributions from individual Maxwell units,commonly called relaxation times;and n ϭnumber of Maxwell unit.Fig.1illustrates simplified 1D form of the generalized Max-well model represented in Eq.͑21͒.Notice that the generalized Maxwell model discussed herein follows the recommendations made by Mukherjee and Paulino ͑2003͒for ensuring success of the correspondence principle.For the generalized Maxwell model,the global stiffness matrix K of the system can be rewritten asK ij ͑x ,t ͒=K ij 0͑x ͒Exp ͩ−t ijͪ=K ij 0͑x ͒K ij t͑t ͒͑no sum ͒͑22͒where K ij 0=elastic contribution of stiffness matrix and K t=time dependent portion.Using Eqs.͑20͒and ͑22͒,one can summarize the problem asK ij 0͑x ͒K ˜ij t ͑s ͒U ˜j ͑s ͒=F ˜i ͑x ,s ͒+F ˜i th ͑x ,s ͒͑no sum ͒͑23͒FE ImplementationThe FE formulation described in the previous section was imple-mented and applied to two-dimensional plane and axisymmetricproblems.This section provides the details of the implementation of formulation along with brief description method chosen for numerical inversion from Laplace domain to time domain.The implementation was coded in the commercially available software Matlab.The implementation of the analysis code is di-vided into five major steps as shown in Fig.2.The first step is very similar to the FE method for a time dependent nonhomogeneous problem,whereby local contribu-tions from various elements are assembled to obtain the force vector and stiffness matrix for the system.Notice that due to the time dependent nature of the problem the quantities are evaluated throughout the time duration of analysis.The next step is to trans-form the quantities to the Laplace domain from the time domain.For the generalized Maxwell model,the Laplace transform of the time-dependent portion of the stiffness matrix,K t ,can be directly ͑and exactly ͒determined using the analytical transform given byK ij 0͑x ͒K ˜ij t ͑s ͒U ˜j ͑s ͒=F ˜i ͑x ,s ͒+F ˜i th ͑x ,s ͓͒no sum for K ij 0͑x ͒K ˜ij t ͑s ͔͒͑24͒Laplace transform of quantities other than the stiffness matrix canbe evaluated using the trapezoidal rule,assuming that the quanti-ties are piecewise linear functions of time.Thus,for a given time dependent function F ͑t ͒,the Laplace transform F ˜͑s ͒is estimated asF ˜͑s ͒=͚i =1N −11s 2⌬t͕s ⌬t ͑F ͑t i ͒Exp ͓−st i ͔−F ͑t i +1͒Exp ͓−st i +1͔͒+⌬F ͑Exp ͓−st i ͔−Exp ͓−st i +1͔͖͒͑25͒where ⌬t =time increment;N =total number of increments;and⌬F =change in function F for the given increment.Once the quantities are calculated on the transformed domain the system of linear equations are solved to determine the solu-tion,which in this case produces the nodal displacements in thetransformed domain,U˜͑s ͒.The inverse transform provides the solution to the problem in the time domain.It should be noted that()1C x ()2C x ()n C x τττ12nFig.1.Generalized Maxwell modelDefine problem in time-domain (evaluate load vector F(t)and stiffnessmatrix components K 0(t)and K t (x ))Perform Laplace transform to evaluate F(s)and K t (s)~~Solve linear system of equations to evaluate nodal displacement,U(s)Perform inverse Laplace transforms to get the solution,U(t)~Post-process to evaluate field quantities of interestFig.2.Outline of finite-element analysis procedure42/JOURNAL OF MATERIALS IN CIVIL ENGINEERING ©ASCE /JANUARY 2011the formulation as well as its implementation is relatively straight forward using the correspondence principle based transformed ap-proach when compared to numerically solving the convolution integral.The inverse Laplace transform is of greater importance in the current problem as the problem is ill posed due to absence of a functional description in the imaginary prehensive comparisons of various numerical inversion techniques have been previously presented ͑Beskos and Narayanan 1983͒.In the current study,the collocation method ͑Schapery 1962;Schapery 1965͒was used on basis of the recommendations from previous work ͑Beskos and Narayanan 1983;Yi 1992͒.For the current implementation the numerical inverse trans-form is compared with exact inversion using generalized Maxwell model ͓c.f.Eq.͑21͔͒as the test function.The results,shown in Fig.3,compare the exact analytical inversion with the numerical inversion results.The numerical inversion was carried out using 20and 100collocation points.With 20collocation points,the average relative error in the numerical estimate is 2.7%,whereas with 100collocation points,the numerical estimate approaches the exact inversion.Verification ExamplesIn order to verify the present formulation and its implementation,a series of verifications were performed.The verification was di-vided into two categories:͑1͒verification of the implementation of GIF elements to capture material nonhomogeneity,and ͑2͒verification of the viscoelastic portion of the formulation to cap-ture time and history dependent material response.Verification of Graded ElementsA series of analyzes were performed to verify the implementation of the graded elements.The verifications were performed for fixed grip,tension and bending ͑moment ͒loading conditions.The material properties were assumed to be elastic with exponential spatial variation.The numerical results were compared with exact analytical solutions available in the literature ͑Kim and Paulino 2002͒.The comparison results for fixed grip loading,tensile load-ing,and bending were performed.The results for all three casesshow a very close match with the analytical solution verifying the implementation of the GIF graded parison for the bending case is presented in Fig.4.Verification of Viscoelastic AnalysisVerification results for the implementation of the correspondence principle based viscoelastic functionally graded analysis were performed and are provided.The first verification example repre-sents a functionally graded viscoelastic bar undergoing creep de-formation under a constant load.The analysis was conducted for the Maxwell model.Fig.5compares analytical and numerical results for this verification problem.The analytical solution ͑Mukherjee and Paulino 2003͒was used for this analysis.It can be observed that the numerical results are in very good agreement with the analytical solution.The second verification example was simulated for fixed grip loading of an exponentially graded viscoelastic bar.The numeri-cal results were compared with the available analytical solution24F u n c t i o n ,f (t )T e s t Time (sec)Fig.3.Numerical Laplace inversion using collocation method-y -y D i r e c t i o n (M P a )E (x)--S t r e s s i n -x (mm)parison of exact ͑line ͒and numerical solution ͑circular markers ͒for bending of FGM bar ͑insert illustrates the boundary value problem along with material gradation ͒m )y e n t i n y D i r e c t i o n (m E(x)D i s p a l c e m x (mm)parison of exact and numerical solution for the creep ofexponentially graded viscoelastic barJOURNAL OF MATERIALS IN CIVIL ENGINEERING ©ASCE /JANUARY 2011/43͑Mukherjee and Paulino 2003͒for a viscoelastic FGM.Fig.6compares analytical and numerical results for this verification problem.Notice that the results are presented as function of time,and in this boundary value problem the stresses in y-direction are constant over the width of bar.Excellent agreement between nu-merical results and analytical solution further verifies the veracity of the viscoelastic graded FE formulation derived herein and its successful implementation.Application ExamplesIn this section,two sets of simulation examples using the gradedviscoelastic analysis scheme discussed in this paper are presented.The first example is for a simply supported functionally graded viscoelastic beam in a three-point bending configuration.In order to demonstrate the benefits of the graded analysis approach,com-parisons are made with analysis performed using commercially available software ͑ABAQUS ͒.In the case,of ABAQUS simula-tions,the material gradation is approximated using a layered ap-proach and different refinement levels.The second example is that of an aged conventional asphalt concrete pavement loaded with a truck tire.Simply Supported Graded Viscoelastic BeamFig.7shows the geometry and boundary conditions for the graded viscoelastic simply supported beam.A creep load,P ͑t ͒,is imposed at midspanP ͑t ͒=P 0t͑26͒The viscoelastic relaxation moduli on the top ͑y=y 0͒and bottom ͑y=0͒of the beam are shown in Fig.8.The variation of moduli is assumed to vary linearly from top to bottom as follows:E ͑y ,t ͒=ͩyy 0ͪE Top ͑t ͒+ͩy 0−y y 0ͪE Bottom ͑t ͒͑27͒The problem was solved using three approaches namely,͑1͒graded viscoelastic analysis procedure ͑present paper ͒;͑2͒com-mercial software ABAQUS with different levels of mesh refine-ments and averaged material properties assigned in the layered manner;and ͑3͒assuming averaged material properties for the whole beam.In the case of the layered approach using commer-cial software ABAQUS,three levels of discretization were used.A sample of the mesh discritization used for each of the simula-tion cases is shown in Fig.9.Table 1presents mesh attributes for each of the simulation cases.The parameter selected for comparing the various analysis op-tions is the mid span deflection for the beam problem discussed earlier ͑c.f.Fig.7͒.The results from all four simulation options are presented in Fig.10.Due to the viscoelastic nature of the problem,the beam continues to undergo creep deformation with increasing loading time.The results further illustrate the benefit of using the graded analysis approach as a finer level of meshTable 1.Mesh Attributes for Different Analysis Options Simulation case Number of elements Number of nodes Total degrees of freedom FGM/average/6-layer 7201,5733,1469-layer 1,6203,4396,87812-layer2,8806,02512,050y E 0(x )t i me (sec)parison of exact and numerical solution for the exponen-tially graded viscoelastic bar in fixed grip loadingy()()0P t P h t =xx 0=10y 0=1x 0/2Fig.7.Graded viscoelastic beam problemconfigurationE 0(M P a )l x a t i o n M o d u l u s ,E (t )/N o r m a l i z e d R e 10101010time (sec)Fig.8.Relaxation moduli on top and bottom of the graded beamFG M A verage 6-Layer 9-Layer 12-LayerFig.9.Mesh discretization for various simulation cases ͑1/5th beam span shown for each case ͒。
机械专业笔试题(整理)
格力电器机械2011笔试试题一、填空题1、链传动是依靠链条与链轮轮齿的啮合来传递运动和动力的,所以应属于挠性传动。
2、EDM的中文含义是电火花加工(ElectricalDischargeMachining)。
3、不随时间变化的应力称为静应力,随时间变化的应力称为变应力,具有周期性的变应力称为交变应力。
4、对于直齿圆柱齿轮传动,其齿根弯曲疲劳强度主要取决于模数,其表面接触疲劳强度主要取决于直径。
5、φ30的轴,上偏差是-0.010,下偏差是-0.036,其最大极限尺寸是φ29.990,最小极限尺寸是φ29.964,其公差是0.026。
6、合理的刀具耐用度包括最高生产耐用度与最低生产成本耐用度两种。
7、刚度是指机械零件在载荷作用下抵抗弹性变形的能力。
零件材料的弹性模量越小,其刚度就越大。
8、开式齿轮传动的主要失效形式是齿面磨粒磨损和轮齿的弯曲疲劳折断。
9、定位基准面和定位元件制造误差引起的定位误差称基准位置(基准不重合、基准位置)误差,工件以平面定位时,可以不考虑基准位置(基准不重合、基准位置)误差。
10、齿轮的模数m=D/Z,其中D为分度圆直径,Z为齿数。
二、不定项选择题1、45号钢经调质处理,在常温下工作的轴,当计算表明其刚度不够时,应采取的正确措施是(C)A、改用合金钢B、改变表面粗糙度C、增大轴的直径D、提高轴的表面硬度2、焊接厚度薄的不锈钢器具应采用(C、D)A、氧气焊B、钎焊C、氩弧焊D、气体保护焊3、渐开线花键通常采用的定心方式是(D)A、齿侧定心B、外径定心C、内径定心D、齿形定心4、为了提高承受轴向变载荷的紧螺栓联接的抗疲劳破坏的能力,应当(A、D)A、增大被联接件的厚度B、增大螺栓的刚度C、减小被联接件的厚度D、减小螺栓的刚度5、若被连接件之一厚度较大,材料较软,强度较低,需要经常更换时,宜采用(B)A、螺栓连接B、双头螺栓连接C、螺钉连接D、紧定螺钉连接6、在凸轮机构的从动件选用等速运动规律是,其从动件的运动(A)A、将产生刚性冲击B、将产生柔性冲击C、没有冲击D、既有刚性冲击又有柔性冲击7、在滚子链传动的过程中,为了减小滚子的接触强度,应(D)A、增大链节距和滚轮齿数B、增大链节距和减小滚轮齿数C、减小链节距和滚轮齿数D、减小链节距和增大滚轮齿数8、对中性高且对轴的削弱又不大的键应该是(A)联接A、普通平键B、半圆键C、楔键D、切向键9、对于平面连接机构,当(B)时,机构处于死点位置A、传动角γ=90°B、压力角α=90°C、压力角α=0°D、传动角γ=45°10、对于四绞链机构,在满足杆长和的条件时,若取(A)为机架,将得到双摇杆机构。
智能材料的数学模型和方法
智能材料的数学模型和方法Mauro Fabrizio, Barbara Lazzari,Department of Mathematics, University of Bologna, ItalyAngelo Morro, DIBE, University of Genoa, Italy (Eds.)Mathematical Models and Methods for Smart MaterialsSeries on Advances in Mathematics for Applied Sciences Vol.6220XX年, 374pp.Hardcover $ 110.00ISBN 981-238-235-6World Scientific本书是《应用科学的数学进展》系列丛书的第62卷,是20XX 年6月在意大利举行的“智能材料的数学模型和方法”国际会议的论文集。
全书分为四部分,共收入35篇论文。
第一部分材料科学中的方法,主要研究涉及液晶、带内变量的材料、非结晶材料和热弹性材料等物理系统的数学技术,也经典连续力学模型和动力系统的稳定性及可控制性分析的方法。
第二部分智能材料的模拟,集中阐述超流体、超导体、带记忆材料、非线性弹性材料和损伤1/ 2材料的模型,在模型的建立时,在描述本构性能中,热力学方面起主要作用。
第三部分带记忆材料中的适定性,包括经常用积分-微分方程表示的问题解的存在性、唯一性和稳定性,也注意到粘弹性中的指数衰减、带记忆的热传导中的反问题和抛物型方程的自动控制。
第四部分相变中的解析问题,讨论与相变、迟滞性和可能包括衰减记忆效应有关的非线性偏微分方程,对于带记忆的相-场模型、Cattaneo型方程的Stefan问题、热-粘-塑性中的迟滞性和固体固体相变问题发展了特有的应用。
本书可供相关专业的研究人员和技术人员阅读,也可供大学生和研究生阅读参考。
吴永礼,研究员(中国科学院力学研究所)Wu Yongli, Professor(Institute of Mechanics,the Chinese Academy of Sciences)2/ 2。
Phenylalanine Anhydrous and Monohydrate Forms
Solubility of L-Phenylalanine Anhydrous and Monohydrate Forms: Experimental Measurements and Predictions
Jie Lu,*,† Qing Lin,† Zhen Li,† and Sohrab Rohany
■
models.6 EOS's are widely used for phase equilibrium calculations; however, predicting the solid−liquid equilibria of nonideal systems using EOS with ordinary parameters is generally not reliable, and special mixing rules are required to use such equations.7 On the other hand, solubility prediction using activity coefficient models is based on the estimation of the solute ideal solubility and activity coefficient of the solute in a particular solvent.8 Using the thermal properties of a solute, for example, the heat of fusion and melting temperature, the ideal solubility of the solute can be calculated. Then activity coefficients will be calculated from a particular model, which expresses the excess Gibbs free energy of the mixtures as a function of the composition.9−11 To date, various semipredictive models such as Wilson,12 nonrandom two-liquid (NRTL), and modified models,13−17 universal quasichemical (UNIQUAC) and modified models,18−20 and so forth, are widely used to calculate the activity coefficients due to the requirement for only a small number of adjustable parameters to be known, together with structural parameters that may be readily calculated or read from tables.21,23
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Models and Methodologies for Simulating Mobile Ad-Hoc NetworksVinay Sridhara Electrical Engineering University of Delaware Newark,DE,USA vsridhar@Jonghyun KimElectrical EngineeringUniversity of DelawareNewark,DE,USAkim@Stephan BohacekElectrical EngineeringUniversity of DelawareNewark,DE,USAbohacek@AbstractIt is a truism that simulations of mobile ad hoc networks (MANETs)are not realistic.While the protocols are sim-ulated reasonably realistically,the propagation of wireless transmissions and the mobility of nodes are not.Today,sim-ulations typically model propagation with either the free-space model or a”two-ray”model that includes a ground reflection.Such models are valid only in open space where there are no hills and buildings.Since wireless signal at the frequencies used for MANETs is partly reflected off of build-ings and is partly transmitted into the building,the presence of buildings greatly influences propagation.Consequently, these open-space propagation models are not accurate in outdoor urban areas.Indoors,the open-space models are not applicable.There has been little effort in developing realistic mobility models.In urban areas,the mobility of vehicles and pedestrians is greatly influenced by node in-teraction.For example,on a congested street or a sidewalk, nodes cannot travel at their desired speed.Furthermore, the location of streets,sidewalks,hallways,etc.restricts the position of nodes.Traffic lights also have a direct impact on theflow of nodes.In this paper,simulation of propagation and mobility for MANETs in urban areas is addressed.Techniques for simulation,models,model pa-rameters,computational complexity,and accuracy are all examined.The techniques for propagation are validated against propagation measurements.Nearly all aspects of the mobility models and model parameters can be derived from urban planing and traffic engineering research.The simulation approaches discussed here are implemented in a suite of simulation tools that are available for download. 1IntroductionMobile ad hoc networks(MANETs)will likely be de-ployed in the future military operations.Furthermore,cities such as Philadelphia are planning to deploy ad hoc networks to provide wireless access to the entire135square mile city [36].While the details have not beenfinalized yet,the ini-tial plans for Philadelphia are that the network will include a large number offixed wireless relays and perhaps mo-bile relays as s Vegas has a pilot project already deployed for use by public safety organizations which is capable of supporting applications such as monitoring and controlling vehicular traffic for emergency response and re-mote situation assessment[6].Over two hundred other local governments are considering similar projects.In such net-works,end-hosts will certainly be mobile.Thus,large-scale deployment of multi-hop wireless ad hoc networks appears imminent.It is well known that the variability of node-to-node com-munication is a major challenge facing MANETs.For ex-ample at one moment,high quality communication between two nodes may be possible while a short time later,commu-nication between the nodes may not be possible.In the case of wide bandwidth communication,such drastic changes in link quality are typically the result of node mobility.For example,if a node moves around a corner of a building, then,since the signal is not easily able to penetrate through buildings;the communication between the two nodes may be severed.Thus,a combination of node mobility and com-plex propagation due to the environment results in rapid variability of communication links.However,while great strides have been made in protocols for MANETs,there has been very little effort devoted to understanding how to best simulate MANETs,specifically,how to best sim-ulate the node mobility and signal propagation.This lack of effort contrasts the simulation of wired networks where there has been extensive work focused on simulation issues such as background traffic and topology(e.g.,[11],[25], [13],[24]).This paper focuses on the techniques for sim-ulating propagation and mobility of MANETs in urban en-vironments and related issues.The simulation techniques presented here have been incorporated into a suite of simu-lation tools”UDelModels”that are available for download.At the frequencies used in today’s wide band com-munication,wireless signals may undergo reflections off of buildings,reflections off of the ground,transmissions through walls,and diffractions over and around buildings. Thus,a wireless communication extends far beyond what line-of-sight(LOS)communication will offer.Indeed,our simulations show that majority of a node’s neighbors(i.e., the nodes with which a node can communicate)are not within LOS.Similarly,Table6provides an example where the coverage area of a single transmissions increases by 450%when reflection,transmission,and diffraction are in-cluded.As will be discussed in Section5.3,the variation of the signal strength under LOS propagation is significantly different from the variation of the signal strength in reality. Goals of realistic propagation simulation include simulat-ing realistic coverage and realistic variation of the signal strength.There has been extensive work on modeling and under-standing realistic topologies that arise in wired networks (e.g.,[13],[24]).In MANETs,the study of topology is complicated by the dependence on the propagation charac-teristics of the environment and location of the nodes.Prop-agation and the location of nodes is not random,but is dom-inated by structure.For example,streets,especially well traveled,wide,and straight,have high node density and excellent propagation properties.Thus,nodes on a major street will have a large number of other nodes within com-munication range.However,these nodes will not be able to directly communicate with nodes on parallel streets since such communication requires transmissions through build-ings or over them;something that is difficult if the buildings are large.Hence,the topology in an urban environment with large buildings will consist of well-connected nodes along the streets.Nodes near intersections will provide connec-tivity between two streets.Hence,the topology of outdoor nodes looks like a street map of the city.Within buildings, nodes have a smaller propagation range.Thus,the local topology of indoors and outdoors is very different.Realis-tic topologies can be simulated only if the propagation and mobility simulations are realistic.Current approaches to mobility will be discussed in Sec-tion6.There is little doubt that these mobility models are not realistic.To some extent,since open-space(i.e.,free-space and two-ray)propagation models that neglect the im-pact of objects have been used in the past,there has been little reason to use mobility models where nodes avoid or interact with objects.However,when propagation in ur-ban environments is considered,mobility must also be ad-dressed.Specifically,the mobility model must take into ac-count the structure of the urban environment such as streets, sidewalks and buildings.One of the reasons that mobility models must not be overly simplified is that in reality pedestrians and vehicles tend to move in clusters[38],[46].That is,the locations of nodes are correlated.Furthermore,there is a well-studied relationship between node density and node speed(e.g.,re-call the”two-second rule”that specifies the safe driving dis-tance between cars).Since the spatial distribution of nodes has an important impact on the behavior of MANET proto-cols,mobility models must be realistic.In summary,the objectives of the simulation approach discussed here is to provide realistic simulation of mobility and propagation.Specifically,for mobility,the goal is to provide realistic–node distribution,–node clustering(i.e.,correlation in node location),–trips including trip lengths,paths,and generation rates,–and node speeds.For propagation simulation,the goal is to provide realis-tic–propagation range,–signal strength,–and spatial variation of the link quality.Together,the mobility and propagation simulators pro-vide realistic–topologies,–and variations of topologies.The mobility simulation objectives can be achieved by employing models and model parameters that have been de-veloped and verified by the urban planning and traffic engi-neering research communities.The propagation simulation objectives can be achieved by verifying and by comparing the propagation model to observations.If the mobility and propagation are realistic,then the topology and the dynam-ics of the topology should be realistic.However,this can only be verified when MANETs are deployed.It is important to note that the objective is realistic sim-ulation,not accurate simulation.By this we mean that the simulation should provide mobility and propagation similar to what could occur in an urban environment,not necessar-ily what would occur in a particular urban environment.As will be discussed,accurate prediction requires substantial knowledge of the modeled urban environment.For exam-ple,accurate prediction requires precise knowledge of loca-tion and dimensions of buildings and other large to moder-ate sized structures,as well as knowledge of the building materials used and the layout of building interiors.Fur-thermore,accurate mobility simulation requires knowledge of details such as the types of establishments within each building(e.g.,restaurant,office,shopping,etc.)and origin-destinationflow matrices for vehicle traffic.Realistic sim-ulation,on the other hand,merely needs realistic dimen-sions and locations of buildings,building materials,layout of buildings interiors,and realistic trip generation for vehi-cles and pedestrians.The motivation for realistic simulation rather than accu-rate prediction is to reduce the complexity of simulation. There are two types of complexity that are relevant here, computational complexity and usage complexity.The lat-ter refers to the difficulty in defining the simulated environ-ment.This paper provides models and parameter values, and discusses tools to develop simulated environment that satisfy the goal of realistic simulation.If the goal is realistic simulation then the complexity of use is pu-tational complexity is treated in detail in Section5.1.Propagation,vehicle mobility,and pedestrian mobility modeling are all active areas in research.Addressing all these issues is beyond the scope of this paper.Instead the focus of this paper is on topics that are most critical.The remainder of the paper proceeds as follows.In the next section,previous work related to simulation of prop-agation and mobility for MANETs is discussed.Section 3provides a short overview of the steps involved in simu-lating MANETs.Section4discusses different approaches to defining city maps that can be used for mobility and propagation simulation.Section5discusses characteris-tics and simulations of propagation.Section5.1examines the computational complexity of propagation simulation for MANETs.Section5.2discusses the impact of reflections and diffractions in propagation in urban areas.Section5.3 provides validation of the propagation models.Section6 discusses mobility models for realistic MANET simulation. This discussion is broken down into the following sections. Section6.1the dynamics of nodes and section6.3discusses trip generation.Section6.4provides some validation of the pedestrian mobility model.Section7provides concluding remarks.2Related workCurrently,Open-space propagation(i.e.,free-space and the two-ray model)is the most popular propagation model for MANETs research.For example,ns-2[29],[30]only supports open-space propagation models.On the other hand,QualNet[42]supports open-space propagation as well as stochastic propagation models such as Rayleigh,Ri-cian and Lognormal fading.QualNet also supports path loss tracefiles.Furthermore OPNET[33]supports open-space propagation models as well as an enhanced open-space model that accounts for hills,foliage and atmospheric affects.While less popular,stochastic models such as Rayleigh, Rician and Lognormal fading[39]have been used by sev-eral investigators.In order to include correlations,Markov model based stochastic models have been suggested[23], [43]While such propagation modeling is useful to com-pare physical layer techniques,they have limited use in MANETs.The drawback of stochastic propagation mod-els is that they fail to model the propagation structure found in urban areas.As mentioned earlier,due to the difficulty of propagating through buildings and the ease of propagat-ing down the streets,the topology of the outdoor nodes in a MANET resembles the street map of the city.Also,propa-gation indoors exhibits structure due to thefloors and hall-ways.In[18]and[17]obstacles were included in the simulated environment and propagation was limited to line-of-sight. In[17]the obstacles were randomly placed buildings.As will be shown most of the communication in an urban area is not line-of-sight.Since streets play an important role in MANET topology,the random placement of buildings will result in non-realistic topologies.There has been limited work that includes accurate prop-agation modeling along with MANET simulation.For ex-ample,[8]suggests using ray tracing indoors to enhance ns-2’s propagation model.Instead of simulation,there has been some effort in de-veloping desktop test-beds[21].Such test-beds augment protocol simulation with live wireless transmissions over a small wireless network.A significant drawback of such an approach is that it is not able to realistically model the multi-path reflection,transmissions,and diffractions that occur in a complicated propagation environment.There are several commercial packages that can be used to predict coverage of a single or a small number of mo-bile phone base stations or wireless access points(exam-ples include[48]and[47]).While many of the propagation techniques used by these tools are employed by a MANET propagation simulation(e.g.,[41]),these tools have limited applicability to MANET simulation,due to different goals (realistic vs.prediction).Specifically(as discussed ear-lier)the goal of accurate prediction increases the compu-tational complexity as well as the complexity of use.Most tools focus on outdoor coverage for mobile phones,or in-door coverage for wireless base stations;they neglect mixed indoor/outdoor simulation.These tools do not produce a propagation matrix as required for simulation.There are several mobility models used for MANET sim-ulation.The most popular is the random waypoint model [19]where a node picks a next destination at random.The node travels in a straight line to the destination at a ran-domly selected speed(often uniformly distributed between 1m/s and20m/s).Upon arriving at the location,the node waits for a random amount of time before selecting the next location.There are many variations in such random(see[5] for details and references)mobility models.In[18]several scenario based mobility models were considered.However, as mentioned in[18],these mobility models are not meant to be realistic.In[2],the Manhattan mobility model is in-troduced where nodes are restricted to a grid,resembling the street map of Manhattan.This model does not include any realistic node mobility dynamics(e.g.,node interaction,traffic lights)or realistic trip generation.In[34],mobility patterns from multi-user games were used,but did not ver-ify that the mobility of characters in games resemble the mobility of pedestrians or vehicles.3MANET simulation overviewThere are several stages to MANET simulation.The first step is to define the simulated city map.This step is discussed in Section4.The second step is to determine the propagation matrix for the city.The propagation ma-trix includes channel characteristics such as path loss,delay spread and angle of arrival for each source-destination in the city.This step is discussed in Section5Next,the city map is used to generate one or more mobility tracefiles. This step is discussed in Section6.From the mobility trace file and the propagation matrix,the propagation tracefile is computed;the propagation tracefile provides the propaga-tion statistics between all pairs of nodes at every moment. The propagation tracefile can then be used by the protocol simulator.4City mapsIn order to model MANETs over urban areas,it is nec-essary to have a model of the urban area.There are sev-eral ways that maps suitable for MANET simulation can be developed.First,a random city can be built as was done in[17].In this case buildings are placed at random and a V oronoi diagram is used to construct sidewalks between the buildings.One drawback of such an approach is that important aspects of cities such as long thoroughfares and big intersections are neglected.It is well known that streets play an important role in mobile phone communication and it has been shown that streets play an important role in ur-ban MANET connectivity[4].A more realistic way to generate cities is to utilize the detailed GIS datasets[12].These datasets include3-dimensional building map information that provides enough detail for realistic simulation.There is an abundant number of such datasets.For example,there are GIS datasets for most,if not all,American cites.Our map building suite of tools converts GIS datasets into format suitable for a spe-cialized graphical editor.The graphical editor is used to ”touch-up”the GIS map(e.g.,remove spurious buildings, add roads,sidewalks,traffic lights,andfixed base stations). The graphical editor is also used to define locations where vehicles enter and exit the modeled area.A third way to generate city maps is to develop a map directly in the editor.For example,idealized grid city could be generated within the editor.Andfinally,there has been some work on generating random,yet realistic cities[35].Often,random cities produce GIS datasets,and hence are easily used for propagation and mobility simulation.These realistic random cities are often generated to meet certain aesthetic requirements.It is unclear if these random cities would span a relevant range of mobility and propagation.In the same way that random wired network topology gener-ation required substantial effort before relevant topologies were developed,random city generation for MANET simu-lation will also take considerable effort.While GIS datasets have details of building heights and position,they typically do not provide any details about the interiors of the building.In lieu of actual interiors,they must be automatically generated.Our suite of tools assumes that all buildings are office buildings with offices that are 3.5meters wide and3/8of the building depth deep and the width of hallways is1/4of the depth of the building.The hallway runs in the center of the building and stairs are on each end of the building.Incorporating automatic genera-tion of heterogeneous building interiors will be left for fu-ture work.5Propagation modelingThe main factors that affect the probability of a packet error are signal strength,delay spread,Doppler spread,and noise,which include interference.Of these,current simu-lators only consider signal strength and interference.De-lay spread accounts to the fact that a single transmission might result in several delayed signals arriving at the re-ceiver.Each of these signals follows a different path and hence arrive at a different time and with different amplitude. If the delay between these signals is sufficiently large,they can increase the probability of transmission errors.Sim-ilarly Doppler spread also contributes to increased packet error rate.Doppler spread results when the transmitter,re-ceiver,or an object that the signal reflects off of is moving.There has been little work that relates delay spread and Doppler spread to packet error probability.The reason for this might be the fact that the signal strength plays a more significant role in the packet error probability[39].If signal strength can be computed,it is straightforward to compute delay spread(our implementation determines delay spread) but further investigations are necessary to arrive at a rela-tionship between delay spread and packet error probability. The section focuses on estimating the signal strength1in ur-ban environmentsThe signal strength at the receiver is given by P Received= P transmitted×C×Path Loss,where C is a constant that de-pends on the antennas and the frequency,and is often on the order of-30dB to-40dB.Assuming that C is known,and if the transmitted power is known,then knowing the path1Note that signal strength is also used to determine interference.loss is equivalent to knowing the signal strength.Thus,theterms path loss and received signal strength are used inter-changeable.A large volume of research has shown that at the dis-tances and frequencies considered here,the propagation of electromagnetic waves can be modeled as rays(see[40] and reference therein).These rays reflect off of the ground and walls,are transmitted through walls,and diffract around corners.While traveling through free-space,the ray’s sig-nal strength decays like1/d2where d is the distance.When the ray makes a reflection,transmission,or diffraction,it experiences an additional decrease in signal strength and a change in phase.Thus,the path loss for a particular ray is given byPath loss=1/d2×Attenuation,(1) where Attenuation is a complex number that depends on the details of each reflection,transmission,and diffraction. The received signal strength can be determined byfinding all the rays that hit the receiver and determining the length and the attenuation experienced by each ray.Determining the received signal strength at a particular frequency re-quires the addition of signal strength provided by each ray. For wide band communication,the signal strength is the av-erage power of the signal averaged over the bandwidth.For example,in802.11b,the signal is averaged over the22MHz wide channel that is centered at2.414GHz.Averaging is not necessary when narrow band communication is used.The attenuation and change in phase due to a reflection or transmission depends on the frequency and polarization of the signal2,the angle of incidence,and the type and the thickness of the material that the signal is reflecting off of or transmitting through.If the material is known and is ho-mogeneous,the loss and change in phase can be found in a straightforward manner(e.g.,see[20]).Figure1illustrates how attenuation of the signal depends on the material and the angle of incidence.Figure1shows that the difference between glass and concrete is less than10dB.Other mate-rials such as brick result in similar variations in loss,while materials such as wood have a significantly different behav-ior.Since it is not possible to know the material used in the construction of all buildings,the attenuation from reflection and transmission is difficult to be exactly determined.How-ever,since the goal is for the simulations to merely be re-alistic,path loss can be obtained by assuming that common building materials are used(e.g.,concrete,brick,and glass, which all have similar propagation characteristics).Besides reflection and transmission,diffraction plays an important role in propagation.Diffraction allows wireless transmissions around the corners and over the buildings. Whether a signal is more easily diffracted over the building 2It is typical to assume vertical polarization.Transmission (Concrete)-20-5Loss(dB)Angle of IncidenceReflection (Concrete)Reflection (Glass)Figure1.Loss due to Reflection and Trans-mission.The plot assumes that the concreteis20cm thick and the glass is2cm thick.or transmitted through the building depends on the size and height of the building.Thus,both transmission and diffrac-tion must be modeled.The Uniform Geometrical Theory of Diffraction has been shown to provide a realistic model for diffraction.[26].Once the map,bandwidth,and building materials have been defined,propagation can be determined.However,ex-treme care must be taken to reduce the computation.As-suming that all walls are vertical significantly decreases computational.Specifically,the3-D ray tracing problem re-duces to a2-D ray tracing problem thatfinds vertical plane paths.The2-D ray tracing problem is illustrated in the right-hand plot in Figure2,where two vertical plane paths are shown.Once the vertical plane paths are found,the3-D ray paths restricted to the vertical plane paths can be com-puted easily.The left-handfigure in Figure2shows the paths of a ray in the vertical plane.One vertical plane path has three ray paths,(a1)one that diffracts over a building, (b1)one that reflects off of the ground and passes through a building,and(c1)the one that passes straight through a building.The other vertical plane path has two ray paths, (a2)one reflecting off of the wall of a neighboring build-ing and(b2)one reflecting off of the wall of neighboring building and undergoing a ground reflection.In one vertical plane path there are potentially many ray paths that include repeated reflection off of the ground,transmission through buildings,and diffractions over buildings.In our simula-tor,we include three types of ray paths,direct paths(line of sight or transmissions through buildings),ground reflected paths,and paths that diffract over buildings without being transmitted through the buildings.For paths that diffract over buildings,if the transmitter or receiver is indoors,then the ray path passes through the building where the trans-mitter and/or receiver is,but must pass over all other build-ings intersected by the vertical plane path.Such ray pathsFigure2.Left:Two vertical plane paths and5ray paths.Right:a top-view of the scene onthe left.do not have a significant impact on the computed path loss since transmissions through buildings and diffractions over buildings greatly reduce the signal strength.A straightforward implementation of even2-D ray-tracing is not computationally efficient.Instead,a tech-nique that is more appropriately called beam tracing can be performed.Like ray tracing,the goal of beam tracing is to determine the paths from the transmitter to receiver. Beam tracing begins with the source broadcasting the sig-nal in all directions(assuming an omnidirectional antenna). This transmission is not modeled as a large number of rays, but as a small number of beams.When a beam intersects a building,two beams are generated,one is reflected off of the building and one is transmitted into the building.If only a part of the beam intersects the building,the beam is split into three with one part of the beam continuing to the next wall(if it exists)and the other part of the beam generating two beams,a reflected beam and a transmitted beam.Fi-nally,if the receiver is found to be included within the span of a beam,the ray from transmitter to receiver can be com-puted easily.The beam tracing computation can be further simplified by dividing the2-D space into a grid and the determining the propagation between the center points of each square. Each square of the grid is called afloor-tile.Outdoors and indoors are discretized in this manner.Indoors,eachfloor of the building is discretized into set offloor-tiles.To reduce the number offloor-tiles,the entire space is not discretized. Rather,floor-tiles are placed only along the centerlines of sidewalks,hallways,and roads.For rooms,floor-tiles are placed in every location that a mobile node can be present. The walls of buildings are also divided into wall-tiles.Since the beam tracing is in2-D,the wall-tiles are segments(1-D tiles).The computation is divided into two parts,preprocess-ing and beam tracing.During preprocessing,ray neighborswall tile Figure3.Beam Tracing.Suppose that the(yellow)tile on the lower left has been deter-mined to be hit by a beam.In particular,thisbeam hits the end points such that the re-flected rays are as shown.From these rays,the virtual source,shown in the lower left,isfound.The angle at which the beam hits theend points of the(blue)tile in the upper rightis found as shown.This tile generates a re-flected and transmitted beam and the processcontinues.for each tile are found.A tile’s ray neighbors are all the tiles that could be directly reached(i.e.,without reflection,trans-mission through a wall,or diffraction)by a ray emanating from the tile.Once the ray neighbors are found,beam trac-ing can be performed efficiently.Figure3illustrates how the beam tracing computation is performedThis process of beam tracing as shown in Figure3is car-ried out in a breadthfirst manner with each beam continued to be reflected,transmitted,and,perhaps,subdivided until either the beam exits the modeled area or until the estimated path loss of the beam surpasses a threshold.The trade-off between the number of reflection/transmissions/diffractions and accuracy and computational complexity is investigated in the next section.Beam tracing can be performed indoors as well as out-doors.However,the computational complexity depends on the number of walls.Since building interiors have a large number of walls,beam tracing inside all the build-ings within a large region of a city exceeds today’s compu-tational abilities.Fortunately,it has been found that a real-istic estimate of indoor propagation can be performed with-out using beam tracing.Specifically,the attenuation factor (AF)model has been shown to provide realistic path loss es-timates,with the error found to be within4dB[39].The AF model assumes that communication indoors takes a straight line path(i.e.,no reflections off of interior walls).Further-more,transmissions through each interior wall and trans-missions through eachfloor result in attenuation.While the。