Simulation of the Viscoplastic Material Behaviour of Cast Aluminium Alloys due to Thermal-
Al_Si合金凝固组织的数值模拟(微观组织模拟paper)
摘 要凝固组织对铸件的性能有重要影响，对凝固组织的控制研究，过去一般采用物理实验的方法，浪费了大量的人力和物力，实验周期长，使得该方法在实际应用中的范围受到了一定限制。
随着金属凝固理论的日益完善以及计算机技术在材料科学、冶金学上应用的迅猛发展，使得计算机技术对凝固组织进行准确的模拟成为可能。
本文建立了有限元（Finite Element）和元胞自动机法（Cellular Automaton）相结合的宏微观耦合的CA-FE模型，采用有限元法（FE）计算宏观温度场，元胞自动机法（CA）计算微观凝固组织形成，与宏观传热进行耦合。
在微观计算中，形核计算采用了基于高斯分布的连续形核模型，生长计算采用了扩展的KGT模型，使其适用范围由二元合金扩展至多元合金。
应用CA-FE模型模拟了Al-Si合金的三维凝固组织，并进行了热态验证实验，应用修正的数学模型模拟并分析了原始成分、形核参数、浇注条件和铸模对凝固组织的影响。
研究结果表明：（1）模拟结果能够较为准确地反映出等轴晶和柱状晶的分布位置、比例和大小，并能较好描述凝固过程中晶粒生长情况，说明CA-FE模型是模拟凝固组织的有效模型；（2）降低原始成分Si含量以及提高过冷度是有利于柱状晶的发展，而增大形核密度是有利于等轴晶的发展，且能细化晶粒；（3）提高浇注温度，凝固组织中柱状晶增多，且晶粒明显变得粗大，而铸模外界冷却强度对铸件凝固组织的影响不大；（4）增大铸模厚度和使用冷却能力强的铸模都将使凝固组织中柱状晶比例增大，当使用冷却能力差的硅砂模时，凝固组织没有柱状晶而全为等轴晶。
关键词：有限元；元胞自动机法；数值模拟；凝固组织；等轴晶；柱状晶AbstractSolidification structure has an important influence on the performance of casting. In the past, the method of physical experiment was applied to the research of controling the solidification structure generally, however, a great deal of time and efforts should be put while using this method. so it is limited in the practical application. With the improvement of metal solidification theory and the rapid development of computer technology used in materials science and metallurgy, it has become possible to simulate the solidification structure accurately with computer technology.The CA-FE model was built through coupling the finite element and cellular automaton method. The finite element method was used to calculate macro temperature, and the cellular automaton method was used to simulate solidification microstructure with coupling the macro temperature calculation. In microstructure simulation, the nucleation adopts the continuous nucleation model based on Gaussian distribution, and the growth adopt the extended KGT model which fit complex alloy expanded from binary alloy. The three-dimensional solidification structures of Al-Si alloy was simulated by CA-FE model with hot verification test. In addition, the effects of primitive composition, nucleation parameters, casting conditions and the mold on solidification structures were analysised.The results show as follows:(1) The simulated results can accurately reflect the distribution, proportion, size of equiaxed grain and columnar grain，and can describe the grain growth well in the solidification process, so the CA-FE model is a effective model to simulate the solidification structure.(2) Reducing primitive composition of Si element and increasing undercooling are conducive to the development of columnar grains, but increasing nucleation density is conducive to the development of equiaxed grains, and can fine grains.(3) Raising the casting temperature, the proportion of columnar grain will increase, and the grains become coarse obviously，but the effect of the cooling intensity outside the mold on solidification structure is slight.(4) Enlarging the thickness of the mold or using the mold with strong cooling capacity, the proportion of columnar grain will increase. While using the Silica Sand mold with weak cooling capacity, the solidification structure were composed with all equiaxed grains and without columnar grain.Key words：finite element; cellular automaton; numerical simulation; solidification structure;equiaxed grain; columnar grain目 录第一章文献综述 (1)1.1 引言 (1)1.2 凝固组织的形成与控制 (2)1.2.1 铸件的凝固组织 (2)1.2.2 凝固组织的形成及影响因素 (3)1.2.3 凝固组织对铸件性能的影响 (4)1.2.4 凝固组织的控制 (5)1.3 凝固组织模拟的研究方法 (7)1.3.1 确定性方法(Deterministic Method) (7)1.3.2 随机性（概率）方法( Stochastic Method) (8)1.3.3 相场法(Phase field Method) (10)1.3.4 三种方法的对比 (11)1.4 凝固组织数值模拟的国内外研究进展 (12)1.4.1 国外研究 (12)1.4.2 国内研究 (15)1.4.3 存在问题及今后发展趋势 (16)1.5 本文所研究的主要工作 (17)第二章铸件凝固过程宏微观耦合模型 (19)2.1 宏观温度场计算模型 (19)2.1.1 热传递的基本方式 (19)2.1.2 热传导微分方程 (20)2.1.3 瞬态温度场的有限元解法 (21)2.2 微观动力学模型 (23)2.2.1 形核模型 (23)2.2.2 枝晶尖端动力学模型 (26)2.3 耦合计算模型 (29)2.3.1 耦合计算流程 (29)2.3.2 凝固潜热处理 (31)2.3.3 固相分数的确定 (32)2.4 本章小结 (33)第三章数学模型的计算与验证 (34)3.1 实验 (34)3.1.1 实验材料 (34)3.1.2 实验设备 (34)3.1.3 实验步骤 (35)3.1.4 实验结果 (35)3.2 数值模拟过程 (35)3.2.1 网格划分 (35)3.2.2 热物性参数 (35)3.2.3 初始条件 (36)3.2.4 边界条件 (37)3.2.5 生长系数 (37)3.2.6 形核参数 (38)3.3 模拟结果及分析 (38)3.3.1 模拟结果 (38)3.3.2 柱状晶生长 (40)3.3.3 中心等轴晶生长 (42)3.4 本章小结 (43)第四章 AL-SI合金凝固组织的数值模拟与分析 (44)4.1 原始成分对凝固组织的影响 (44)4.2 形核参数对凝固组织的影响 (45)4.2.1 过冷度对凝固组织的影响 (45)4.2.2 形核密度对凝固组织的影响 (46)4.3 浇注条件对凝固组织的影响 (47)4.3.1 浇注温度对凝固组织的影响 (47)4.3.2 外界冷却强度对凝固组织的影响 (49)4.4 铸模对凝固组织的影响 (50)4.4.1 铸模厚度对凝固组织的影响 (50)4.4.2 铸模材料对凝固组织的影响 (52)4.5 本章小结 (53)第五章：结论 (54)参考文献 (55)致谢 (58)附录：发表的论文 (59)第一章文献综述1.1 引言众所周知，决定铸件产品机械性能的最本质因素是铸件内部晶粒在宏观上的几何形态，即铸件的凝固组织结构，包括晶粒的形貌、大小、取向和分布等情况。
DRAFT6-08Sept02 page 1 Simulation of Progressive Cutting on Surface Mesh Model
DRAFT6-08Sept02 page1 Simulation of Progressive Cutting on Surface Mesh ModelHui Zhang, Shahram Payandeh and John DillRobotics and Computer Graphics Laboratories,School of Engineering ScienceSimon Fraser UniversityBurnaby, BC V5A 1S6, Canada{hzhang | shahram | dill}@cs.sfu.caAbstractSurgical simulation is a promising technology for training medical students and surgery planning. An important requirement for such simulation systems is a method to generate realistic cuts through soft tissue models. In this paper, we propose a surface mass-spring model to simulate the virtual cutting operation using an input device such as a haptic device, multi-dimensional joystick, or mouse. We introduce novel algorithms to subdivide the surface and generate interior structures, which follow the motion of the input device. Two types of progressive cutting are supported in our simulator and implementation methods are discussed. Eventually, these cutting techniques will be coupled with a force feedback (haptic) device and be integrated into a training environment for both open surgery and minimally invasive surgery.1. IntroductionVirtual reality has been utilized in many application domains; in medicine the use of virtual environments opens new possibilities in the areas of surgical training and planning. Surgical simulators are currently being developed at many research centers and companies to create environments to help train doctors with new surgical instruments and techniques [12][7]. There are many aspects in developing various surgical procedures.The first challenge for a surgical simulation is that objects must look and behave realistically. Thus models must be based on physical laws governing the dynamic behavior of rigid and deformable objects. The choice between the two commonly used physics-based models, mass-spring model and the finite element method, has long existed. Though finite element method (FEM) offers more accurate modeling than mass-spring models it is computationally more demanding and requires several simplifications for real-time applications. Contrary to standard modeling approaches concerned with fixed mesh topology and which are used in interactions between virtual instrument and object (e.g. probing) cutting modifies the topology of the model significantly. Modification precludes any pre-computation for soft-tissue simulation. In general, simulators utilizing FEM need to introduce considerable simplifications for real-time applications [7] [8] [11]. For example, [1] introduced a novel idea, which maps 3D problem into a 2D auxiliary surface to simplify the FEM calculation. Mass-spring models are widely used in simulation of cutting since it is relatively simple and easy to implement [2] [4] [13] [15].Soft tissue simulation can be implemented utilizing either surface or volumetric models. In general, volumetric models such as tetrahedral model are chosen since they can simulate objects with interior structure. However, topology modification of volumetric models is extremely complex. For example, tetrahedral elements cut by planar surfaces will fall into one of five different topological cases, based on the number of cut edges and intersected faces [3]. Even with the minimal new elements creation method introduced in [11], five to nine new elements arecreated for each cut element. To maintain the model is composed only by tetrahedral after topology modification, one interacted tetrahedral is finally split into 17 new ones [6]. Surface mesh models are relatively easy to manipulate compared to volumetric model. The reason hinder people using surface model is that normal surface model cannot denote object interior structure for cutting results.Less attention has been given to the problem of modifying the topology of deformable models. For example, [11] detailed a method to modify the tetrahedral model simultaneously with instrument movement by introducing a temporary subdivision. Progressive cutting can be denoted in two categories. One meaning is that cuts should occur as the user moves the cutting instrument through the object without lag, as described in [11]. The other is that users may try to follow a specific cutting trail by performing several cuts and join them together. The simulator should allow those separate cuts to be joined together if they are close enough to each other.Therefore, how to implement a realistic simulation of surgical cutting, which is an important component of a typical surgical simulator, is still an open area. In this paper, we propose a new method and model to generate interior structure within a surface mesh model according to the model’s interaction with a cutting instrument. Our simulator can model the two types of progressive cutting we just described. The topology modification method will be described below.This paper is organized as follows: Section 2 explains the notation we use for cutting. Section 3 introduces our surface model. Section 4 describes our simplification for collision detection and collision response. Section 5 details our method of progressive cutting and generating interior structures. Finally, a discussion and suggestions for future work are given in Section 6.2. Conceptual OverviewOur surgical training environment is intended to simulate cutting operations in both open surgery and minimally invasive surgery. There is no difference in the underlying topology modification schemes for these two types of simulation; the differences lie in the cutting instruments used. The parameters of the physics-based models, such as spring constants, can be adjusted to simulate different material properties that the system tries to simulateIn our simulation, a cutting operation is defined as the movement of a cutting instrument while penetrating an object. Two contact states between cutting instrument and object exist. One is when the force exerted on the object by instrument is not big enough to penetrate the surface; we call this a contact state. Here, the instrument deforms the object. In the other state, the cutting instrument has penetrated the object surface, and cutting is allowed, we call this a penetration state.Figure 1: Example of cutting operation.Figure 1 shows an example of part of an object surface model composed of triangles. Once the instrument makes contact with the object, e.g. triangle T1, we deem it as the start of one cut. As the instrument moves, the underlying mesh that represents the object is modified by local subdivision. This subdivision algorithm will be explained in Section 5. Depending on the relative size of the mesh and the instrument size, the instrument path may not be a straight line inside a triangle, e.g. the dashed line in Figure 1; however, we approximate any path within a triangle by a straight line segment connecting the first and the last intersection points in the triangle (solid line). If the instrument is lifted up and loses contact with the object, the algorithm enters the termination state. For example, triangle T7 in Figure 1 is the last triangle that the instrument has contacted. The cutting operation in the example starts at triangle T1, goes through triangles T2…T6 and finally finishes at triangle T7. In this paper, triangles like T1 and T7 are called end triangles, T2…T6are referred to as midway triangles.2.1 Surface Mesh ModelA surface mesh model is relatively simple for calculating both the vertex displacements and topological modification. This is done through solution of differential equations that model the mass-spring system. However, the surface mesh model lacks volume coherency: if the model is put into a gravitational field, it collapses if no modification is added to the model. We use a rigid kernel which represents the initial rest shape of the object [13], and which is used in the mass-spring model to solve for deformed states with respect to this referenceconfiguration.Figure 2: A spring model with rigid kernelIn our model, the simulated surface is divided into small triangles, where each vertex is a mass point (a node).A linear spring is defined along each triangle edge. These springs are called “mesh springs” because they model the surface of the object. When a soft elastic object deforms, the interior of the object also contributes to the shape of deformation. To reflect this fact in our model, each node is also connected by a spring to its initial position, thus the name “home springs”. The initial position is called “home position” (home position and rest shape refer to the same configuration). The set of home positions comprise the rigid kernel of the deformable model, which preserves the object’s shape. We also added damping to the mesh byapplying a force proportional to the velocity of each mass point [10]. Figure 2 shows part of the modeled surface.2.2 Groove GenerationSurface models typically do not represent the interior of a cut. In our model, we propose a novel approach to generate interior surfaces, referred to as a “groove”, which is a function of cutting instrument and object intersection.This topology modification is implemented by surface subdivision and groove generation as explained in the following section. New vertices are added to the initial mesh. These new vertices are connected with vertices of the original mesh and they have home springs connecting them to their initial positions.We have developed algorithms to subdivide the object surface and generate groove triangles as a function of the path of the cutting instrument.3.Collision DetectionCutting instruments come in different shapes and functionalities. As a result, different rendering and collision detection algorithms are needed for determining the state of contact between the tool and the surface.ShaftCauteryTipABCBShaftACDBladeFigure 3: Instrument representation for collision detectionFor the purpose of graphical display, instruments are represented by many triangles that can enhance the realistic graphic rendering of the instrument. For collision detection purposes, the instrument representation is simplified to a small set of straight line segments. Collision detection then reduces to detecting intersections between line segments and triangles.For example, in Figure 3, Line segment AB representsthe shaft of the instrument. If it makes contact with the object, it can deform the object without cutting. The user will be able to feel the reaction force, obtained by solving the surface mesh equation [9], using a haptic device. Line segment AC represents the scalpel blade or cautery tip.Figure 4:Pseudo-code for cutting (including haptic feedback)In the scalpel model, if AC intersects the object surface, the first step is to decide whether the cutting threshold is exceeded. This threshold represents the border between deformation and cutting. The value of the threshold can be tuned experimentally based on real measurements. In our simulation model, the threshold is currently set on the amount of pushing force exerted on the object surface by the instrument. An alternative threshold could be set on surface displacement. Line CD can be used to constrain the movement of the scalpel since only one edge (AC) is considered sharp. This constraint could be conveyed to the user through a haptic force feedback device. The pseudo-code in Figure 4 illustrates this part of the algorithm.Collision detection for a cautery hook is carried out between line segment CD, which is the extension of line segment AC (cautery tip), and the object surface. When the segment CD intersects the object surface, a cut is allowed. D is the virtual tip for the cautery hook. AC here can also act as a "probe" in that it can deform the surface without cutting and the user can feel such deformation if a force feedback device is used. The length of segment CD is proportional to the intensity of the cauterization. Point D is the virtual tip of the cautery hook.In all of the above algorithms, we are assuming that all motions are quasi static, i.e. the instruments move slowly in at the surgical site [12] [13]. Hence, movements of the instruments are assumed to be continuous and smooth so the collision detection can be continued locally with neighboring triangles of the current intersected triangle. Global collision detection is only used to find the first intersection triangle, enhancing system performance.4. Surface subdivision and groove generationWe subdivide surface triangles to simulate the “tearing open” process, i.e. cutting. Due to the nature of the cutting task described in section 2, separate subdivision algorithms are needed for triangles, e.g. end and midway triangles.As shown in Figure 5a, for example, if the instrument path P1P2 (P1 is the initial contact of the instrument with the surface) only intersects one edge of the triangle (ABC), this triangle can be either the start or the end of a cut. This triangle is subdivided into four new triangles; say (ABV1, ACV1, BV1V2, CV1V3) in b, where V1 is at the position of P1 and V2 and V3 are corresponded to P2. Here the newly generated vertices V2 and V3 are coincident where they are connected to the object surface by springs along the edges of the triangle. Though V2 and V3 are initially coincident, spring forces, obtained through solution of the new mesh equations, will move them apart (Figure 5c and d).As mentioned above, since the objects are simulated by a surface mesh, when they are cut, the inside of the cut is not represented, i.e. appears be empty. We have proposed aif (AB intersects one object triangle)if (AC intersects that triangle)check the movement direction of the scalpel;if ( move in the “correct” direction)cut;elsecalculate the force feedback;deform the object;elseif (BD intersects that triangle)AC has totally inside the surface,calculate the force feedback;push AC out of the surface;elsecalculate the force feedback;deform the object with the scalpelelsedo collision detection againmethod to generate a cutting groove in the opening as afunction of the depth of the instrument penetration, see Figure 5c. When intersection of the surface and tip of instrument is below the surface, we use the positions at the start and end of cut inside this triangle (ABC) to define the bottom of the groove (G1G2). In Figure 5, G1 is the corresponding tip position of the instrument when it is at the intersection point P1 and G2 for P2. As a result, we can generate four triangles inside the opening as groove triangles, as (V1V2G1, V1V3G1, G1G2V2, G1G2V3).a)b)Figure 5:Surface subdivision and groove generation for start and end trianglesThe algorithm we just described deals with either the start or the end triangle of a cut. We need another algorithm to subdivide surface triangles and continue the groove generation for midway triangles. If the instrument path intersects two edges (AB and AC in Figure 6a) of a triangle, that triangle must be in the middle of a cutting process.a)b)Figure 6: Surface subdivision and groove generation for midway trianglesAs shown in Figure 6b, triangle ABC is subdivided into three new triangles (A V1V3, V2V4C, BCV4). Only two new vertices (V3 and V4) are created since the other two (V1 and V2) were created by the previous subdivision algorithm. Similar to the previous algorithm, the two new vertices are initially coincident but will move apart later. The bottom of the groove is generated at instrument tip positions (G1 and G2) as before, as are the four groove triangles (V1V3G2, V1G1G2, V2V4G2, V2G1G2). After applying spring forces, the midway triangle will open up with its groove, shown as the final state in Figure 6d.Figure 7 shows a shaded wire frame image of a cut on an ellipsoid.Figure 7: Screen capture illustrating surface subdivision and groove generation5. Progressive CuttingIn cutting through soft tissue, the user expects immediate visual and haptic feedback as the cut processes, and a simulator that supports this progressive cutting is desirable. The first type of progressive cutting is implemented by generating temporary subdivisions within the element that is currently intersected by the instrument. The temporarily generated elements will be replaced by permanent ones when the instrument moves out of that triangle. The second type of progressive cutting, which results in joining two cuts, is implemented by a re-subdivision method. We will explain these two types of progressive next.5.1Progressive cutting with temporary subdivisionWe have devised a method of progressive cutting to split triangle exactly when following cutting instrument motion. If the instrument is inside one triangle, that triangle is subdivided according to the current position of the instrument. However, this subdivision is a temporary since the final expected intersection of the instrument and the triangle is still unknown.The main idea of this progressive cutting is to temporarily subdivide the triangle, which is intersectingthe instrument. As shown in Figure 8, if the instrument goes from triangle T1 to triangle T2, (dashed lines represent the path of the instrument (P1P2P3)), triangle T2 will be subdivided by assuming the cut is in terminated state. See Figure 9a for better understanding. P2 and P2’ are at the same initial position as P2in Figure 8. If the instrument moves within triangle T2, the current topology is maintained and the temporary elements are updated using the new position of the instrument, which results in the new point P3, e.g. Figure 9b.Figure 8:Progressive cutting illustration -1P1P2P3P2'a)P1P2P3P2'b)Figure 9: Example of progressive cutting – 1T3 Figure 10: Progressive cutting illustration -- 2When the instrument goes into another triangle (shown in Figure 10), say triangle T3, triangle T2 will be restored to its original shape before subsequent subdivision. Temporarily generated elements (four new surface triangles and groove triangles) are deleted. The procedure then repeats where for example, triangle T2 is subdivided as a midway triangle, and triangle T3 will repeat the same temporary subdivision process as triangle T2. When the whole cut is completed, i.e. the instrument is pulled out from the object, it generates the last triangle which has already been subdivided as an end triangle and the lastvertex (P 4in Figure 10) is kept as the last intersection point position.An example of this process is shown in Figure 11.P 1P 2P 2'P 3P 3'P 4Figure 11: Example of progressive cutting -- 25.2 Joining two progressive cutsSo far, our subdivision algorithms result in "free form" cuts composed of sequences of straight line segments. We have defined a cutting operation as the movement of the instrument while it is in contact and penetrating the object. However, with the current algorithm, two individual cuts cannot be joined together and it is impossible to form a loop cut if the instrument goes back into the start triangle.3Figure 12: Example of one cut after subdivisionWe now extend our current algorithm to deal with this case. Dashed lines in Figure 12 represent the instrument path of a cut. P 1 is the start point and P 8 is the end point. Each cut has four such end triangles (shown in gray shaded area). If the cutting instrument goes into any existing end triangles, the new cut will join together with the previous cut.As shown in Figure 13, triangle ABC has already been subdivided in previous cut. If the cutting instrument goes into the triangle ABV 1 from edge AB side, AB V 1 issubdivided into two new triangles and vertex V 1 is split into two separate vertices (V 1 and V 1’). Triangles inside the groove also need to be changed to join newly generated groove triangles. The two cuts are then joined together to form a loop cut (Figure 14). Figure 13: Joining two progressive cutsFigure 14: Screen capture of a loop cut6.Conclusions and future workTo simulate progressive cutting of a deformable object we have extended the surface mesh model such that the interior structure of a cut is modeled and can be visualized. The method to subdivide the surface mesh and generate groove topology is novel and efficient compared to the widely utilized volumetric model. We have implemented a simulator that may be useful as part of a surgical training environment. It can be applied to both open surgery and minimally invasive surgery.There are several areas for future work. An immediate task is adding support for generating forces to be used to generate haptic feedback. Our current design is aimed at doing this. A second addition would be the ability to “continue” a cut, i.e. to support performing a series of short, joined cuts, as is often done in real surgical cutting. Other areas include investigating behaviors of other cutting instruments and operation methods and dividing an object into two parts.References[1] Basdogan, C., Ho, C., and Srinivasan, M.A, “Simulation of Tissue Cutting and Bleeding for Laparoscopic Surgery Using Auxiliary Surfaces”, Medicine Meets Virtual Reality. IOS Press, Amsterdam (1999) pp. 38-44.[2] Beisler, D., Gross, M, “Interactive Simulation of Surgical Cuts”, Proceedings of Pacific Graphics, IEEE Computer Society Press, (2000) pp. 116-125.[3] Beisler, D, V.A. Maiwald, and M.H Gross. “Interactive cuts through 3-dimensional soft tissue”, Proceedings of the Eurographics ’99, volume 18, pages C31-C38, 1999[4] Bruyns, C; Montgomery, K, "Generalized Interactions Using Virtual Tools Within the Spring Framework: Cutting", Medicine Meets Virtual Reality (MMVR02), Newport Beach, CA, January 23-26,2001.[5] F.Ganovelli, C.O'Sullivan, "Animating cuts with on-the-fly re-meshing", Eurographics 2001 - short presentations, pp. 243-247.[6] F.Ganovelli, P.Cignoni,C.Montani and R.Scopigno, "Enabling Cuts on Multiresolution Representation" Proceedings of CGI (Computer Graphics International) page. 183-191[7] G. Picinbono, H. Delingette, and N. Ayache, “Improving Realism of a Surgery Simulator: Linear Anisotropic Elasticity, Complex Interactions and Force Extrapolation”. Technical report RR-4018, INRIA, 2000 [8] Han-Wen Nienhuys and A. Frank van der Stappen, “Supporting cuts and finite element deformation in interactive surgery simulation”. Tech Report 2001/16[9] Hui Zhang, “Simulation of Soft Tissue Deformation”, Robotics and Computer Graphics Laboratories, Internal Report, Simon Fraser University, 2002[10] Jian Zhang, Shahram Payandeh, and John Dill, "Haptic Subdivision: An Approach to Defining Level-of-detail in Haptic Rendering", IEEE HAPTICS 2002, Florida, March 2002.[11] Mor, A., Kanade, T, “ Modifying Soft Tissue Models: Progressive Cutting With Minimal New Element Creation”. MICCAI 2000, LNCS 1935, Springer, Berlin Heidelberg, (2000) pp. 598-607.[12] Montgomery, K; Bruyns, C; Brown, J; Thonier, G; Tellier, A; Latombe, JC; "Spring: A General Framework for Collaborative, Real-Time Surgical Simulation", Medicine Meets Virtual Reality (MMVR02), Newport Beach, CA, January 23-26,2001.[13] P. Meseure et C. Chaillou, "Deformable Body simulation with Adaptive Subdivision and Cuttings", Proceedings of the WSCG'97 , Plzen, République Tchèque, 10-14 février 1997, pp 361-370.[14] S. Cotin, H. Delingette, and N. Ayache, “Real-time elastic deformations of soft tissues for surgery simulation”, IEEE Transactions On Visualization and Computer Graphics, January-March 1999,5(1):62--73.[15] Voss, G., Hahn, J.K., Muller, W., Lineman, R.W, “Virtual Cutting of Anatomical Structures”, Medicine Meets Virtual Reality, IOS Press, Amsterdam (1999)pp.381-383.。
Visual Simulation of Smoke译文
虚拟烟雾模拟摘要：在这篇文章中，我们提出一种计算机图形应用领域中新的烟雾数值模拟的方法，即使用非粘性的欧拉方程作为烟雾的物理模型，这是一种稳定、快速并有很少的数值耗散的方法。
相比采用N-S方程的物理方法，它更加适合气体建模，并且计算量要小得多。
此外，我们还引入物理上一致的漩涡限制来保证烟雾在粗糙网格（相比使用更精细的计算流体力学文献中网格）上小尺度特征的模拟，并正确地处理与运动物体相互作用。
关键词：烟雾；计算流体动力学；Navier-Stokes方程；欧拉方程；半拉格朗日方法；稳定流体；漩涡限制；participating media参与媒体Ronald Fedkiw, Jos Stam and Henrik Wann Jensen, "Visual Simulation of Smoke", In SIGGRAPH 2001 Conference Proceedings, Annual Conference Series, August 2001, 15-221.引言：由于气体如烟雾的运动是极其复杂并难以捉摸的，所以模拟自然现象如烟雾等，在计算机图形领域仍然是一个具有挑战性的问题。
可视化的烟雾模型，广泛应用于包括特殊效果和互动游戏等相关行业领域，一个好的模型应该易于使用和生成并且具有很强的现实意义。
很显然，烟雾和气体的造型在其它工程领域也是非常重要的。
更普遍地讲，计算流体动力学广泛应用于气体和其他液体，例如水的模拟。
可直到最近，计算机图形学的研究人员才开始从大量的CFD文献中挖掘可以用于或修改计算机图形应用的方法。
不幸的是，目前的烟雾模型不是太缓慢，就是受到过多的数值耗散。
在本文中，我们采用CFD文献中有关气体如烟雾的动画仿真技术，提出了一种稳定、快速且没有过多数值耗散的模型，它使用了一种相对粗糙的网格，来生成复杂的滚动烟雾动画。
1.1 以往工作在过去的二十年里，烟雾及其它气体现象的建模，在计算机图形领域一直受到广泛关注。
The “Simulation Thing”“模拟物”
Particle Simulations
Particle Simulations
These particles can represent different entities depending on the simulation. This could be:
atoms molecules dust particles snooker balls asteroids planets galaxies
Particle Simulations
Once a collision has been detected the system must respond to the collision. For our hockey pucks, simply reverse the velocity in the direction of the collision.
Particle Simulations
• main loop – for all particles • ‘move’ particle • if ‘collision’ with boundary – respond to collision – for all particles • for all other particles – if ‘collision’ between particles » respond to collision
Particle Simulations
Second Law: The acceleration a of a body is parallel and directly proportional to the net force F acting on the body, is in the direction of the net force, and is inversely propotional to the mass m of the body.
219463770_基于运动轨迹和径向距离的高炉料面堆积形状建模方法
基于运动轨迹和径向距离的高炉料面堆积形状建模方法蒋朝辉 1, 2周 科 1桂卫华 1, 2曹 婷 2潘 冬 1朱既承1摘 要 高炉料面形貌是反映煤气流分布和煤气利用率的关键指标, 研究高炉料面炉料堆积形状数学建模方法对实现高炉精准布料控制和“双碳”战略在钢铁行业落地具有重要意义. 针对高炉多环布料情况下料面堆积形状预测难的问题, 本文提出了一种基于炉料运动轨迹和径向移动距离的高炉料面炉料堆积形状建模方法. 首先, 提出了一种与炉料初始状态和溜槽状态相关的炉料运动轨迹建模方法, 获取炉料从节流阀至料面的炉料运动轨迹, 并确定炉料在炉喉空区的内轨迹曲线和外轨迹曲线. 然后, 基于炉料运动轨迹和初始料面形状, 以体积守恒原则为约束, 提出了一种基于炉料径向移动距离的高炉料面炉料堆积形状数学建模方法, 获取炉料在料面的堆积形状. 最后, 基于某钢铁厂2# 高炉的尺寸建立离散单元法 (Dis-crete element method, DEM) 仿真模型, 模型仿真结果验证了所提方法的准确性和有效性.关键词 高炉料面, 数学建模, 运动轨迹, 径向距离, 堆积形状, 离散单元法引用格式 蒋朝辉, 周科, 桂卫华, 曹婷, 潘冬, 朱既承. 基于运动轨迹和径向距离的高炉料面堆积形状建模方法. 自动化学报,2023, 49(6): 1155−1169DOI 10.16383/j.aas.c220768A Modeling Method of Blast Furnace Burden Surface Accumulation ShapeBased on the Motion Trajectory and Radial DistanceJIANG Zhao-Hui 1, 2 ZHOU Ke 1 GUI Wei-Hua 1, 2 CAO Ting 2 PAN Dong 1 ZHU Ji-Cheng 1Abstract The blast furnace burden surface is the key index to reflect the distribution of gas flow and the utiliza-tion rate of gas. Studying the mathematical modeling method of burden flow accumulation shape on the blast fur-nace burden surface is of great significance to realize the precise charging control and the implementation of “dual carbon” strategy in the steel industry. Aiming at the difficulty of predicting the burden flow accumulation shape in the blast furnace multi-ring charging, a modeling method for the accumulation shape of the burden flow on the blast furnace burden surface based on the burden flow motion trajectory and radial movement distance is proposed.Firstly, a modeling method of burden flow motion trajectory relate to the burden flow state and chute state is pro-posed to obtain the motion trajectory of burden flow from throttle valve to the burden surface, and further determ-ine the internal and external trajectory of burden flow in the blast throat. Secondly, a mathematical modeling meth-od of burden flow accumulation on the blast furnace burden surface based on the radial moving distance is pro-posed to obtain the accumulation shape of burden flow on the burden surface according to the motion trajectory,initial shape of burden surface, and the principle of volume conservation. Finally, a discrete element method (DEM)simulation model is established based on the 2# blast furnace of a steel plant, and the simulation results verify the accuracy and effectiveness of the proposed method.Key words Blast furnace burden surface, mathematical model, motion trajectory, radial distance, accumulation shape, discrete element method (DEM)Citation Jiang Zhao-Hui, Zhou Ke, Gui Wei-Hua, Cao Ting, Pan Dong, Zhu Ji-Cheng. A modeling method of blast furnace burden surface accumulation shape based on the motion trajectory and radial distance. Acta Automat-ica Sinica , 2023, 49(6): 1155−1169钢铁工业是国民经济的重要基础产业, 是国家工业发展的重要支柱产业, 也是衡量国家经济水平和综合国力的重要标志. 高炉炼铁是钢铁工业中的上游核心工序, 其炼铁产量占世界生铁产量的95%收稿日期 2022-10-04 录用日期 2023-02-10Manuscript received October 4, 2022; accepted February 10,2023国家重大科研仪器研制项目(61927803), 国家自然科学基金基础科学中心项目(61988101), 湖南省科技创新计划(2021RC4054), 国家自然科学基金青年基金(62103206), 中国博士后科学基金(2021M701804)资助Supported by National Major Scientific Research Equipment of China (61927803), National Natural Science Foundation of China Basic Science Center Project (61988101), Science and Techno-logy Innovation Program of Hunan Province (2021RC4054), Na-tional Natural Science Foundation for Young Scholars of China (62103206), and Postdoctoral Science Foundation of China (2021M701804)本文责任编委 董峰Recommended by Associate Editor DONG Feng1. 中南大学自动化学院 长沙 4100832. 鹏城实验室 深圳5180001. School of Automation, Central South University, Changsha 4100832. Peng Cheng Laboratory, Shenzhen 518000第 49 卷 第 6 期自 动 化 学 报Vol. 49, No. 62023 年 6 月ACTA AUTOMATICA SINICAJune, 2023以上, 是钢铁制造过程中能耗最大、CO2排放最多和成本最高的环节[1−2]. 炉料在高炉料面的堆积形状是判断煤气流分布是否合理、及时发现异常情况的关键指标, 而高炉布料制度直接决定了炉料在高炉料面的堆积形状. 因此, 研究高炉料面炉料堆积形状数学建模方法对实现高炉精准布料控制和“双碳”战略在钢铁行业中落地具有重要意义.当前料面形状建模主要有基于实体模型的比例模型实验法、基于数值计算的离散单元法(Discrete element method, DEM)和基于物料运动规律的机理模型法. 比例模型实验法是以实体高炉为参考,搭建等比例或缩比例的物理模型, 模拟高炉布料全过程, 并安装高精度检测设备获取料流运动轨迹和料面堆积形状. 例如, Jimenez等[3]用1/10的比例高炉测试布料模式和煤气流对炉料分布的影响. Mitra 等[4]用多段折线描述料面堆积轮廓, 并在1/10的高炉模型中进行验证. Kajiwara等[5]使用等比例模型研究高炉布料全流程, 发现高炉料面混合层的存在,并基于实验结果建立高炉布料仿真模型. 比例模型实验法能够直接观察炉料运动状态及料面堆积形状, 但模型费用高、实施过程繁琐、数据精度难保证, 该方法难以作为一种常规研究方法为研究者提供帮助.DEM以数值仿真软件为基础, 设定高炉布料初始条件, 仿真分析高炉布料运动过程. 随着计算机性能的增强, 国内外研究学者采用DEM对高炉炉顶炉料运动进行了大量的研究, 包括高炉布料操作参数[6−9]、旋转溜槽形状[10−12]、颗粒属性[13−15]等对炉料运动速度的影响. 此外, 诸多学者将比例模型实验法和DEM结合进行了大量相关研究. 例如, Mio 等[16]使用高速相机记录1/3比例模型的高炉布料行为, 并与DEM仿真结果进行对比, 验证了DEM仿真预测粒子运动轨迹具有较高的可靠性. Wei等[17]基于DEM研究了粒子滚动系数和摩擦系数对炉料堆积休止角的影响, 并利用比例模型实验确定了DEM 仿真中粒子的摩擦系数. Holzinger等[18]基于DEM 研究了溜槽起始倾斜角度和旋转方向对布料过程料面堆积料层的质量分数的影响, 并用工业生产温度数据进行了验证. Yu等[19]将物理试验和DEM结合, 研究了高炉炉顶料流运动轨迹及料面堆积轮廓的形成, 发现焦炭在下落轨迹与料面的交汇处堆积,而球团则向高炉中心运动. Mitra等[20−21]使用1/10比例模型和DEM研究了高炉料面焦炭的塌陷和混合层的形成, 并定量评估了焦炭的混合和塌陷程度. DEM不仅能很容易获取粒子的空间运动状态, 还具有较高的精度, 获得了大量研究者的青睐, 被广泛应用于实验室环境仿真高炉冶炼, 但因其计算时间长、对计算机性能要求高, 难以应用于工业现场.机理模型法是通过物料的受力情况分析炉料运动轨迹及炉料在料面的堆积形状. Radhakrish-nan等[22]提出了一种二维数学模型来描述高炉顶部料流的运动轨迹和料面堆积形状. 朱清天等[23]在考虑煤气流的情况下建立料流运动轨迹模型, 为实现布料控制奠定了基础. 杜鹏宇等[24]在建立料流运动数学模型时重点考虑了炉料受力变化对料流宽度的影响, 进而建立了无钟炉顶布料的料流宽度数学模型. Fu等[25]建立了料面分布数学模型, 并考虑了料面下降对料面分布的影响. 张森等[26]提出了一种基于雷达数据和机理模型双驱动的高炉料面形状建模方法, 用一条概率分布的带来描述高炉料面形状. Fojtik等[27]根据料流落点位置、颗粒半径和最大休止角确定内外堆积角度, 并通过大量实验来确定修正系数, 进而确定料面堆积形状. Nag等[28]基于激光检测仪获取料线高度, 提出了一种正态分布函数来描述料面堆积轮廓, 并基于体积守恒原则确定正态分布曲线的参数. Li等[29]以料流运动轨迹模型为基础, 并基于炉料运动散射距离建立料面轮廓模型,进而开发高炉布料模型.前人的研究对高炉高效冶炼做出了巨大的贡献, 但仍存在一些问题需要解决: 1) 所建炉料运动轨迹模型仅能获取单质点的运动轨迹, 难以确定料流在料面的落点宽度; 2) 料面堆积形状建模需要通过大量实验获取散射距离, 忽视了炉料运动速度与料面堆积形状之间的关系. 因此, 本文提出了一种基于炉料运动轨迹和径向移动距离的高炉料面炉料堆积形状建模方法.本文的主要贡献是:1)提出了一种基于坐标变换的炉料运动轨迹建模方法. 该方法分别计算节流阀不同位置处炉料颗粒在高炉炉顶的运动轨迹, 形成料流运动轨迹集合, 并找出料流运动轨迹在炉喉空区的内轨迹与外轨迹以进一步计算料面堆积形状. 在计算炉料在溜槽上滑动的初始运动速度时充分考虑碰撞位置和炉料碰撞前的速度, 以此求解炉料与溜槽碰撞后的三维运动速度. 同时, 利用绝对运动与相对运动和牵连运动之间的关系, 将炉料在溜槽上的运动分析从静坐标系转移到与溜槽一同旋转的动坐标系中, 减小炉料在旋转溜槽上运动建模的复杂程度.2)提出了一种基于径向移动距离的炉料堆积形状建模方法. 以炉料在炉喉空区的内外轨迹和运动速度为基础, 计算炉料在料面的落点位置以及炉料落到料面后的最大径向移动距离, 并以体积守恒原则为约束建立料面堆积形状描述方法, 实现高炉多环布料时的料面堆积形状预测.1156自 动 化 学 报49 卷1 基于坐标变换的炉料运动轨迹建模高炉布料过程实际上是炉料颗粒从节流阀流出经中心喉管、旋转溜槽、炉喉空区落到料面, 堆积形成新的料面形状的运动过程, 如图1所示. 为简化数学模型, 炉料运动过程机理建模时做出以下假设[22]:1) 炉料颗粒离开节流阀时的水平速度分量为零;2) 炉料颗粒只有质量, 没有形状大小; 3) 高炉布料过程中炉料颗粒之间互不影响; 4) 炉料在溜槽上运动时始终在溜槽上滑动且不存在滚动摩擦力; 5) 炉料在料面运动中其摩擦系数保持不变, 且只存在滑动摩擦.称量料罐节流阀中心喉管旋转溜槽高炉料面炉喉空区图 1 高炉炉顶炉料运动过程示意图Fig. 1 Schematic diagram of the moving process ofburden flow on the blast furnace top1.1 坐标变换方法n 高炉布料过程中料流由 个初始速度相同、初OXY Z Z βY r γO ′X ′Y ′Z ′始位置不同的小颗粒组成. 因此, 不同位置的颗粒离开节流阀时的运动轨迹不同, 为快速计算不同初始位置炉料在高炉炉顶的运动轨迹, 建立相对高炉静止的静坐标系和与溜槽一同旋转的动坐标系, 如图2所示. 溜槽运动过程中, 溜槽到达的任意位置均可由溜槽初始位置经两次旋转到达. 围绕静坐标系 的 轴旋转角度 , 得到过度旋转坐标系;再绕过度旋转坐标系的 轴旋转角度 即可得到溜槽当前的位置, 即动坐标系 . 颗粒在静坐标系和动坐标系之间的位置关系为(x,y,z )(x ′,y ′,z ′)其中 为颗粒在静坐标系中的位置; 为颗粒在动坐标系中的位置.1.2 炉料运动轨迹建模n 炉料运动过程机理建模分为5个部分: 炉料离开节流阀、炉料在中心喉管自由下落、炉料与溜槽发生碰撞、炉料在旋转溜槽上运动、炉料在炉喉空区运动. 本节对料流运动过程进行力学分析, 建立炉料到达料面的运动轨迹数学模型,并根据 个炉料颗粒的运动轨迹集合确定料流在炉喉空区的内轨迹曲线和外轨迹曲线.1.2.1 节流阀排料模型节流阀是高炉炉顶布料操作的关键设备之一,(a) 整体示意图(a) Overall schematic(b) 绕 Z 轴旋转(b) Rotate around the Z -axis(c) 绕 Y r 轴旋转(c) Rotate around the Y r -axisY r图 2 坐标变换过程示意图Fig. 2 Schematic diagram of the coordinate transformation process6 期蒋朝辉等: 基于运动轨迹和径向距离的高炉料面堆积形状建模方法1157v 0是调节排料速度和排料时间的唯一手段. 炉料离开节流阀时的速度可以通过水力学连续性方程计算,炉料离开节流阀时的位置和速度可以表示为Q ρS L s d x 0,y 0,h a 其中 为料流质量流量, 单位为kg/s; 为炉料的堆积密度, 单位为kg/m 3; 为料流在节流阀处的流通面积, 单位为m 2; 为节流阀打开长度, 单位为m; 为炉料的平均直径, 单位为m. 分别表示炉料离开节流阀时在静坐标系中的三维空间位置.1.2.2 炉料在中心喉管下落模型炉料离开节流阀后进入中心喉管, 在重力的作用下做自由落体运动, 则炉料落到溜槽前其运动速度表示为g h w β0γ0h w 其中 为重力加速度, 单位为m/s 2; 为溜槽悬挂点到炉料与溜槽接触时的有效高度, 单位为m. 假设炉料从节流阀开始运动至到达溜槽表面, 溜槽水平旋转了 , 倾斜了 , 则 可以表示为e θ0R 其中 为溜槽倾动距, 单位为m; 为炉料落到溜槽上时在溜槽上的偏析角度, 单位为 °; 为溜槽半径, 单位为m. 则炉料与溜槽碰撞前的位置和速度在动坐标系中表示为r ′1v ′1其中 和 分别表示炉料与溜槽碰撞前在动坐标系中的位置和速度.1.2.3 炉料与溜槽碰撞模型n 炉料与溜槽碰撞后存在速度损失, 且速度损失可以分解为法向速度损失和切向速度损失. 图3显示了炉料与溜槽碰撞前后的入射速度与出射速度之间的关系, 其中 为碰撞点的法向量, 由碰撞点的位置直接决定, 表示为f (·)θint 其中 为溜槽曲面表达式. 为入射速度与法向量之间的夹角, 与入射速度和碰撞点法向量相关,表示为v ′2=[v ′2,x ,v ′2,y ,v ′2,z ]T当炉料与溜槽碰撞时入射速度和碰撞点均已求出, 即法向量和入射角度可求出. 角 为待求出射速度, 表示为θout为炉料与溜槽碰撞后出射速度与碰撞点法向量之间的夹角, 出射角与出射速度和法向量之间的关系表示为根据图3的几何关系可得e n e t 其中 为炉料与溜槽的法向碰撞恢复系数, 与碰撞物的材质有关, 为定值. 为炉料与溜槽碰撞的切向恢复系数, 与碰撞物的材质及碰撞时的入射角相关, 表示为θout 根据式(10)可以求出炉料与溜槽碰撞后的出射角 为1图 3 炉料与溜槽碰撞前后速度关系示意图Fig. 3 Schematic diagram of the velocity relationshipbetween the burden flow and chute collision1158自 动 化 学 报49 卷()进一步可以求出炉料与溜槽碰撞后的速度大小同时, 炉料与溜槽碰撞前后的速度以及碰撞点的法向量符合共面性质, 即出射速度可以表示为a b 其中 和 为常数. 将式(14)展开表示为a b v ′2,x v ′2,y v ′2,z v ′2联立式(8)、(9)和(15)可分别求出 、 、 、 和 , 即可求出颗粒与溜槽碰撞后的出射速度 .1.2.4 炉料在溜槽上滑动模型炉料在旋转溜槽上运动时受到重力、支持力、摩擦力、科氏力等的作用, 在动坐标系内分析炉料的受力情况有助于减少分析复杂程度, 能简单、快速解出炉料在溜槽上的运动轨迹.在动坐标系中, 颗粒相对溜槽的位置如图4所示. 炉料在溜槽内的相对位置、速度和加速度分别表示为[30]θY ′其中 为颗粒在溜槽上的偏析角, 规定颗粒在 负轴时为正值.在溜槽上与颗粒接触的点为牵连点, 牵连点的位置、速度和加速度分别为ωa a r a e a c 其中 为溜槽的角速度, 为溜槽的角加速度. 溜槽旋转时, 炉料的绝对加速度为相对加速度 、牵连加速度 和科氏加速度 之和, 表示为a c =2ω×v r G ′F ′N F ′f 其中 , 为科氏加速度. 在动坐标系中,炉料受到重力、支持力和摩擦力 的作用,分别表示为F N µ其中 为颗粒受到支持力大小, 单位为N; 为颗粒与溜槽的摩擦系数. 则颗粒在溜槽上受到的合力为(a) 整体示意图(a) Overall schematic (b) O ′X ′Z ′ 截面(b) O ′X ′Z ′ section(c) O ′Y ′Z ′ 截面(c) O ′Y ′Z ′ section图 4 炉料在溜槽上位置示意图Fig. 4 Schematic diagram of the positionof the burden flow on the chute6 期蒋朝辉等: 基于运动轨迹和径向距离的高炉料面堆积形状建模方法1159结合牛顿第二定律, 联立式(18)和(20)并进行化简, 得到r 3v 3Runge-Kutta 算法是一种求解微分方程使用最广泛、最有效的方法之一, 利用计算机仿真求解时可以省去求解微分方程的复杂过程[31]. 调用MAT-LAB 软件中的ode45函数迭代求解炉料在溜槽上运动不同时刻的位置、速度和加速度. 则炉料离开溜槽末端时在静坐标系中的位置 和速度 可以表示为β1γ1r ′3v ′3其中 和 分别表示炉料颗粒到达溜槽末端时, 相对离开节流阀水平旋转的角度和倾斜的角度. 和 分别表示在动坐标系中炉料在溜槽末端的位置和速度.1.2.5 炉料在炉喉空区斜抛模型X Y Z 炉料离开溜槽后, 在炉喉空区受到重力和煤气阻力的影响. 若在炉喉空区只考虑重力对炉料运动轨迹的影响, 则炉料在 轴和 轴做匀速运动, 在 轴做匀加速运动, 则炉料在空区的运动轨迹表示为v 3,x v 3,y v 3,z x 3y 3z 3其中 、 和 表示炉料离开溜槽末端时的三维空间速度; 、 和 表示炉料离开溜槽末端t 时的三维空间位置; 表示炉料从溜槽末端到料面的运行时间, 由炉料离开溜槽末端时的位置和速度以及料面高度直接决定.在多环布料中, 假设料面形状对称, 布料操作所形成的料流落点也对称, 因此, 可以用炉料在炉喉的径向移动距离和落点高度表示炉料落点位置,表示为S r S z Z 其中 和 分别表示炉料的径向移动距离和 轴移动距离.Z v 4,z OXY v 4,p OXY v 4,r v 4,n OXY OP θ3炉料落到料面后的速度可以分解为 轴速度 和 平面速度 , 其中 平面速度又可以分解为径向速度和切向速度 . 图5显示了炉料在炉喉水截面的速度分布几何关系, 根据几何关系可以求出 平面速度与 之间的夹角 , 表示为P 4Z 则炉料在落点 处的 轴速度、径向速度和切向速度分别表示为v 4,r 根据炉料在落点处的径向速度 可以求出炉料在料面处的最大径向移动距离.图 5 炉料在料面落点位置和速度分布示意图Fig. 5 Schematic diagram of the position and velocity distribution of the burden flow on the burden surface1160自 动 化 学 报49 卷1.2.6 炉料在炉喉空区内外轨迹模型n f int f out 节流阀不同位置处的炉料在高炉炉顶形成不同的运动轨迹, 根据第1.2.1 ~ 1.2.5节求出 个颗粒在高炉炉顶的运动轨迹集, 并确定炉喉空区中距离高炉中心轴最近的轨迹为内轨迹 , 距离高炉炉壁最近的轨迹为外轨迹 .2 基于径向移动距离的料面堆积形状建模炉料离开溜槽落到料面后堆积形成料面形状.料面形状可以采用高斯分布[28]、两段直线[32]、两段直线和一段曲线[33]等方法描述. 为了简化模型, 本文采用两段直线方法描述料面堆积形状. 根据物料堆积特性, 当物料自由堆积时形成圆锥形状, 即堆积的截面为等腰三角形. 高炉布料时在料面的堆积截面也可看作三角形, 但由于炉料落到料面时存在径向速度, 即炉料会向炉墙方向移动一段距离, 因此,炉料的外堆角比内堆角小.2.1 等体积原则基于质量守恒原理, 离开节流阀的炉料质量与堆积在料面的炉料质量相同. 为更好研究基于高炉布料矩阵的料面堆积形状, 作出如下假设: 1) 炉料堆积过程中堆积密度保持不变; 2) 同一节流阀开度下炉料经过节流阀的流量恒定; 3) 高炉布料过程中溜槽旋转的圈数为整数, 即保证炉料在料面堆积形状高度对称. 则高炉布料的实际体积为Q ∆t ρ其中 为炉料离开节流阀的质量流量, 单位为kg/s; 为炉料经过节流阀的时间, 单位为s; 为炉料在称量料罐和料面的堆积密度, 单位为kg/m 3.则高炉布料操作完成后, 炉料在料面的堆积体积为f b 1(r )f b 0(r )R f 其中 为布料结束后料面形状, 为布料开始前料面形状, 为炉喉半径. 根据体积守恒原则, 料面堆积炉料的体积与离开节流阀的炉料体积应一致, 即η式中 为允许的误差范围, 本文为2.5%.2.2 料面堆积形状建模f b 0(r )f int (r )f out (r )S 0Q 0O ′′R ′′Z ′′R ′′OXY Z X Y R ′′=√X 2+Y 2Z ′′Z 高炉料面对称时, 料面形状可以用料面径向轮廓表示. 炉料堆积过程如图6所示. 图6(a)展示了炉料在料面的堆积过程, 原始料面函数表示为, 料流内轨迹函数为 , 料流外轨迹函数为 , 料流内轨迹和外轨迹分别与初始料面相较于点 和 . 在炉喉建立局部二维坐标系, 径向坐标系的原点与静坐标系的原点重合; 径向坐标系的 轴为静坐标系 的 轴和 轴的二维范数, 即 ; 径向坐标系的 轴为静坐标系的 轴. 图6(b)和6(c)分别展示了炉料未到达炉壁和到达炉壁的两种料面堆积示意图.φint φmax S (r s ,z s )φint g int (r )炉料落到料面后在内外轨迹间开始堆积, 形成料面, 当内堆积角 小于最大自然堆角 时,炉料从 点开始堆积, 且内堆角 逐渐增大, 则内堆积直线 表示为g int (r )f out (r )联立 和 可求解内堆直线与料流f (r )f b 0(r )S 0Q 0f out (r)高炉中心高炉中心(a) 炉料堆积(a) Accumulation(b) 炉料未到达炉壁(b) The burden flow can not reachthe wall(c) 炉料到达炉壁(c) The burden flow reach the wall图 6 炉料堆积过程示意图Fig. 6 Schematic diagram of burden flow accumulation6 期蒋朝辉等: 基于运动轨迹和径向距离的高炉料面堆积形状建模方法1161Q (r Q ,z Q )Q T QT 外轨迹函数的交点 . 炉料落到料面后, 因存在径向移动速度而会向右继续移动, 直到径向移动速度为零. 设 点的炉料会移动到位置 , 则 之间的距离表示为v Q,r Q v 4,r µ1η2∈(0,1]其中 为 点的径向移动速度, 可根据式(26)中的 计算获取; 为炉料与料面的摩擦系数,与原始料面粒子属性和当前布料炉料属性有关;, 为径向移动距离修正系数. 则炉料到达的最远位置为r max ≤R f T 若 , 即炉料未到达炉壁, 如图6(b)所示, 点的位置表示为QT g out (r )直线 所形成的直线为外堆角直线 表示为r max >R f 若 , 即炉料到达高炉炉壁时其径向移动速度还不为零, 则炉料开始纵向堆积, 如图6(c).此时修正外堆角直线, 表示为T 点的位置表示为g int (r )g out (r )f b 0(r )函数 、 和 包围的形状即为二维径向坐标系中的炉料堆积形状.Q 当内堆积角度达到最大自然堆角所形成的料面堆积形状仍然不满足体积守恒原则, 则堆积过程中内堆角为最大自然堆积角度, 且 点将会向左移进行炉料堆积.2.3 料面堆积形状求解过程V cal V act 根据料流运动轨迹可以确定料流在料面的落点范围, 再根据炉料在料面落点处的径向移动速度即可求出料流在料面的最大径向移动距离, 进而可以求出炉料在料面的堆积区域及堆积形状. 进一步的,根据体积约束原则, 使得新料面形状与原始料面形状之间的堆积体积 与离开节流阀的炉料体积 在误差范围内, 即可求出布料完成后的新料面形状, 主要流程如图7所示, 具体步骤说明如下:f b 0(r )i =1步骤 1. 初始化. 设置高炉参数, 包括中心喉管高度、溜槽倾动距、溜槽长度等几何参数; 炉料属性, 包括炉料与溜槽的摩擦系数、炉料与溜槽碰撞的法向恢复系数等; 高炉布料参数, 包括节流阀开度、溜槽旋转速度和溜槽倾斜角度等; 初始料面形状 ; .f int (r )f out (r )S i Q i 步骤 2. 确定炉料运动轨迹及炉料落点位置. 根据第2.2节的炉料运动轨迹模型计算出节流阀不同位置处炉料在高炉炉顶的运动轨迹, 并求出在炉喉空区最靠近中心的内轨迹曲线函数 和最靠近炉墙的外轨迹曲线函数 ; 同时计算内轨迹曲线函数与料面轮廓函数的交点 和外轨迹曲线函数与料面轮廓函数的交点 .T i Q i D i T i 步骤 3. 计算料面轮廓最远点 . 根据外轨迹曲线计算炉料在料面落点位置的径向移动速度, 并根据式(31)计算 在料面的最远移动距离 , 进而根据式(32) ~ (36)计算堆积形状最远点 的位置.S i Q i T i V cal S i Q i Q i T i S i Q i T i V cal 步骤 4. 确定料面堆积轮廓 , 计算料面堆积体积 . 以 所形成的直线为内堆直线, 内堆直线与水平面所形成的夹角为内堆角; 所形成的直线为外堆直线, 外堆直线与水平面所形成的夹角为外堆角; 为料面堆积轮廓. 根据料面堆积轮廓和初始料面形状计算料面堆积体积 .|V cal −V act |/V act <η步骤 5. 判断布料是否结束. 判断当前料面堆积体积与实际布料体积的绝对误差百分比, 若 , 则转到步骤11, 否则转到步骤6.|φint,i −φmax |≥1◦步骤 6. 判断内堆角是否需要更新. 若 , 则转到步骤7, 否则转到步骤10.φint,i <φmax −1◦步骤 7. 更新内堆角. 若 , 则转到步骤8, 否则转到步骤9.Q i i =i +1φint,i =φint,i −1+1◦S i S i Q i 步骤 8. 更新 . , , 保证 的位置不变, 根据 的位置和内堆角计算内堆积直线函数, 更新 , 使其为内堆角直线与外轨迹曲线函数的交点坐标; 转到步骤3.i =i +1φint,i =φint,i −1−1◦Q i Q i S i 步骤 9. 更新 , ,保证 的位置不变, 根据 的位置和内堆角计算内堆积直线函数, 计算内堆积直线与料面的交点 ;转到步骤3.S i Q i φint,i =φint,i −1Q ir Q,i =r Q,i −1−∆r Q i Z Q i Q i S i 步骤 10. 更新 和 . , 令 的径向坐标为 , 根据外轨迹曲线计算此时 的 轴坐标, 更新 ; 根据 的位置和内堆角更新内堆积直线函数, 更新 , 使其为内堆角直线与料面轮廓函数的交点坐标; 转到步骤3.步骤 11. 输出料面轮廓, 结束.通过上述步骤, 可以获取单环布料时的料面堆积形状. 改变布料操作参数, 并重复步骤1 ~ 11, 即1162自 动 化 学 报49 卷。
HyperWorks OPSTRUCT 材料简单整理
注：
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材料说明 | 2015/12/1
Poisson’s ratio ( for uniaxial loading in 1-direction). Note that for uniaxial loading in 2-direction is related to by the relation
.
No default (Real)
注：
O P S T R U C T 材料说明 | 2015/12/1
2015/12/1
T)之间的关系：
参考应变率. 默认为0，若 DESPS < DESPS0,则无应变率作用。
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➢ 它是在温度和应变率作用下的弹塑性法则，遵守以下法则：
➢ 若塑性应变到达最大值EPSMAX ，壳单元被删除，实体单元不被删除，但是应力被置为0； ➢ IIC 控制应变率作用。
➢ ROD 单元不考虑应变率作用
➢温度影响：
P S T R U C T 材料说明 | 2015/12/➢ 空气压力计算公式
其中，体积应变；
Φ 多孔性, P 0 是初始空气压力，
是初始体积应变； < 0 时为压缩。
➢ 若TID 为空或者0，有σy = A + B(1+ C γ), with = V/V0 - 1 = ρ/ρ0 - 1 = -μ/(1+μ)
➢ 若TID 定义了，则σy vs. is 数据来自TID ；
➢
杨氏模量计算公式为E = max(E, E 1 + E 2)
Piece-wise Linear Elastic-plastic。
托福阅读tpo60R-1原文+译文+题目+答案+背景知识
TPO60 阅读-1 Underground Life原文 (1)译文 (2)题目 (3)答案 (7)背景知识 (7)原文Underground Life①Until about the late 1980s, most scientists believed that life was restricted to the top few meters of the soil or ocean sediments. The few reports of organisms being recovered from great depths within Earth were dismissed as contamination with material from the surface layers. Two technical developments changed this view. The first was the development of drilling techniques that gave confidence that samples could be retrieved from depth without contamination. Samples were recovered using a diamond-studded drill bit that headed a great length of rotating steel pipe from a drilling derrick. A concentrated tracer material was added to the lubricating fluid so that when a deep sample of rock was removed, any contaminated material could be identified and cut away to leave a pristine sample of rock from deep within Earth. The second development was the advent of techniques for identifying microorganisms without having to grow them in culture. All organisms contain DNA, and their presence can be revealed by dyes that either stain DNA directly or can be attached to nucleic acid probes. By varying the nucleic acid probe, scientists can demonstrate the presence of different types of microorganisms.②The first scientists to use these techniques were involved in the Subsurface Science Program of the United States Department of Energy (DOE). They were interested in the possibility that if organisms existed in the depths of Earth, they might degrade organic pollutants and help maintain the purity of groundwater or, rather less usefully, degrade the containers in which the DOE was proposing to deposit the radioactive waste from nuclear facilities. They demonstrated the presence of many different types of microorganisms in rocks at depths down to 500 meters beneath the surface. Since then, microbes have been discovered in many different types of rocks and deep within ocean sediments. The record depth at which life has been found is at the bottom of a South African gold mine, 3.5 kilometers below ground. Pressure and temperature increase as you go deeperinto Earth. Some scientists think that subsurface bacteria could withstand temperatures as high as 150℃. This would allow organisms to exist to depths of about 7 kilometers beneath the seafloor and to 4 kilometers below the surface of the land. Although the organisms are often sparsely distributed, this is such an enormous volume that it has been estimated that the total biomass of deep subsurface organisms exceeds that of those living on, or just below, the surface.③Bacteria are the most numerous of these subsurface organisms, but there are also fungi and protozoa. Some 10,000 strains of microorganism have been isolated from subsurface cores. Each gram of rock contains anything from 100 bacteria to 10 million bacteria(compared with more than 1 billion per gram in agricultural soils); ocean sediments contain even higher numbers. The protozoa feed on the bacteria, forming part of a simple subterranean food chain, but what do the bacteria feed on? Sedimentary rocks are formed from sands and from ocean, river, or lake sediments that have organic material trapped within them. Microbes living in pores within the sediments can utilize these ancient nutrients and grow. As sedimentary rocks are buried more deeply, they become increasingly compacted and their pores filled with minerals. The distribution of microorganisms is thus likely to become more patchy, condensed into the remaining pores and concentrations of nutrients. The bulk of Earth's crust, however, consists of igneous rocks, such as granite and basalt, which are solidified from molten magma. These rocks were too hot to support life when they were first formed; the organisms that inhabit cracks and fissures within the rocks are carried there by the groundwater flowing through them. Subsurface bacteria do not just rely on nutrients trapped within the rock or carried there by groundwater. Some are chemotrophs, deriving their energy from the oxidation of iron or sulfur compounds and building organic material directly from the carbon dioxide and hydrogen gas dissolved in the rock. These bacteria excrete organic compounds that are then utilized by other types of bacteria. These ecosystems based on chemotrophic bacteria are completely independent of material and solar energy from the surface.译文地下生活①直到大约20世纪80年代末，大多数科学家仍认为生命仅限于土壤或海洋沉积物的顶部几米。
The use of visco-elastoplastic damage constitutive model to simulate nonlinear behavior of concrete
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ACTA MECHANICA SOLIDA SINICA
2011
angle effect, etc. (3) The damage surface built mostly by stress or strain type, is only for calculating the elastic energy release rate without the proper consideration of the plastic part even though the energy release type calculation is adopted. (4) In the process of model derivation, some artificial assumptions are enforced, which potentially are not be compatible with the thermodynamic consistency. These defects of the current constitutive model caused big errors or distortion in the simulating result under complex loading conditions, and can hardly guarantee the convergence of numerical computation due to the singularity at corners. A visco-elastoplastic coupling damage constitutive model is presented in this paper strictly based on the thermodynamic theory. Hardening effect is considered in yield surface establishing by considering irreversible deformations in effective stress space, and so does Lode angle effect. The yield surface is presented as a smooth surface in effective stress space without corners. In nominal stress space, damage surface is established through the energy release rate, including both the elastic and plastic contribution to account for stiffness degradation and softening effect. The different mechanical characteristics under uniaxial tensile and compressive loading conditions of concrete are described using bi-scalar damage variable and stress spectral decomposition. Based on the rate-independent model, a rate dependent model is developed by introducing a Duvaut-lions viscosity concept into the inelastic strain and damage variable. Rate sensitivity of the elastic properties is included in the proposed constitutive model via an additional elastic condition. Fully implicit backward-Euler integration algorithm characterized by unconditional stability is employed in the numerical implementation of model. The proposed model is numerically simulated and the obtained numerical results agree well with tests using uniaxial, biaxial, triaxial and uniaxial cyclical loading. At the end, failure processes of single-edge-notched beam and double-edge-notched specimen are also simulated to further validate the proposed model. The tensor product and contractions in this paper are operated using notational convention as a ⊗ b = aij bkl , a · b = aik bkj , a : b = aij bij , and A : b = Aijkl bkl , where repeated indices mean summation.
磁控溅射薄膜生长的模拟方法
表面技术第51卷第2期磁控溅射薄膜生长的模拟方法王晓倩，赵晋，刘建勇（天津工业大学 纺织科学与工程学院，天津 300387）摘要：磁控溅射技术制备的薄膜膜层均匀，内部无气孔，密度高，与衬底的附着性良好，薄膜质量高，被广泛应用于科学研究和工业生产中，且适合应用计算机模拟来研究溅射过程和溅射结果，这样既可以检验模拟的准确性，又可以对实验现象的内在意义进行挖掘，为后续实验提供参考信息。
在介绍磁控溅射薄膜生长常用模拟方法原理的基础上，详细讨论了第一性原理（First-principles calculations）、分子动力学（Molecular dynamics，MD）和蒙特卡洛（Monte Carlo，MC）等3种方法的适用条件和模拟结果，从3种方法适合解决的问题、相互之间的区别等方面，对国内外最新的研究进展进行总结与分析。
发现3种方法在精确度和计算量上依次递减，在可模拟的时间和空间尺度上依次递增，在模拟对象上，第一性原理方法由于其高度的精确性被广泛应用于对薄膜本身的性质或对粒子间的运动等方面，且模拟结果可以是具体数值，从而对实验进行更加精确的预测和指导，分子动力学方法多用于模拟薄膜生长过程和原子间行为等方面，蒙特卡洛方法相较于前两者，用途更加广泛，可模拟的对象除了薄膜本身，也可以对电磁场等进行模拟。
最后，对磁控溅射薄膜生长模拟未来的研究方向进行了展望。
关键词：磁控溅射；第一性原理方法；分子动力学方法；蒙特卡洛方法；数值模拟；薄膜中图分类号：O484 文献标识码：A 文章编号：1001-3660(2022)02-0156-09DOI：10.16490/ki.issn.1001-3660.2022.02.014Simulation Method of Magnetron Sputtering Film GrowthWANG Xiao-qian, ZHAO Jin, LIU Jian-yong(School of Textile Science and Engineering, Tiangong University, Tianjin 300387, China)ABSTRACT: The film prepared by magnetron sputtering technology is uniform and free from pores inside, with high density, good adhesion to the substrate and excellent quality and has been widely used in scientific research and industrial production.Such film is suitable for the simulation by computer to study sputtering process and sputtering results, which can not only check the accuracy of simulation, but also excavate the intrinsic meaning of experimental phenomena and provide reference information for subsequent experiments. Based on the introduction of the principles of the commonly used simulation methods for the growth of magnetron sputtering films, the applicable conditions and simulation results of the three methods, first-principles calculations, molecular dynamics (MD) and Monte Carlo (MC), were discussed in detail and the latest research收稿日期：2020-09-02；修订日期：2021-07-12Received：2020-09-02；Revised：2021-07-12作者简介：王晓倩（1995—），女, 硕士研究生,主要研究方向为纺织品功能整理。
Simulation有限元分析建模指南
Simulation有限元分析建模指南作者：刘军来源：《CAD/CAM与制造业信息化》2013年第04期在国家产业结构升级及自主创新的需求下，随着三维参数化设计软件的普及，有限元分析的市场需求越来越大。
Simulation是一款操作简单、易学易用并且与SolidWorks无缝集成的有限元分析软件，设计分析一体化的理念使分析的效率更高。
本文将重点介绍Simulation有限元建模的基本方法，为分析工程师提供参考。
有限元分析建模的基本原则是：在保证计算精度的前提下，尽量减少计算规模。
具体建模方法有：单元降维、细节简化、局部控制、替代简化、等效简化和对称结构等。
一、单元降维Simulation支持三种单元类型，分别是四面体实体单元、三角形壳单元和杆、梁单元，其中实体单元为三维单元，壳单元为二维单元，杆、梁单元为一维单元，如图1所示。
在分析过程中，通过分析合理降低模型中单元的维度，不仅能减少网格划分的难度和单元数量，还可以大大减少计算的规模。
产品的结构特点不同，选择的单元类型也不同，具体选择方法可以参考以下7种结构。
1.三维实体结构三维实体结构为3D模型，适用于所有结构，载荷可以是任意载荷。
模型的特点是三维实体，典型模型如图2所示。
2.平面应力结构平面应力结构问题解决的是薄板拉压问题，在Simulation中可以采用2D简化中的平面应力简化。
结构的几何条件是等厚度薄板，且截面尺寸是厚度尺寸的10倍以上。
载荷的条件是必须平行于板面，并且沿板厚方向均匀分布。
模型的特点是等厚度的薄板。
典型模型如图3所示。
3.平面应变结构平面应变结构解决的是薄板剪切问题，在Simulation中可以采用2D简化中的平面应变简化。
结构的几何条件是等截面长体，并且长度尺寸是截面尺寸的10倍以上。
载荷的条件是必须垂直于长度方向，并且沿长度方向均匀分布。
模型的特点是等截面长体。
典型模型如图4所示。
4.轴对称结构轴对称结构解决的是轴对称问题，在Simulation中可以采用2D简化中的轴对称简化。
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 ͒。
visual simulation
viscoelastic_material
Analysis of Viscoelastic Materials
Viscoelastic materials have a time-dependent response, even if the loading is constant. Many polymers and biological tissues exhibit such a behavior. Linear viscoelasticity is a commonly used approximation, where the stress depends linearly on the strain and its time derivatives. Linear viscoelastic material models are expressed in integral equation (Equation 0-1) or differential equation (Equation 0-2) models.
VISCOELASTIC MATERIAL
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3
Note that aT(T0)=1, so that T0 is the temperature at which the original material data is given. Usually T0 is taken as the glass temperature of the material. If the temperature drops below T0-C2, the WLF equation is no longer valid. The constants C1 and C2 are material dependent, but with T0 as the glass temperature the values C1=17.4 and C2=51.6 K are reasonable approximations for many polymers if a base 10 logarithm is assumed. If you think of the shift function as a multiplier to the viscosity in each of the dashpots in the generalized Maxwell model, Equation 0-7 will for a TRS material be modified to 1 · · -q = e q m + -----------------------------a T ( T ( t ) )λ m m (0-13)
Simulacra and Simulation From Wikipedia
Simulacra and Simulation From Wikipedia, the free encyclopediaSimulacra and Simulation (Simulacres et Simulation in French) is a philosophical treatise by Jean Baudrillard seeking to interrogate the relationship among reality, symbols, and society.[edit] Overview“ The simulacrum is never that which conceals the truth--it is the truth which conceals that there is none. The simulacrum is true.[1] ”—The quote is credited to Ecclesiastes, but the words do not occur there. It can be seen as an addition,[2] a paraphrase and an endorsement of Ecclesiastes' condemnation[3] of the pursuit of wisdom as folly and a 'chasing after wind' - see for example Ecclesiastes 1.16.Simulacra and Simulation is most known for its discussion of symbols, signs, and how they relate to contemporaneity. Baudrillard claims that our current society has replaced all reality and meaning with symbols and signs, and that human experience is of a simulation of reality. Moreover, these simulacra are not merely mediations of reality, nor even deceptive mediations of reality; they are not based in a reality nor do they hide a reality, they simply hide that anything like reality that is irrelevant to our current understanding of our lives. The simulacra that Baudrillard refers to are the significations and symbolism of culture and media that construct perceived reality, the acquired understanding by which our lives and shared existence is rendered legible; Baudrillard believed that society has become so saturated with these simulacra and our lives so saturated with the constructs of society that all meaning was being rendered meaningless by being infinitely mutable. Baudrillard called this phenomenon the "precession of simulacra"."Simulacra and Simulation" breaks the sign-order into 4 stages:The first stage is a faithful image/copy, where we believe, and it may even be correct that, a sign is a "reflection of a profound reality" (pg 6), this is a good appearance, in what Baudrillard called "the sacramental order".The second stage is perversion of reality, this is where we believe the sign to be an unfaithful copy, which "masks and denatures" reality as an "evil appearance - it is of the order of maleficence". Here, signs and images do not faithfully show us reality, but can hint at the existence of something real which the sign itself is incapable of encapsulating.The third stage masks the absence of a profound reality, where the simulacrum pretends to be a faithful copy, but it is a copy with no original. Signs and images claim to represent something real, but no representation is taking place and arbitrary images are merely suggested as things which they have no relationship to. Baudrillard calls this the "order of sorcery".The fourth stage is pure simulation, in which the simulacrum has no relationship to any reality whatsoever. Here, signs merely reflect other signs and any claim to reality on the part of images or signs is only of the order of other such claims.Simulacra and Simulation identifies three types of simulacra and identifies each with a historical period:First order, associated with the premodern period, where the image is clearly an artificial placemarker for the real item. The uniqueness of objects and situations marks them as irreproducibly real and signification obviously gropes towards this reality.Second order, associated with the modernity of the Industrial Revolution, where distinctions between image and reality break down due to the proliferation of mass-reproducible copies of items, turning them into commodities. The commodity's ability to imitate reality threatens to replace the original version, especially when the individual person is only concerned with consuming for some utility a functional facsimile.Third order, associated with the postmodernity, where the simulacrum precedes the original and the distinction between reality and representation vanishes. There is only the simulacrum, and originality becomes a totally meaningless concept.[4]Baudrillard theorizes that the lack of distinctions between reality and simulacra originates in several phenomena:Contemporary media including television, film, print and the Internet, which are responsible for blurring the line between goods that are needed and goods for which a need is created by commercial images.Exchange value, in which the value of goods is based on money rather than usefulness. Multinational capitalism, which separates produced goods from the plants, minerals and other original materials and the processes used to create them.Urbanization, which separates humans from the natural world.Language and ideology, in which language is used to obscure rather than reveal reality when used by dominant, politically powerful groups.A specific analogy that Baudrillard uses is a fable derived from On Exactitude in Science by Jorge Luis Borges. In it, a great Empire created a map that was so detailed it was as large as the Empire itself. The actual map grew and decayed as the Empire itself conquered or lost territory. When theEmpire crumbled, all that was left was the map. In Baudrillard's rendition, it is the map that people live in, the simulation of reality, and it is reality that is crumbling away from disuse.The transition from signs which dissimulate something to signs which dissimulate that there is nothing, marks the decisive turning point. The first implies a theology of truth and secrecy (to which the notion of ideology still belongs). The second inaugurates an age of simulacra and simulation, in which there is no longer any God to recognize his own, nor any last judgment to separate truth from false, the real from its artificial resurrection, since everything is already dead and risen in advance.[4]It is important to note that when Baudrillard refers to the "precession of simulacra" in Simulacra and Simulation, he is referring to the way simulacra have come to precede the real in the sense mentioned above, rather than to any succession of historical phases of the image. Referring to "On Exactitude in Science", he argued that just as for contemporary society the simulated copy had superseded the original object, so, too, the map had come to precede the geographic territory (c.f. Map–territory relation), e.g. the first Gulf War (see below): the image of war preceded real war.Henceforth, it is the map that precedes the territory - precession of simulacra - it is the map that engenders the territory and if we were to revive the fable today, it would be the territory whose shreds are slowly rotting across the map.[4][edit] See alsoSimulated reality。
act 科学 题目 1
Passage IUnmanned spacecraft taking images of Jupiter's moon Europa have found its surface to be very smooth with few meteorite craters. Europa's surface ice shows evidence of being continually resmoothed and reshaped. Cracks, dark bands, and pressure ridges (created when water or slush is squeezed up between 2 slabs of ice) are commonly seen in images of the surface. Two scientists express their views as to whether the presence of a deep ocean beneath the surface is responsible for Europa's surface features. Scientist 1A deep ocean of liquid water exists on Europa. Jupiter's gravitational field produces tides within Europa that can cause heating of the subsurface to a point where liquid water can exist. The numerous cracks and dark bands in the surface ice closely resemble the appearance of thawing ice covering the polar oceans on Earth. Only a substantial amount of circulating liquid water can crack and rotate such large slabs of ice. The few meteorite craters that exist are shallow and have been smoothed by liquid water that oozed up into the crater from the subsurface and then quickly froze.Jupiter's magnetic field, sweeping past Europa, would interact with the salty, deep ocean and produce a second magnetic field around Europa. The spacecraft has found evidence of this second magnetic field.Scientist 2No deep, liquid water ocean exists on Europa. The heat generated by gravitational tides is quickly lost to space because of Europa's small size, as shown by its very low surface temperature (–160°C). Many of the features on Europa's surface resemble features created by flowing glaciers on Earth. Large amounts of liquid water are not required for the creation of these features. If a thin layer of ice below the surface is much warmer than the surface ice, it may be able to flow and cause cracking and movement of the surface ice. Few meteorite craters are observed because of Europa's very thin atmosphere; surface ice continually sublimes (changes from solid to gas) into this atmosphere, quickly eroding and removing any craters that may have formed.1.Which of the following best describes how the 2 scientists explain how cratersare removed from Europa's surface?1.Scientist 1Scientist 22.A.SublimationFilled in by water3.B.Filled in by waterSublimation4.C.Worn smooth by windSublimation5.D.Worn smooth by windFilled in by water2.According to the information provided, which of the following descriptions ofEuropa would be accepted by both scientists?1.F. Europa has a larger diameter than does Jupiter.2.G. Europa has a surface made of rocky material.3.H. Europa has a surface temperature of 20°C.4.J. Europa is completely covered by a layer of ice.3.With which of the following statements about the conditions on Europa or theevolution of Europa's surface would both Scientist 1 and Scientist 2 most likely agree? The surface of Europa:1.A. is being shaped by the movement of ice.2.B. is covered with millions of meteorite craters.3.C. is the same temperature as the surface of the Arctic Ocean on Earth.4.D. has remained unchanged for millions of years.4.Which of the following statements about meteorite craters on Europa would bemost consistent with both scientists' views?1.F. No meteorites have struck Europa for millions of years.2.G. Meteorite craters, once formed, are then smoothed or removed byEuropa's surface processes.3.H. Meteorite craters, once formed on Europa, remain unchanged for billionsof years.4.J. Meteorites frequently strike Europa's surface but do not leave any craters.5.Scientist 2 explains that ice sublimes to water vapor and enters Europa'satmosphere. If ultraviolet light then broke those water vapor molecules apart, which of the following gases would one most likely expect to find in Europa's atmosphere as a result of this process?1.A. Nitrogen2.B. Methane3.C. Chlorine4.D. Oxygen6.Based on the information in Scientist 1's view, which of the following materialsmust be present on Europa if a magnetic field is to be generated on Europa?1.F. Frozen nitrogen2.G. Water ice3.H. Dissolved salts4.J. Molten magma7.Assume Scientist 2's view about the similarities between Europa's surfacefeatures and flowing glaciers on Earth is correct. Based on this assumption and the information provided, Earth's glaciers would be least likely to exhibit which of the following features?1.A. Pressure ridges2.B. Cracks3.C. Meteorite craters4.D. Dark bands。
ROHM Solution Simulator 3.5V-40V 2A 2.2MHz 汽车级双向 D
User’s Guide ROHM Solution Simulator3.5V to 40V Input, 2A Single 2.2MHz Buck DC/DC Converter for AutomotiveBD9P255MUF-C / Line ResponseThis circuit simulate the line response of BD9P255MUF-C. You can observe the fluctuation of the output voltage when the load current is abruptly changed. You can customize the parameters of the components shown in blue, such as VIN, IOUT, or peripheral components, and simulate the Line response with desired operating condition.General CautionsCaution 1: The values from the simulation results are not guaranteed. Please use these results as a guide for your design.Caution 2: These model characteristics are specifically at Ta=25°C. Thus, the simulation result with temperature variances may significantly differ from the result with the one done at actual application board (actual measurement).Caution 3: Please refer to the datasheet for details of the technical informationCaution 4: The characteristics may change depending on the actual board design and ROHM strongly recommend to double check those characteristics with actual board where the chips will be mounted on.1 Simulation SchematicFigure 1. Simulation Schematic2 How to simulateThe simulation settings, such as simulation time or convergence options, are configurable from the ‘Simulation Settings’shown in Figure 2, and Table 1 shows the default setup of the simulation.In case of simulation convergence issue, you can change advancedoptions to solve. Default statement in ‘Manual Options’ sets the time t o startsaving the result to 1.2ms. You can modify or delete it.Figure 2. Simulation Settings and execution Table 1.Simulation settings default setupParameters Default NoteSimulation Type Time-Domain Do not change Simulation TypeEnd Time 3msAdvanced options Balanced Convergence AssistManual Options “.tran 0 3m 1.2m”SimulationSettingsSimulateVINVOUT3 Simulation ConditionsTable 2. List of the simulation condition parametersInstance Name Type Parameters DefaultValueVariable Range UnitsMin MaxVBAT Voltage Source Initial_value 16 3.5 40 VPulse_value 8 3.5 40 Vramptime_initial_to_pulse 10 No constraint(Note1)µsramptime_pulse_to_initial 10 No constraint(Note1)µsStart_delay 1.5 - msPulse_width 1.0 - msPeriod 3.0 - ms VEN Voltage Source Pulse_value 16 Use the same value as thevoltage_level of VBATVVOCP_SEL Voltage Source voltage_level 0 0: Max output current =2A,or 5: Max output current=1.5AVVMODE Voltage Source voltage_level 5 0: Auto mode,or 5: FPWM modeV IOUT Current source Current_level 2 0 2 A (Note 1) This is a constraint of the simulation settings and does not guarantee the operation of the IC.3.1 VBAT parameter setupFigure 3 shows how the VBAT parameters correspond to the VIN stimulus waveform.(a) Overall view(b) Magnified viewFigure 3.VIN parameters and its waveform VOUT VOUT VIN VINStart_delay Period(to the next falling edge)Ramptime_initial_to_pulsePulse_valueInitial_valueRamptime_pulse_to_initial Pulse_width*0.2ms of soft start period Waveforms recorded from t=1.2ms4 BD9P255MUF-C_Tran modelTable 3 and Table 4 shows the model terminal function implemented. Note that BD9P255MUF-C_Tran is the behavior model for its load/line response operation, and no protection circuits or the functions not related to the purpose are not implemented.Table 3. BD9P255MUF-C_Tran model terminals used for the simulationTerminals DescriptionEN Enable inputVIN Power supply inputPVIN Power supply inputPGND Power groundSW Switching nodeOCP_SEL Over current selector inputMODE PWM mode selector inputGND GroundVOUT_SNS Phase compensation.VREG 3.3V output for internal circuit.Table 4. BD9P255MUF-C_Tran model terminals NOT used for the simulationTerminals DescriptionEN Input is ignored (always enable)BST Input is ignored (Bootstrap not implemented)SSCG Input is ignored (SSCG not implemented)RESET The function is not implementedVOUT_DIS Input is ignoredVCC_EX Input is ignored (function not implemented)(Note 2) This model is not compatible with the influence of ambient temperature.(Note 3) This model is not compatible with the external synchronization function.(Note 4) Use the simulation results only as a design guide and the data reported herein is not a guaranteed value.4.1 Parameter TSSBD9P255MUF-C_Tran model has the property ‘TSS’, which is the soft start time described in page 7 of the datasheet. The product has 3ms (typical) of the startup time of the output voltage. You can short cut the soft start by changing TSS value. The default TSS value is set to 0.2ms in this simulation and you can modify the value in the property editor.Figure 4. TSS property of BD9P255MUF-C_Tran5 Peripheral Components5.1 Bill of MaterialTable 5 shows the list of components used in the simulation schematic. Each of the capacitor and inductor has the parameters of equivalent circuit shown below. The default value of equivalent components are set to zero except for the parallel resistance of L1. You can modify the values of each component.Table 5. List of capacitors used in the simulation circuitType Instance Name Default Value UnitsCapacitor CBLK 220 µFCIN1 0.1 µFCIN2 4.7 µFCREG 1.0 µFCOUT1 22 µFCOUT2 22 µFInductor L1 3.3 µH5.2 Capacitor Equivalent Circuits(a) Property editor (b) Equivalent circuitFigure 5. Capacitor property editor and equivalent circuit5.3 Inductor Equivalent Circuits(a) Property editor (b) Equivalent circuitFigure 6. Inductor property editor and equivalent circuitThe default value of PAR_RES is 6.6kohm.(Note 5) These parameters can take any positive value or zero in simulation but it does not guarantee the operation of the IC in any condition. Refer to the datasheet to determine adequate value of parameters.6 Link to the product information and tools6.1 Product webpage link:https:///products/power-management/switching-regulators/integrated-fet/buck-converters-synchronous/bd9p255muf-c-product6.2 Related documentsThe application notes ar e available from ‘Documentation’ tab of the product page.6.3 Design assist tools are available from ‘Tools’ tab of the product page.The Circuit constant calculation sheet is useful for Febiding the application circuit constants.NoticeROHM Customer Support System/contact/Thank you for your accessing to ROHM product informations.More detail product informations and catalogs are available, please contact us.N o t e sThe information contained herein is subject to change without notice.Before you use our Products, please contact our sales representative and verify the latest specifica-tions :Although ROHM is continuously working to improve product reliability and quality, semicon-ductors can break down and malfunction due to various factors.Therefore, in order to prevent personal injury or fire arising from failure, please take safety measures such as complying with the derating characteristics, implementing redundant and fire prevention designs, and utilizing backups and fail-safe procedures. ROHM shall have no responsibility for any damages arising out of the use of our Poducts beyond the rating specified by ROHM.Examples of application circuits, circuit constants and any other information contained herein areprovided only to illustrate the standard usage and operations of the Products. The peripheral conditions must be taken into account when designing circuits for mass production.The technical information specified herein is intended only to show the typical functions of andexamples of application circuits for the Products. ROHM does not grant you, explicitly or implicitly, any license to use or exercise intellectual property or other rights held by ROHM or any other parties. ROHM shall have no responsibility whatsoever for any dispute arising out of the use of such technical information.The Products specified in this document are not designed to be radiation tolerant.For use of our Products in applications requiring a high degree of reliability (as exemplifiedbelow), please contact and consult with a ROHM representative : transportation equipment (i.e. cars, ships, trains), primary communication equipment, traffic lights, fire/crime prevention, safety equipment, medical systems, servers, solar cells, and power transmission systems.Do not use our Products in applications requiring extremely high reliability, such as aerospaceequipment, nuclear power control systems, and submarine repeaters.ROHM shall have no responsibility for any damages or injury arising from non-compliance withthe recommended usage conditions and specifications contained herein.ROHM has used reasonable care to ensur e the accuracy of the information contained in thisdocument. However, ROHM does not warrants that such information is error-free, and ROHM shall have no responsibility for any damages arising from any inaccuracy or misprint of such information.Please use the Products in accordance with any applicable environmental laws and regulations,such as the RoHS Directive. For more details, including RoHS compatibility, please contact a ROHM sales office. ROHM shall have no responsibility for any damages or losses resulting non-compliance with any applicable laws or regulations.W hen providing our Products and technologies contained in this document to other countries,you must abide by the procedures and provisions stipulated in all applicable export laws and regulations, including without limitation the US Export Administration Regulations and the Foreign Exchange and Foreign Trade Act.This document, in part or in whole, may not be reprinted or reproduced without prior consent ofROHM.1) 2)3)4)5)6)7)8)9)10)11)12)13)。
多自由度粘弹性耗能结构的随机地震动响应的简明显示解
多自由度粘弹性耗能结构的随机地震动响应的简明显示解发布时间：2021-09-07T10:09:22.447Z 来源：《城市建设》2021年9月上17期作者：徐长春1 冯超1 彭俚2[导读] 粘弹性阻尼器广泛应用于各类工程的减振。
针对多自由结构设置粘弹性阻尼器基于Kanai-Tajimi谱的结构相对于地面的绝对位移和层间位移等系列响应进行了研究，获得了耗能结构系列响应的简明显示解。
1.广西华蓝工程管理有限公司徐长春1 冯超1 广西南宁 5300122.中国移动通信集团广西有限公司彭俚2 广西南宁 530028摘要：粘弹性阻尼器广泛应用于各类工程的减振。
针对多自由结构设置粘弹性阻尼器基于Kanai-Tajimi谱的结构相对于地面的绝对位移和层间位移等系列响应进行了研究，获得了耗能结构系列响应的简明显示解。
首先根据6参数粘弹性阻尼器计算见图获得其微分型本构关系;其次与结构的地震动微分方程联立;最后利用复模态方法和虚拟激励法获得了结构的系列响应的简明显示解。
算例表明本文方法的简洁性和正确性。
关键词：六参数粘弹性阻尼器模型；Kanai-Tajimi谱；简明显示解;虚拟激励法；复模态法中图分类号：TU318文献标识码：A文章编号：Conciseandexplicitsolutionsofrandomseismicresponseofmulti-degree-of-freedomstructurewithviscoelasticenergydissipationXUChang-chun1，FENGChao1，PENGLi2（1.GuangxiHualanEngineeringManagementCo.,Ltd.,Nanning530012,China;2.ChinaMobileGroupGuangxiCo.,Ltd.,Nanning530028,China）Abstract:Viscoelasticdampersarewidelyusedinvariousengineeringtoreducevibration.BasedonKanaiTajimispectrum,aseriesofresponsesofamulti-degree-of-freedomstructurewithviscoelasticdampers,suchasabsolutedisplacementsandinter-storydisplacements,arestudied.Firstly,thedifferentialconstitutiverelationofthe6-parameterviscoelasticdamperisobtainedaccordingtothecalculationfigure.Secondly,theaboveconstitutiverelationiscombinedwiththestructuralmotiondifferentiale 金项目：广西重点研发计划项目（桂科AB18281010）通讯作者：徐长春（1981-），南宁，湖北通山人，广西华蓝工程管理有限公司总经理助理，博士。
以李时珍为话题的英语作文
In the vast annals of Chinese history, few figures stand out as prominently as Li Shizhen, a renowned physician and pharmacologist of the Ming Dynasty. His monumental work, the Compendium of Materia Medica Bencao Gangmu, has not only shaped the course of traditional Chinese medicine but also left an indelible mark on the world of science and medicine.Born in 1518 in Qichun, Hubei Province, Li Shizhen was destined for a life of scholarly pursuits. His family, wellversed in medicine, provided him with a solid foundation in the field. However, it was his insatiable curiosity and relentless pursuit of knowledge that propelled him to delve deeper into the mysteries of nature and its healing properties.One of the most remarkable aspects of Li Shizhens life was his commitment to empirical research. Unlike many scholars of his time who relied heavily on ancient texts, Li Shizhen was a firm believer in the power of observation and experimentation. He spent countless hours in the wild, meticulously documenting the characteristics and medicinal properties of various plants, animals, and minerals. His dedication to fieldwork was unparalleled, and it is this handson approach that has earned him the title of the father of Chinese materia medica.The Compendium of Materia Medica, completed in 1578, is a testament to Li Shizhens unwavering dedication to his craft. This encyclopedic work, consisting of 1,892,000 Chinese characters, covers 1,892 medicinal substances, 11,096 medical prescriptions, and 1,160 illustrations. It is a comprehensive guide to the medicinal properties of plants, animals, andminerals, and it has been instrumental in shaping the practice of traditional Chinese medicine for centuries.One of the most fascinating aspects of the Compendium is its classification system. Li Shizhen organized the substances into 16 categories based on their medicinal properties, ranging from herbs and minerals to animal products and human body parts. This systematic approach to classification was groundbreaking at the time and has greatly influenced the way we understand and categorize medicinal substances today.Li Shizhens work has had a profound impact on the field of pharmacology, both in China and around the world. His meticulous documentation of the medicinal properties of various substances has provided invaluable insights into the healing potential of nature. Moreover, his emphasis on empirical research and experimentation has set a precedent for the scientific method, which is still widely used today.In addition to his contributions to medicine, Li Shizhen was also a skilled poet and calligrapher. His literary works, though overshadowed by his scientific achievements, reflect his deep appreciation for the beauty and complexity of the natural world. His poetry often draws on his experiences in the field, offering a unique perspective on the interconnectedness of all living things.Despite the passage of centuries, Li Shizhens legacy continues to inspire and inform. His commitment to the pursuit of knowledge, his innovative approach to classification, and his unwavering belief in the power ofnature to heal have left a lasting impact on the world of medicine. As we continue to explore the mysteries of the natural world and seek new ways to promote health and wellbeing, we can look to the life and work of Li Shizhen as a guiding light.In conclusion, Li Shizhens life and work serve as a powerful reminder of the importance of curiosity, dedication, and innovation in the pursuit of knowledge. His contributions to the field of medicine have had a lasting impact, and his legacy continues to inspire new generations of scholars and practitioners. As we navigate the challenges of the modern world, we can draw inspiration from the life of Li Shizhen and strive to embrace the healing power of nature in all its forms.。