外文翻译 对于有限元分析的介绍
英译汉-有限元方法的一般描述
General Description of the Finite Element Method In the finite element method, the actual continuum or body of matter like solid, liquid or gas is represented as an assemblage of subdivisions called finite elements.These elements are considered to be interconnected at specified joints which are called nodes or nodal points.The nodes usually lie on the element boundaries where adjacent elements are considered to be connected. Since the actual variation of the field variable (like displacement,stress,temperature,pressure or velocity) inside the continuum is not known, we assume that the variation of the field variable inside a finite element can be approximated by a simple function.These approximating functions (also called interpolation models) are defined in terms of the field variable. By solving the field variable will be known. Once these are known, the approximating functions define the field variable throughout the assemblage of elements.The solution of a general continuum problem by the finite element method always follows an orderly step-and-step process. With reference to static structural problems, the step-by-step procedure can be stated as follows:Step(i) : Discretization of the structureThe first step in the finite element method is to divide the structure or solution region into subdivisions or element. Hence the structure that is being analyzed has to be modeled with suitable finite elements. Thenumber, type, size and arrangement of the elements have to be decided.Step(ii) : Selection of a proper interpolation or displacement model Since the displacement solution of a complex structure under any specified load conditions cannot be predicted exactly, we assume some suitable solution within an element to approximate the unknown solution. The assumed solution must be simple from computational point of view, but it should satisfy certain convergence requirements. In general, the solution or the interpolation model is taken in the form of a polynomial.Step(iii) : Derivation of element stiffness matrices and load vectors From the assumed displacement model, the stiffness matrix [）（e K ]and the load vector (e)p , of element “e ” are to be derived by usingeither equilibrium conditions or a suitable variational principle.Step(iv) : Assemblage of element equations to obtain the overall equilibrium equationsSince the structure is composed of several finite elements, the individual elements, the individual element stiffness matrices and load vectors are to be assembled in a suitable manner and the overall equilibrium equations have to be formulated as[]P K =Φ For linear problems, the vector Φ can be solved very easily. But fornonlinear problems, the solution has to be obtained in a sequence of steps, each step involving the modification of the stiffness matrix [K] and/or theload vector P .From the known nodal displacements , if required, the element strainsand stresses can be computed by using the necessary equations of solid or structural mechanics.The terminology used in the above six steps has to be modified if we want to extend the concept to other fields. For example, we have to use the term continuum or domain in place of structure ，field variable in place of displacement, characteristic matrix in place of stiffness matrix, and element resultants in place of element strains.有限元方法的一般描述在有限元方法中，固体物质的实际连续体或主体如固体，液体或气体作为细分的组合称为有限元素。
有限元应用的参考译文
有限元应用参考译文Finite Element AnalysisFinite Element Analysis (FEA), also known as the Finite Element Method (FEM), is probably the most important tool added to the mechanical design engineer's toolkit this century. The development of FEA has been driven by the desire for more accurate design computations in more complex situations, allowing improvements in both the design procedure and products. The growing use of FEA has been made possible by the creation of computation engines that are capable of handling the immense volume of calculations necessary to prepare and carry out an analysis and easily display the results for interpretation. With the advent of very powerful desktop workstations, FEA is now available at a practical cost to virtually all engineers and designers.有限元分析(FEA)，也称为有限元法(FEM)，可能是本世纪提供给机械设计工程师使用的最重要的设计工具之一。
有限元分析法英文简介
The finite element analysisFinite element method, the solving area is regarded as made up of many small in the node connected unit (a domain), the model gives the fundamental equation of sharding (sub-domain) approximation solution, due to the unit (a domain) can be divided into various shapes and sizes of different size, so it can well adapt to the complex geometry, complex material properties and complicated boundary conditionsFinite element model: is it real system idealized mathematical abstractions. Is composed of some simple shapes of unit, unit connection through the node, and under a certain load.Finite element analysis: is the use of mathematical approximation method for real physical systems (geometry and loading conditions were simulated. And by using simple and interacting elements, namely unit, can use a limited number of unknown variables to approaching infinite unknown quantity of the real system.Linear elastic finite element method is a ideal elastic body as the research object, considering the deformation based on small deformation assumption of. In this kind of problem, the stress and strain of the material is linear relationship, meet the generalized hooke's law; Stress and strain is linear, linear elastic problem boils down to solving linear equations, so only need less computation time. If the efficient method of solving algebraic equations can also help reduce the duration of finite element analysis.Linear elastic finite element generally includes linear elastic statics analysis and linear elastic dynamics analysis from two aspects. The difference between the nonlinear problem and linear elastic problems:1) nonlinear equation is nonlinear, and iteratively solving of general;2) the nonlinear problem can't use superposition principle;3) nonlinear problem is not there is always solution, sometimeseven no solution. Finite element to solve the nonlinear problem can be divided into the following three categories:1) material nonlinear problems of stress and strain is nonlinear,but the stress and strain is very small, a linear relationship between strain and displacement at this time, this kind of problem belongs tothe material nonlinear problems. Due to theoretically also cannotprovide the constitutive relation can be accepted, so, general nonlinear relations between stress and strain of the material based on the test data, sometimes, to simulate the nonlinear material properties available mathematical model though these models always have their limitations. More important material nonlinear problems in engineering practice are: nonlinear elastic (including piecewise linear elastic, elastic-plasticand viscoplastic, creep, etc.2) geometric nonlinear geometric nonlinear problems are caused dueto the nonlinear relationship between displacement. When the object the displacement is larger, the strain and displacement relationship is nonlinear relationship. Research on this kind of problemIs assumes that the material of stress and strain is linear relationship. It consists of a large displacement problem of largestrain and large displacement little strain. Such as the structure ofthe elastic buckling problem belongs to the large displacement little strain, rubber parts forming process for large strain.3) nonlinear boundary problem in the processing, problems such as sealing, the impact of the role of contact and friction can not be ignored, belongs to the highly nonlinear contact boundary.At ordinary times some contact problems, such as gear, stamping forming, rolling, rubber shock absorber, interference fit assembly, etc., when a structure and another structure or external boundary contact usually want to consider nonlinear boundary conditions. The actual nonlinear may appear at the same time these two or three kinds of nonlinear problems.Finite element theoretical basisFinite element method is based on variational principle and the weighted residual method, and the basic solving thought is the computational domain is divided into a finite number of non-overlapping unit, within each cell, select some appropriate nodes as solving the interpolation function, the differential equation of the variables inthe rewritten by the variable or its derivative selected interpolation node value and the function of linear expression, with the aid of variational principle or weighted residual method, the discrete solution of differential equation. Using different forms of weight function and interpolation function, constitute different finite element methods. 1. The weighted residual method and the weighted residual method ofweighted residual method of weighted residual method: refers to the weighted function is zero using make allowance for approximate solution of the differential equation method is called the weighted residual method. Is a kind of directly from the solution of differential equation and boundary conditions, to seek the approximate solution of boundary value problems of mathematical methods. Weighted residual method is to solve the differential equation of the approximate solution of a kind of effective method.Hybrid method for the trial function selected is the most convenient, but under the condition of the same precision, the workload is the largest. For internal method and the boundary method basis function must be made in advance to meet certain conditions, the analysis of complex structures tend to have certain difficulty, but the trial function is established, the workload is small. No matter what method is used, when set up trial function should be paid attention to are the following:(1) trial function should be composed of a subset of the complete function set. Have been using the trial function has the power series and trigonometric series, spline functions, beisaier, chebyshev, Legendre polynomial, and so on.(2) the trial function should have until than to eliminate surplus weighted integral expression of the highest derivative low first order derivative continuity.(3) the trial function should be special solution with analytical solution of the problem or problems associated with it. If computing problems with symmetry, should make full use of it. Obviously, anyindependent complete set of functions can be used as weight function. According to the weight function of the different options for different weighted allowance calculation method, mainly include: collocation method, subdomain method, least square method, moment method andgalerkin method. The galerkin method has the highest accuracy.Principle of virtual work: balance equations and geometricequations of the equivalent integral form of "weak" virtual work principles include principle of virtual displacement and virtual stress principle, is the floorboard of the principle of virtual displacementand virtual stress theory. They can be considered with some control equation of equivalent integral "weak" form. Principle of virtual work: get form any balanced force system in any state of deformationcoordinate condition on the virtual work is equal to zero, namely the system of virtual work force and internal force ofthe sum of virtual work is equal to zero. The virtual displacement principle is the equilibrium equation and force boundary conditions of the equivalent integral form of "weak"; Virtual stress principle is geometric equation and displacement boundary condition of the equivalent integral form of "weak". Mechanical meaning of the virtual displacement principle: if the force system is balanced, they on the virtual displacement and virtual strain by the sum of the work is zero. On the other hand, if the force system in the virtual displacement (strain) and virtual and is equal to zero for the work, they must balance equation. Virtual displacement principle formulated the system of force balance, therefore, necessary and sufficient conditions. In general, the virtual displacement principle can not only suitable for linear elastic problems,and can be used in the nonlinear elastic and elastic-plastic nonlinear problem.Virtual mechanical meaning of stress principle: if the displacement is coordinated, the virtual stress and virtual boundary constraint counterforce in which they are the sum of the work is zero. On the other hand, if the virtual force system in which they are and is zero for the work, they must be meet the coordination. Virtual stress in principle, therefore, necessary and sufficient condition for the expression of displacement coordination. Virtual stress principle can be applied to different linear elastic and nonlinear elastic mechanics problem. But it must be pointed out that both principle of virtual displacement and virtual stress principle, rely on their geometric equation and equilibrium equation is based on the theory of small deformation, they cannot be directly applied to mechanical problems based on large deformation theory. 3,,,,, the minimum total potential energy method of minimum total potential energy method, the minimum strain energy method of minimum total potential energy method, the potential energy function in the object on the external load will cause deformation, the deformation force during the work done in the form of elastic energy stored in the object, is the strain energy.The convergence of the finite element method, the convergence of the finite element method refers to when the grid gradually encryption, the finite element solution sequence converges to the exact solution; Or when the cell size is fixed, the more freedom degree each unit, thefinite element solutions tend to be more precise solution. Convergence condition of the convergence condition of the finite element finite element convergence condition of the convergence condition of the finiteelement finite element includes the following four aspects: 1) within the unit, the displacement function must be continuous. Polynomial is single-valued continuous function, so choose polynomial as displacement function, to ensure continuity within the unit. 2) within the unit, the displacement function must include often strain. Total can be broken down into each unit of the state of strain does not depend on different locations within the cell strain and strain is decided by the point location of variables. When the size of the units is enough hours, unit of each point in the strain tend to be equal, unit deformation is uniform, so often strain becomes the main part of the strain. To reflect the state of strain unit, the unit must include the displacement functions often strain. 3) within the unit, the displacement function must include the rigid body displacement. Under normal circumstances, the cell for a bit of deformation displacement and displacement of rigid body displacement including two parts. Deformation displacement is associated with the changes in the object shape and volume, thus producing strain; The rigid body displacement changing the object position, don't change the shape and volume of the object, namely the rigid body displacement is not deformation displacement. Spatial displacement of an object includes three translational and three rotational displacement, a total of six rigid body displacements. Due to a unit involved in the other unit, other units do rigid body displacement deformation occurs willdrive unit, thus, to simulate real displacement of a unit, assume that the element displacement function must include the rigid body displacement. 4) the displacement function must be coordinated in public boundary of the adjacent cell. For general unit of coordination isrefers to the adjacent cell in public node have the same displacement,but also have the same displacement along the edge of the unit, that is to say, to ensure that the unit does not occur from cracking and invade the overlap each other. To do this requires the function on the common boundary can be determined by the public node function value only. For general unit and coordination to ensure the continuity of the displacement of adjacent cell boundaries. However, between the plate and shell of the adjacent cell, also requires a displacement of the first derivative continuous, only in this way, to guarantee the strain energy of the structure is bounded. On the whole, coordination refers to the public on the border between neighboring units satisfy the continuity conditions. The first three, also called completeness conditions, meet the conditions of complete unit is complete unit; Article 4 is coordination requirements, meet the coordination unit coordination unit; Otherwise known as the coordinating units. Completeness requirement is necessary for convergence, all four meet, constitutes a necessary and sufficient condition for convergence. In practical application, to make the selected displacement functions all meet the requirements of completeness and harmony, it is difficult in some cases can relax the requirement for coordination. It should be pointed out that, sometimes the coordination unit than its corresponding coordination unit, its reason lies in the nature of the approximate solution. Assumed displacement function is equivalent to put the unit under constraint conditions, the unit deformation subject to the constraints, this just some alternative structure compared to the real structure. But the approximate structure due to allow cell separation, overlap, become soft, the stiffness of the unit or formed (such as round degree between continuous plate unit in the unit, and corner is discontinuous, just to pin point) for the coordination unit, the error of these two effectshave the possibility of cancellation, so sometimes use the coordination unit will get very good results. In engineering practice, the coordination of yuan must pass to use "small pieces after test". Average units or nodes average processing method of stress stress average units or nodes average processing method of stress average units or nodes average processing method of stress of the unit average or node average treatment method is the simplest method is to take stress results adjacent cell or surrounding nodes, the average value of stress.1. Take an average of 2 adjacent unit stress. Take around nodes, the average value of stressThe basic steps of finite element method to solve the problemThe structural discretization structure discretization structure discretization structure discretization to discretization of the whole structure, will be divided into several units, through the node connected to each other between the units; 2. The stiffness matrix of each unit and each element stiffness matrix and the element stiffness matrix and the stiffness matrix of each unit (3) integrated global stiffness matrix integrated total stiffness matrix integrated overall stiffness matrix integrated total stiffness matrix and write out the general balance equations and write out the general balance equations and write out the general balance equations and write a general equation4. Introduction of supporting conditions, the displacement of each node5. Calculate the stress and strain in the unit to get the stress and strain of each cell and the cell of the stress and strain and the stress and strain of each cell.For the finite element method, the basic ideas and steps can be summarized as: (1) to establishintegral equation, according to the principle of variational allowance and the weight function or equation principle of orthogonalization, establishment and integral expression of differential equations is equivalent to the initial-boundary value problem, this is the starting point of the finite element method. Unit (2) the area subdivision, according to the solution of the shape of the area and the physical characteristics of practical problems, cut area is divided into a number of mutual connection, overlap of unit. Regional unit is divided into finite element method of the preparation, this part of the workload is bigger, in addition to the cell and node number and determine the relationship between each other, also said the node coordinates, at the same time also need to list the natural boundary and essential boundary node number and the corresponding boundary value.(3) determine the unit basis function, according to the unit and the approximate solution of node number in precision requirement, choose meet certain interpolation condition basis function interpolation function as a unit. Basis function in the finite element method is selected in the unit, due to the geometry of each unit has a rule in the selection of basis function can follow certain rules. (4) the unit will be analysis: to solve the function of each unit with unit basis functions to approximate the linear combination of expression; Then approximate function generation into the integral equation, and the unit area integral, can be obtained with undetermined coefficient (i.e., cell parameter value) of each node in the algebraic equations, known as the finite element equation.(5) the overall synthesis: after the finite element equation, the area of all elements in the finite element equation according to certain principles of accumulation, the formation of general finite element equations. (6) boundary condition processing: general boundaryconditions there are three kinds of form, divided into the essential boundary conditions (dirichlet boundary condition) and natural boundary conditions (Riemann boundary conditions) and mixed boundary conditions (cauchy boundary conditions). Often in the integral expression fornatural boundary conditions, can be automatically satisfied. Foressential boundary conditions and mixed boundary conditions, should bein a certain method to modify general finite element equations satisfies. Solving finite element equations (7) : based on the general finite element equations of boundary conditions are fixed, are all closed equations of the unknown quantity, and adopt appropriate numerical calculation method, the function value of each node can be obtained.。
车架有限元分析外文文献翻译
南京林业大学本科毕业设计（论文）外文资料翻译翻译资料名称(外文)Stress analysis of heavy duty truck chassis as apreliminary data for its fatigue life predictionusing FEM翻译资料名称(中文)利用重型载货汽车的有限元应力分析的初步数据预测其疲劳寿命院（系）：汽车与交通工程学院专业：机械制造及其自动化（汽车设计方向）姓名：学号：指导教师：完成日期： 2012/5/31利用重型载货汽车的有限元应力分析的初步数据预测其疲劳寿命Roslan Abd Rahman, Mohd Nasir Tamin, Ojo Kurdi马来西亚工程大学机械工程系81310 UTM, Skudai,Johor Bahru摘要本文对一重型货车底盘做了应力分析。
应力分析能够确定零件的最大受力点，是分析零部件疲劳研究和寿命预测的重要手段。
前人已有用商用有限元软件ABAQUS软件对底盘模型进行分析的。
本次研究的底盘长12.35米，宽2.45米，材料是ASTM低合金钢710（3级），屈服极限552MPa，抗拉强度620MPa。
分析结果显示，最大应力点出现在底盘与螺栓连接的空缺处，最大应力为386.9MPa，底盘的疲劳破坏将会从最大应力点开始向车架各部位蔓延。
关键字：应力分析，疲劳寿命预测，货车底盘1.0简介在马来西亚，很多货车的车架寿命都有20多年，20多年架就会有使用安全的问题。
因此，为了确保底盘在工作期间的安全性能，就有必要对底盘作疲劳研究和寿命预测。
利用有限元法作应力分析能够确定受最大应力的关键点，这个关键点是导致底盘疲劳损伤的因素之一。
应力的大小能够预测底盘的寿命，所以可以根据应力分析的结果精确地预测底盘的寿命，应力分析越精确，底盘寿命预测的越合理。
本文是用商用有限元软件ABAQUS 软件完成底盘应力分析的。
汽车工业（汽车总成及各部件）在马来西亚的工业中占据非常重要的地位。
有限元分析中英文对照资料知识讲解
有限元分析中英文对照资料The finite element analysisFinite element method, the solving area is regarded as made up of many small in the node connected unit (a domain), the model gives the fundamental equation of sharding (sub-domain) approximation solution, due to the unit (a domain) can be divided into various shapes and sizes of different size, so it can well adapt to the complex geometry, complex material properties and complicated boundary conditions Finite element model: is it real system idealized mathematical abstractions. Is composed of some simple shapes of unit, unit connection through the node, and under a certain load.Finite element analysis: is the use of mathematical approximation method for real physical systems (geometry and loading conditions were simulated. And by using simple and interacting elements, namely unit, can use a limited number of unknown variables to approaching infinite unknown quantity of the real system.Linear elastic finite element method is a ideal elastic body as the research object, considering the deformation based on small deformation assumption of. In this kindof problem, the stress and strain of the material is linear relationship, meet the generalized hooke's law; Stress and strain is linear, linear elastic problem boils down to solving linear equations, so only need less computation time. If the efficient method of solving algebraic equations can also help reduce the duration of finite element analysis.Linear elastic finite element generally includes linear elastic statics analysis and linear elastic dynamics analysis from two aspects. The difference between the nonlinear problem and linear elastic problems:1) nonlinear equation is nonlinear, and iteratively solving of general;2) the nonlinear problem can't use superposition principle;3) nonlinear problem is not there is always solution, sometimes even no solution. Finite element to solve the nonlinear problem can be divided into the following three categories:1) material nonlinear problems of stress and strain is nonlinear, but the stress and strain is very small, a linear relationship between strain and displacement at this time, this kind of problem belongs to the material nonlinear problems. Due to theoretically also cannot provide the constitutive relation can be accepted, so, general nonlinear relations between stress and strain of the material based on the test data, sometimes, to simulate the nonlinear material properties available mathematical model though these models always have their limitations. More important material nonlinear problems in engineering practice are: nonlinear elastic (including piecewise linear elastic, elastic-plastic and viscoplastic, creep, etc.2) geometric nonlinear geometric nonlinear problems are caused due to the nonlinear relationship between displacement. When the object the displacement is larger, the strain and displacement relationship is nonlinear relationship. Research on this kind of problemIs assumes that the material of stress and strain is linear relationship. It consists of a large displacement problem of large strain and large displacement little strain. Such as the structure of the elastic buckling problem belongs to the large displacement little strain, rubber parts forming process for large strain.3) nonlinear boundary problem in the processing, problems such as sealing, the impact of the role of contact and friction can not be ignored, belongs to the highly nonlinear contact boundary. At ordinary times some contact problems, such as gear, stamping forming, rolling, rubber shock absorber, interference fit assembly, etc., when a structure and another structure or external boundary contact usually want to consider nonlinear boundary conditions. The actual nonlinear may appear at the same time these two or three kinds of nonlinear problems.Finite element theoretical basisFinite element method is based on variational principle and the weighted residual method, and the basic solving thought is the computational domain is divided into a finite number of non-overlapping unit, within each cell, select some appropriate nodes as solving the interpolation function, the differential equation of the variables in the rewritten by the variable or its derivative selected interpolation node value and the function of linear expression, with the aid of variational principle or weighted residual method, the discrete solution of differential equation. Using different forms of weight function and interpolation function, constitute different finite element methods. 1. The weighted residual method and the weighted residual method of weighted residual method of weighted residual method: refers to the weighted function is zero using make allowance for approximate solution of the differential equation method is called the weighted residual method. Is a kind of directly from the solution of differential equation and boundary conditions, to seek the approximate solution of boundary value problems of mathematical methods. Weighted residual method is to solve the differential equation of the approximate solution of a kind of effective method. Hybrid method for the trial function selected is the most convenient, but under the condition of the same precision, the workload is the largest. For internal method and the boundary method basis function must be made in advance to meet certain conditions, the analysis of complex structures tend to have certain difficulty, but the trial function is established, the workload is small. No matter what method is used, when set up trial function should be paid attention to are the following:(1) trial function should be composed of a subset of the complete function set. Have been using the trial function has the power series and trigonometric series, spline functions, beisaier, chebyshev, Legendre polynomial, and so on.(2) the trial function should have until than to eliminate surplus weighted integral expression of the highest derivative low first order derivative continuity.(3) the trial function should be special solution with analytical solution of the problem or problems associated with it. If computing problems with symmetry, should make full use of it. Obviously, any independent complete set of functions can be used as weight function. According to the weight function of the different options fordifferent weighted allowance calculation method, mainly include: collocation method, subdomain method, least square method, moment method and galerkin method. The galerkin method has the highest accuracy.Principle of virtual work: balance equations and geometric equations of the equivalent integral form of "weak" virtual work principles include principle of virtual displacement and virtual stress principle, is the floorboard of the principle of virtual displacement and virtual stress theory. They can be considered with some control equation of equivalent integral "weak" form. Principle of virtual work: get form any balanced force system in any state of deformation coordinate condition on the virtual work is equal to zero, namely the system of virtual work force and internal force of the sum of virtual work is equal to zero. The virtual displacement principle is the equilibrium equation and force boundary conditions of the equivalent integral form of "weak"; Virtual stress principle is geometric equation and displacement boundary condition of the equivalent integral form of "weak". Mechanical meaning of the virtual displacement principle: if the force system is balanced, they on the virtual displacement and virtual strain by the sum of the work is zero. On the other hand, if the force system in the virtual displacement (strain) and virtual and is equal to zero for the work, they must balance equation. Virtual displacement principle formulated the system of force balance, therefore, necessary and sufficient conditions. In general, the virtual displacement principle can not only suitable for linear elastic problems, and can be used in the nonlinear elastic and elastic-plastic nonlinear problem.Virtual mechanical meaning of stress principle: if the displacement is coordinated, the virtual stress and virtual boundary constraint counterforce in which they are the sumof the work is zero. On the other hand, if the virtual force system in which they are and is zero for the work, they must be meet the coordination. Virtual stress in principle, therefore, necessary and sufficient condition for the expression of displacement coordination. Virtual stress principle can be applied to different linear elastic and nonlinear elastic mechanics problem. But it must be pointed out that both principle of virtual displacement and virtual stress principle, rely on their geometric equation and equilibrium equation is based on the theory of small deformation, they cannot be directly applied to mechanical problems based on large deformation theory. 3,,,,, the minimum total potential energy method of minimum total potential energy method, the minimum strain energy method of minimum total potential energy method, the potential energy function in the object on the external load will cause deformation, the deformation force during the work done in the form of elastic energy stored in the object, is the strain energy.The convergence of the finite element method, the convergence of the finite element method refers to when the grid gradually encryption, the finite element solution sequence converges to the exact solution; Or when the cell size is fixed, the more freedom degree each unit, the finite element solutions tend to be more precise solution. Convergence condition of the convergence condition of the finite element finite element convergence condition of the convergence condition of the finite element finite element includes the following four aspects: 1) within the unit, the displacement function must be continuous. Polynomial is single-valued continuous function, sochoose polynomial as displacement function, to ensure continuity within the unit. 2) within the unit, the displacement function must include often strain. Total can be broken down into each unit of the state of strain does not depend on different locations within the cell strain and strain is decided by the point location of variables. When the size of the units is enough hours, unit of each point in the strain tend to be equal, unit deformation is uniform, so often strain becomes the main part of the strain. To reflect the state of strain unit, the unit must include the displacement functions often strain. 3) within the unit, the displacement function must include the rigid body displacement. Under normal circumstances, the cell for a bit of deformation displacement and displacement of rigid body displacement including two parts. Deformation displacement is associated with the changes in the object shape and volume, thus producing strain; The rigid body displacement changing the object position, don't change the shape and volume of the object, namely the rigid body displacement is not deformation displacement. Spatial displacement of an object includes three translational and three rotational displacement, a total of six rigid body displacements. Due to a unit involved in the other unit, other units do rigid body displacement deformation occurs will drive unit, thus, to simulate real displacement of a unit, assume that the element displacement function must include the rigid body displacement. 4) the displacement function must be coordinated in public boundary of the adjacent cell. For general unit of coordination is refers to the adjacent cell in public node have the same displacement, but also have the same displacement along the edge of the unit, that is to say, to ensure that the unit does not occur from cracking and invade the overlap each other. To do this requires the function on the common boundary can be determined by the public node function value only. For general unit and coordination to ensure the continuity of the displacement of adjacent cell boundaries. However, between the plate and shell of the adjacent cell, also requires a displacement of the first derivative continuous, only in this way, to guarantee the strain energy of the structure is bounded. On the whole, coordination refers to the public on the border between neighboring units satisfy the continuity conditions. The first three, also called completeness conditions, meet the conditions of complete unit is complete unit; Article 4 is coordination requirements, meet the coordination unit coordination unit; Otherwise known as the coordinating units. Completeness requirement is necessary for convergence, all four meet, constitutes a necessary and sufficient condition for convergence. In practical application, to make the selected displacement functions all meet the requirements of completeness and harmony, it is difficult in some cases can relax the requirement for coordination. It should be pointed out that, sometimes the coordination unit than its corresponding coordination unit, its reason lies in the nature of the approximate solution. Assumed displacement function is equivalent to put the unit under constraint conditions, the unit deformation subject to the constraints, this just some alternative structure compared to the real structure. But the approximate structure due to allow cell separation, overlap, become soft, the stiffness of the unit or formed (such as round degree between continuous plate unit in the unit, and corner is discontinuous, just to pin point) for the coordination unit, the error of these two effects have the possibility of cancellation, so sometimes use thecoordination unit will get very good results. In engineering practice, the coordination of yuan must pass to use "small pieces after test". Average units or nodes average processing method of stress stress average units or nodes average processing method of stress average units or nodes average processing method of stress of the unit average or node average treatment method is the simplest method is to take stress results adjacent cell or surrounding nodes, the average value of stress.1. Take an average of 2 adjacent unit stress. Take around nodes, the average value of stressThe basic steps of finite element method to solve the problemThe structural discretization structure discretization structure discretization structure discretization to discretization of the whole structure, will be divided into several units, through the node connected to each other between the units; 2. The stiffness matrix of each unit and each element stiffness matrix and the element stiffness matrix and the stiffness matrix of each unit (3) integrated global stiffness matrix integrated total stiffness matrix integrated overall stiffness matrix integrated total stiffness matrix and write out the general balance equations and write out the general balance equations and write out the general balance equations and write a general equation 4. Introduction of supporting conditions, the displacement of each node 5. Calculate the stress and strain in the unit to get the stress and strain of each cell and the cell of the stress and strain and the stress and strain of each cell.For the finite element method, the basic ideas and steps can be summarized as: (1) to establish integral equation, according to the principle of variational allowance and the weight function or equation principle of orthogonalization, establishment and integral expression of differential equations is equivalent to the initial-boundary value problem, this is the starting point of the finite element method. Unit (2) the area subdivision, according to the solution of the shape of the area and the physical characteristics of practical problems, cut area is divided into a number of mutual connection, overlap of unit. Regional unit is divided into finite element method of the preparation, this part of the workload is bigger, in addition to the cell and node number and determine the relationship between each other, also said the node coordinates, at the same time also need to list the natural boundary and essential boundary node number and the corresponding boundary value. (3) determine the unit basis function, according to the unit and the approximate solution of node number in precision requirement, choose meet certain interpolation condition basis function interpolation function as a unit. Basis function in the finite element method is selected in the unit, due to the geometry of each unit has a rule in the selection of basis function can follow certain rules. (4) the unit will be analysis: to solve the function of each unit with unit basis functions to approximate the linear combination of expression; Then approximate function generation into the integral equation, and the unit area integral, can be obtained with undetermined coefficient (i.e., cell parameter value) of each node in the algebraic equations, known as the finite element equation.(5) the overall synthesis: after the finite element equation, the area of all elements inthe finite element equation according to certain principles of accumulation, the formation of general finite element equations. (6) boundary condition processing: general boundary conditions there are three kinds of form, divided into the essential boundary conditions (dirichlet boundary condition) and natural boundary conditions (Riemann boundary conditions) and mixed boundary conditions (cauchy boundary conditions). Often in the integral expression for natural boundary conditions, can be automatically satisfied. For essential boundary conditions and mixed boundary conditions, should be in a certain method to modify general finite element equations satisfies. Solving finite element equations (7) : based on the general finite element equations of boundary conditions are fixed, are all closed equations of the unknown quantity, and adopt appropriate numerical calculation method, the function value of each node can be obtained.有限元分析有限元法求解区域是由许多小的节点连接单元（域），该模型给出了切分的基本方程（子域名）的近似解，由于单位（域）可以分为不同的形状和大小不同的尺寸，所以它能很好的适应复杂的几何形状、材料特性和边界条件复杂，复杂有限元模型：它是真实系统的理想化的数学抽象。
ANSYS有限元分析外文文献翻译、中英文翻译
附录1：外文翻译CAE的技术种类有很多，其中包括有限元法,边界元法,有限差法等。
每一种方法各有其应用的领域，而其中有限元法应用的领域越来越广，现已应用于结构力学、结构动力学、热力学、流体力学、电路学、电磁学等。
ANSYS软件是融结构、流体、电场、磁场、声场分析于一体的大型通用有限元分析软件。
由世界上最大的有限元分析软件公司之一的美国ANSYS开发，它能与多数CAD软件接口，实现数据的共享和交换，如Pro/Engineer, NASTRAN, Alogor, I－DEAS, AutoCAD等，是现代产品设计中的高级CAE工具之一。
ANSYS有限元软件包是一个多用途的有限元法计算机设计程序，可以用来求解结构、流体、电力、电磁场及碰撞等问题。
因此它可应用于以下工业领域：航空航天、汽车工业、生物医学、桥梁、建筑、电子产品、重型机械、微机电系统、运动器械等。
有限元分析（FEA，Finite Element Analysis）的基本概念是用较简单的问题代替复杂问题后再求解。
它将求解域看成是由许多称为有限元的小的互连子域组成，对每一单元假定一个合适的(较简单的）近似解，然后推导求解这个域总的满足条件(如结构的平衡条件），从而得到问题的解。
这个解不是准确解，而是近似解，因为实际问题被较简单的问题所代替。
由于大多数实际问题难以得到准确解，而有限元不仅计算精度高，而且能适应各种复杂形状，因而成为行之有效的工程分析手段。
有限元是那些集合在一起能够表示实际连续域的离散单元。
有限元的概念早在几个世纪前就已产生并得到了应用，例如用多边形（有限个直线单元）逼近圆来求得圆的周长，但作为一种方法而被提出，则是最近的事。
有限元法最初被称为矩阵近似方法，应用于航空器的结构强度计算，并由于其方便性、实用性和有效性而引起从事力学研究的科学家的浓厚兴趣。
经过短短数十年的努力，随着计算机技术的快速发展和普及，有限元方法迅速从结构工程强度分析计算扩展到几乎所有的科学技术领域，成为一种丰富多彩、应用广泛并且实用高效的数值分析方法。
有限元分析报告报告材料英文文献
有限元分析报告报告材料英文文献The Basics of FEA Procedure有限元分析程序的基本知识2.1 IntroductionThis chapter discusses the spring element, especially for the purpose of introducing various concepts involved in use of the FEA technique.本章讨论了弹簧元件，特别是用于引入使用的有限元分析技术的各种概念的目的A spring element is not very useful in the analysis of real engineering structures; however, it represents a structure in an ideal form for an FEA analysis. Spring element doesn’t require discretization (division into smaller elements) and follows the basic equation F = ku.在分析实际工程结构时弹簧元件不是很有用的;然而,它代表了一个有限元分析结构在一个理想的形式分析。
弹簧元件不需要离散化(分裂成更小的元素)只遵循的基本方程F = ku We will use it solely for the purpose of developing an understanding of FEA concepts and procedure.我们将使用它的目的仅仅是为了对开发有限元分析的概念和过程的理解。
2.2 Overview概述Finite Element Analysis (FEA), also known as finite element method (FEM) is based on the concept that a structure can be simulated by the mechanicalbehavior of a spring in which the applied force is proportional to the displacement of the spring and the relationship F = ku is satisfied.有限元分析(FEA),也称为有限元法(FEM)，是基于一个结构可以由一个弹簧的力学行为模拟的应用力弹簧的位移成正比,F = ku切合的关系。
外文翻译--有限元分析软件的发展
中文3240字Steps in Finite Element AnalysisIntroductionRecently there is a trend towards using it in the early stages of design. A designer may use FEA just to validate the structural integrity of a design or she may use it for structural optimization along with the parametrized design techniques.This paper examines the requirements of a structural analysis agent and proposes an architecture to facilitate FEA in a concurrent design environment. The next section briefly describes how FEA is used in a typical industrial set up.Section 3 presents a survey of existing FE tools. Section 4 discusses some issues related to the development of an FEA agent. Section 5 proposes an architecture for the FEA agent that addresses the issues described in Section 4 and finally Section 6 presents the concluding remarks.Steps in Finite Element AnalysisThe process of FEA starts with identification of the region of interest and the formulation of the physical problem。
有限元分析报告
有限元分析报告1. 引言有限元分析（Finite Element Analysis）是一种数值计算方法，用于求解工程和科学领域中的复杂问题。
它利用离散化技术将连续问题转化为离散问题，并应用数值算法进行求解。
本报告将主要介绍有限元分析的基本原理、应用和分析结果。
2. 有限元分析基本原理有限元分析的基本原理是将求解区域划分为互不重叠的有限个小单元，并将问题转化为在每个小单元内求解。
这些小单元通常为简单的几何形状，如三角形或四边形。
然后，在每个小单元内应用适当的数学模型和力学方程，得到相应的微分方程。
接着，通过对每个小单元的微分方程进行积分，并利用边界条件和连续性条件，得到整个求解区域的离散形式。
最后，通过求解离散形式的方程组，得到整个系统的解。
3. 有限元分析应用有限元分析在工程领域有着广泛的应用。
以下是几个典型的应用案例：3.1 结构分析有限元分析在结构分析中的应用非常广泛，可以用于确定结构的强度和刚度，评估结构的安全性，并进行结构优化设计。
通过对结构施加正确的边界条件和加载条件，可以得到结构的应力、应变和变形等重要信息。
3.2 流体力学分析有限元分析在流体力学分析中的应用可以用于模拟流体的流动和传热过程，例如气体和液体的流动、传热设备的设计优化等。
通过分析流体系统的流速、压力和温度等参数，可以对流体系统的性能和行为进行合理评估。
3.3 热力学分析有限元分析在热力学分析中的应用可以用于分析和优化热传导、热辐射和热对流等热问题。
通过模拟物体的温度分布和热流动，可以评估物体的热性能和热耗散效果。
4. 有限元分析结果有限元分析的计算结果可以提供丰富的信息，帮助工程师和科学家理解和优化系统的行为和性能。
以下是一些常见的有限元分析结果：4.1 应力分布通过有限元分析，可以得到结构或部件内的应力分布情况。
这对于评估结构的强度和安全性非常重要，并可以指导优化设计。
4.2 变形分析有限元分析可以给出结构或部件的变形情况。
有限元分析软件外文翻译
南京林业大学本科毕业设计（论文）外文资料翻译翻译资料名称(外文)Stress analysis of heavy duty truck chassis as apreliminary data for its fatigue life predictionusing FEM翻译资料名称(中文)利用重型载货汽车的有限元应力分析的初步数据预测其疲劳寿命院（系）：汽车与交通工程学院专业：机械制造及其自动化（汽车设计方向）姓名：学号：指导教师：完成日期： 2012/5/31利用重型载货汽车的有限元应力分析的初步数据预测其疲劳寿命Roslan Abd Rahman, Mohd Nasir Tamin, Ojo Kurdi马来西亚工程大学机械工程系81310 UTM, Skudai,Johor Bahru摘要本文对一重型货车底盘做了应力分析。
应力分析能够确定零件的最大受力点，是分析零部件疲劳研究和寿命预测的重要手段。
前人已有用商用有限元软件ABAQUS软件对底盘模型进行分析的。
本次研究的底盘长12.35米，宽2.45米，材料是ASTM低合金钢710（3级），屈服极限552MPa，抗拉强度620MPa。
分析结果显示，最大应力点出现在底盘与螺栓连接的空缺处，最大应力为386.9MPa，底盘的疲劳破坏将会从最大应力点开始向车架各部位蔓延。
关键字：应力分析，疲劳寿命预测，货车底盘1.0简介在马来西亚，很多货车的车架寿命都有20多年，20多年架就会有使用安全的问题。
因此，为了确保底盘在工作期间的安全性能，就有必要对底盘作疲劳研究和寿命预测。
利用有限元法作应力分析能够确定受最大应力的关键点，这个关键点是导致底盘疲劳损伤的因素之一。
应力的大小能够预测底盘的寿命，所以可以根据应力分析的结果精确地预测底盘的寿命，应力分析越精确，底盘寿命预测的越合理。
本文是用商用有限元软件ABAQUS 软件完成底盘应力分析的。
汽车工业（汽车总成及各部件）在马来西亚的工业中占据非常重要的地位。
有限元分析法范文
有限元分析法范文有限元分析法（Finite Element Analysis，FEA）是一种工程分析方法，用于解决复杂结构受力、变形等问题。
它将连续体分割为有限数量的小单元，通过数学模型和计算机技术，求解每个小单元上的力学性质，进而得到整个结构的力学行为。
有限元分析法在工程领域得到广泛应用，包括航空、航天、汽车、建筑、电子等各个领域。
有限元分析法最早出现于上世纪50年代，其核心思想是将复杂结构划分为有限个简单的几何单元，如三角形、四边形、六面体等。
每个单元上的位移、应力、应变等力学性质可以通过数学方程描述。
结构中的任何物理量，如位移、应力、应变、温度等，都可以用有限元的方式离散化，最终转化为一个非线性的矩阵方程组。
解得这个方程组，可以得到结构的力学行为。
1.建立几何模型：根据实际问题，使用计算机辅助设计软件建立结构的几何模型。
模型必须准确地描述结构的形状和尺寸。
2.场问题导入：根据结构特征和受力情况，选择合适的力学方程和边界条件，将场问题转化为一个数学问题。
3.离散化：将结构分割为有限个小单元，每个小单元通过一组节点连接。
根据每个小单元上的力学特性，建立相应的数学模型。
4.建立整体刚度矩阵：将每个小单元的刚度矩阵组合成整个结构的刚度矩阵。
这个矩阵描述了结构不同部分之间的约束关系。
5.施加边界条件：对于有固定边界的结构，需要施加相应的边界条件。
这些边界条件包括位移、力、固约束等。
6.求解方程组：通过数值计算方法解线性方程组，得到结构的位移、应力等力学性质。
7.后处理：根据求解结果，绘制位移云图、应力云图、应变云图等，分析结构的强度、刚度、稳定性等。
有限元分析法的优势在于对复杂结构的分析能力，使得工程师可以在设计阶段快速了解结构的强度、刚度、稳定性等。
它可以对结构进行多次迭代和优化，加快设计周期，减少试验次数，节约成本。
此外，有限元分析法还可以考虑非线性和动态载荷情况，对结构的疲劳寿命、震动响应等进行预测和分析。
有限元与CAE技术
4）剪应力互等定律 作用在两个互相垂直的面上并且垂直于该两面交线的剪应力是互等的。(大小相等，正负 号也相同)。因此剪应力记号的两个角码可以对调。
2.应变的概念（物体的变形程度） 变形体：在外力的作用下。若物体内任意两点之间发生相对位移，这样的物体叫做边形体， 它与材料的物理性质密切相关。 1.应变：体素的变形可以分为两类：一类是长度的变化，一类是角度的变化。 （1）线应变(或称正应变)：任一线素的长度的变化与原有长度的比值。 用符号 ε 来表示。沿坐标轴的线应变，则加上相应的角码，分别用εx、εy、εz来表示。当线 素伸长时，其线应变为正。反之，线素缩短时，其线应变为负。这与正应力的正负号规定 相对应。
1、平面应力问题
厚度为t的很薄的均匀木板。只在边缘上受到平行于板面且不沿厚度变化 的面力，同时，体力也平行于板面且不沿厚度变化。 以薄板的中面为xy面，以垂直于中面的任一直线为Z轴。由于薄板两表面 上没有垂直和平行于板面的外力，所以板面上各点均有：
另外由于平板很薄，外力又不沿厚度变化， 可认为在整个薄板内各点均有：
以平面问题的三角形 3 结点单元为例。如图 1-15 所示，单元有三个结点 I、J、M，每 个结点有两个位移 u、v 和两个结点力 U、V。
图 1-15 三角形 3 结点单元
建立结点位移与结点力之间的转换关系
转换矩阵[K]称为单元刚度矩阵。单元分析的主要目的就是要求出单元刚度矩阵。
3.整体分析 对由各个单元组成的整体进行分析，建立节点外载荷与结点位移的关系，以解出结点 位移，这个过程为整体分析。将离散化了的各个单元合成整体结构，利用结点平衡方 程求出结点位移。在位移法中，主要的任务是求出基本未知量---结点位移。为此需要 建立结点的平衡方程。例如在自重作用下的等截面直杆中，我们建立力学平衡方程， 通过解方程组可以得到问题的求解。
汽车安全气囊碰撞有限元分析外文翻译
FINITE ELEMENT ANALYSIS OF AUTOMOBILE CRASH SENSORS FOR AIRBAG SYSTEMSABSTRACTAutomobile spring bias crash sensor design time can be significantly reduced by using finite element analysis as a predictive engineering tool.The sensors consist of a ball and springs cased in a plastic housing.Two important factors in the design of crash sensors are the force-displacement response of the sensor and stresses in the sensor springs. In the past,sensors were designed by building and testing prototype hardware until the force-displacement requirements were met. Prototype springs need to be designed well below the elastic limit of the ing finite element analysis, sensors can be designed to meet forcedisplacement requirements with acceptable stress levels. The analysis procedure discussed in this paper has demonstrated the ability to eliminate months of prototyping effort.MSC/ABAQUS has been used to analyze and design airbag crash sensors.The analysis was geometrically nonlinear due to the large deflections of the springs and the contact between the ball and springs. Bezier 3-D rigid surface elements along with rigid surface interface (IRS) elements were used to model ball-to-springcontact.Slideline elements were used with parallel slideline interface (ISL) elements for spring-to-spring contact.Finite element analysis results for the force-displacement response of the sensor were in excellent agreement with experimental results.INTRODUCTIONAn important component of an automotive airbag system is the crash sensor. Various types of crash sensors are used in airbag systems including mechanical,electro-mechanical, and electronic sensors. An electro-mechanical sensor (see Figure 1) consisting of a ball and two springs cased in a plastic housing is discussed in thispaper. When the sensor experiences a severe crash pulse, the ball pushes two springs into contact completing the electric circuit allowing the airbag to fire. Theforce-displacement response of the two springs is critical in designing the sensor to meet various acceleration input requirements. Stresses in the sensor springs must be kept below the yield strength of the spring material to prevent plastic deformation in the springs. Finite element analysis can be used as a predictive engineering tool to optimize the springs for the desired force-displacement response while keeping stresses in the springs at acceptable levels.In the past, sensors were designed by building and testing prototype hardware until the forcedisplacement requirements were met. Using finite element analysis, the number of prototypes built and tested can be significantly reduced, ideally to one, which substantially reduces the time required to design a sensor. The analysis procedure discussed in this paper has demonstrated the ability to eliminate months of prototyping effort.MSC/ABAQUS [1] has been used to analyze and design airbag crash sensors. The analysis was geometrically nonlinear due to the large deflections of the springs and the contact between the ball and springs. Various contact elements were used in this analysis including rigid surface interface (IRS) elements, Bezier 3-D rigid surface elements, parallel slide line interface (ISL) elements, and slide line elements. The finite element analysis results were in excellent agreement with experimental results for various electro-mechanical sensors studied in this paper.PROBLEM DEFINITIONThe key components of the electro-mechanical sensor analyzed are two thin metallic springs (referred to as spring1 and spring2) which are cantilevered from a rigid plastic housing and a solid metallic ball as shown in Figure 1. The plastic housing contains a hollow tube closed at one end which guides the ball in the desired direction. The ball is held in place by spring1 at the open end of the tube. When the sensor is assembled, spring1 is initially displaced by the ball which creates a preload on spring1. The ball is able to travel in one direction only in this sensor and this direction will be referredto as the x-direction (see the global coordinate system shown in Figure 2) in this paper. Once enough acceleration in the x-direction is applied to overcome the preload on spring1, the ball displaces the spring. As the acceleration applied continues to increase, spring1 is displaced until it is in contact with spring2. Oncethe sensor to perform its function within the airbag system.FINITE ELEMENT ANALYSIS METHODOLOGYWhen creating a finite element representation of the sensor, the following simplifications can be made. The two springs can be fully restrained at their bases implying a perfectly rigid plastic housing. This is a good assumption when comparing the flexibility of the thin springs to the stiff plastic housing. The ball can be represented by a rigid surface since it too is very stiff as compared to the springs. Rather than modeling the contact between the plastic housing and the ball, all rotations and translations are fully restrained except for the xdirection on the rigidsurface representing the ball. These restraints imply that the housingwill have no significant deformation due to contact with the ball. These restraints also ignore any gaps due to tolerances between the ball and the housing. The effect of friction between the ball and plastic is negligible in this analysis.The sensor can be analyzed by applying an enforced displacement in the x-direction to the rigid surface representing the ball to simulate the full displacement of the ball. Contact between the ball and springs is modeled with various contact elements as discussed in the following section. A nonlinear static analysis is sufficient to capture the force-displacement response of the sensor versus using a more expensive and time consuming nonlinear transient analysis. Although the sensor is designed with a ball mass and spring stiffness that gives the desired response to a given acceleration, thereis no mass associated with the ball in this static analysis. The mass of the ball can be determined by dividing the force required to deflect the springs by the acceleration input into the sensor.MeshThe finite element mesh for the sensor was constructed using MSC/PATRAN [2]. The solver used to analyze the sensor was MSC/ABAQUS. The finite element mesh including the contact elements is shown in Figure 2. The plastic housing was assumed to be rigid in this analysis and was not modeled. Both springs were modeled with linear quadrilateral shell elements with thin shell physical properties. The ball was assumed to be rigid and was modeled with linear triangular shell elements with Bezier 3-D rigid surface properties.To model contact between the ball and spring1, rigid surface interface (IRS) elements were used in conjunction with the Bezier 3-D rigid surface elements making up the ball. Linear quadrilateral shell elements with IRS physical properties were placed on spring1 and had coincident nodes with the quadrilateral shell elements making up spring1. The IRS elements were used only in the region of ball contact.To model contact between spring1 and spring2, parallel slide line interface (ISL) elements were used in conjunction with slide line elements. Linear bar elements with ISL physical properties were placed on spring1 and had coincident nodes with the shell elements on spring1. Linear bar elements with slide line physical properties were placed on spring2 and had coincident nodes with the shell elements making up spring2.MaterialBoth spring1 and spring2 were thin metallic springs modeled with a linear elastic material model. No material properties were required for the contact or rigid surface elements.Boundary ConditionsBoth springs were assumed to be fully restrained at their base to simulate a rigid plastichousing. An enforced displacement in the x-direction was applied to the ball. The ball wasfully restrained in all rotational and translational directions with the exception of the xdirection translation. Boundary conditions for the springs and ball are shown in Figure 2.DISCUSSIONTypical results of interest for an electro-mechanical sensor would be the deflected shape of the springs, the force-displacement response of the sensor, and the stress levels in the springs. Results from an analysis of the electro-mechanical sensor shown in Figure 2 will be used asfull ball travel. Looking at the deflected shape of the springs can provide insight into the performance of the sensor as well as aid in the design of the sensor housing.Stresses in the springs are important results in this analysis to ensure stress levels in the springs are at acceptable levels. Desired components of stress can be examined through various means including color contour plots. One of the most important results from the analysis is the force-displacement response for the sensor shown in Figure 4. From this force-displacement response, the force required to push spring1 into contact with spring2 can readily be determined. This force requirement can be used with a given acceleration to determine the mass required for the ball. Based on these results, one or more variations of several variables such as spring width, spring thickness, ball diameter, and ball material can be updated until the force-displacement requirements are achieved within a desired accuracy.A prototype of the sensor shown in Figure 2 was constructed and tested to determine its actual force-displacement response. Figure 4 shows the MSC/ABAQUS results along with the experimental results for the force-displacement response of the sensor. There was an excellent correlation between finite element and experimental results for this sensor as well asfor several other sensors examined. Table 1 shows the difference in percent between finite element and experimental results including force at preload on spring1, force at spring1-tospring2 contact, and force at full ball travel for two sensor configurations. Sensor A in Table 1 is shown in Figure 1. Sensor B in Table 1 is based on the sensor shown in Figure 2.The sensor model analyzed in this paper was also analyzed with parabolic quadrilateral and bar elements to ensure convergence of the solution.Force-displacement results converged to less than 1% using linear elements. The stresses in the springs for this sensor converged to within 10% for the linear elements. The parabolic elements increased solve time by more than an order of magnitude over the linear elements. With more complex spring shapes, a denser linear mesh or parabolic elements used locally in areas of stress concentrations would be necessary to obtain more accurate stresses in the springs.Notes: 1. Sensor A results are based on 1 prototype manufactured and tested. Sensor Bexperimental results are based on the average of 20 prototypesmanufacturedand tested.2. No experimental data for force at full ball travel for Sensor A.3. %Difference=(FEA Result - Experimental Result)/Experimental ResultCONCLUSIONSMSC/ABAQUS has been used to analyze and design airbag crash sensors. The finite element analysis results were in excellent agreement with experimental results for several electromechanical sensors for which prototypes were built and tested. Using finite element analysis, sensors can be designed to meet force-displacement requirements with acceptable stress levels. The analysis procedure discussed in this paper has demonstrated the ability to eliminate months of prototyping effort. This paper has demonstrated the power of finite element analysis as a predictive engineering tool even with the use of multiple contact element types.汽车安全气囊系统撞击传感器的有限单元分析摘要：汽车弹簧碰撞传感器可以利用有限单元分析软件进行设计，这样可以大大减少设计时间。
文献翻译—有限元概述
附录B.英文文献There are many types of CAE technology, including the finite element method, boundary element method, finite difference method. Each method has its own application areas, of which the application of finite element method more and more areas, has been used in structural mechanics, structural dynamics, thermodynamics, fluid mechanics, circuit theory, electromagnetism and so on.ANSYS software is the financial structure, fluid, electric field, magnetic field, acoustic field analysis in one large-scale finite element analysis software. By the world's largest finite element analysis software ANSYS, one of the United States developed it with most CAD software interface for data sharing and exchange, such as Pro / Engineer, NASTRAN, Alogor, I-DEAS, AutoCAD, are modern Advanced CAE product design tools.ANSYS finite element package is a multi-purpose finite element method for computer design program, can be used to solve the structure, fluid, electricity, electromagnetic fields and collision issues. So it can be applied to the following industries: aerospace, automotive, biomedical, bridges, construction, electronics, heavy machinery, micro-electromechanical systems, sports equipment, etc..Finite Element Analysis (FEA，Finite Element Analysis) of the basic concept is tore-place the relatively simple problem to solve complex problems later. As it will solve the do-main is composed of many small-called finite element subdomain interconnection compone-nts，assuming that each unit of an appropriate (relatively simple) approximate solution，and then derived the general solution of the domain satisfy the conditions (such as balanced con-ditions)，thus the solution of the problem. This solution is not exact solutions，but appro-ximate solution，since the actual problem is relatively simple to replace the problem. Since most practical problems it is difficult to be accurate solution，while finite element is not only high accuracy but also to adapt to a variety of complex shapes，thereby becoming an effective means of engineering analysis.FEM together those who are able to express the actual domain for the discrete element. The concept of the finite element as early as several centuries ago and have been applied，for example，polygon (a finite number of straight-line unit) to get close to circle thecir-cumference of a circle，but as a way to be made，it is the most recent matter. Finite ele-ment method was originally known as the matrix approximation method，the structural strength of aircraft used in the calculation，and because of its convenience，practicality and effectiveness arising from research scientists to engage in mechanical interest. Through the efforts of just a few decades，with the rapid development of computer technology and the popularity of the finite element method in structural engineering fromthe intensity of the rapid analysis extended to almost all areas of science and technology，become a rich and colorful，practical and efficient application of a wide range of numerical analysis.Finite element method with other methods of solving the boundary value problemsimil-ar to the fundamental difference is that the approximation of it is limited to relatively small sub-domain. 60 In the early 20th century structure was first proposed the concept of the finite element calculation of Clough (Clough)，Professor vividly describes as: "The finite element method + = Rayleigh Ritz method piecewise function"，that is，the finite element method is the Rayleigh Ritz method a localized situation. Different from the solution of (often difficult) to satisfy the boundary conditions of the definition of domain function to allow the Rayleigh Ritz method，finite element method will be defined in a simple function of geometry (such as two-dimensional problem of arbitrary quadrilateral or triangle) on the unit domain ( piecewise function)，the definition does not consider the whole domain of the complex boundary conditions，this is the finite element method is superior to other similar methods of one of the reasons why.Different physical properties and mathematical models of the problem，finite element method to solve the basic steps are the same，only the specific formula to solve a different derivation and computation. Finite Element Analysis of the basic steps are as follows: The first step: the definition of the problem and solution domain: In accordance with the actual problem solving domain approximation to determine the physical properties and geometry of the region.The second step: Solving domain discretization: The approximate solution of the domain with different size and shape of a limited and linked to each other unit，composed of afin-ite number of discrete domains，the habit of division as the finite element network. Obvio-usly the smaller the unit (the finer t he network) is similar to the level of discrete domain，the better，the more accurate results，but the calculation of the volume and error will be larger，so to solve the discrete domain is the finite element method，one of the core tech-nology.The third step: to determine the state variables and control method: a specific physical problem can usually be handled by a group of state variables include the issue of boundary conditions that the differential equations for the finite element for solving differentialequa-tions are usually translated into the functional equivalent forms of .Step four: unit derived: on the unit to construct a suitable approximate solution，that is derived out of the finite element type，including a reasonable choice of coordinate system units，the establishment of unit test function，to one way or another unit of the stateva-riables given the discrete relations to form the unit matrix (the structure of said mechani-cal stiffness or flexibility matrix array).In order to ensure the convergence of problem solving，there are many principlesde-rived units to follow. In terms of engineering applications，it is important to payatten-tion to each unit of problem-solving performance and constraints. For example，the unit should be based on the rules for shape，and deformed not only low-precision，but also the risk of missing rank，will result in failure to solve.Step five: Solution assembly: assembly to form a discrete unit of the total domain matrix equation (Joint equations)，reflecting the approximate solution of the discrete domain the request domain，that is，the continuity of function modules to meet the conditions for cer-tain. Assembly unit in the adjacent node，the state variables and their derivatives (if possib-le) to establish continuity in the junction point.Sixth step: solving simultaneous equations and the results of the interpretation: the finite element method eventually lead to simultaneous equations. Simultaneous equations can be used to solve the direct method，the election law and the random generation method. Solv-ing a result，the state Department unit node approximation variables. The results for the quality and design guidelines will be provided to allow values to evaluate and determine the need for double-counting.In short，the finite element analysis can be divided into three stages，pre-treatment，processing and post-processing. Pre-processing finite element model is built to complete the unit mesh; post-processing is the acquisition and processing the results of the analysis，a-lows users to extract information easy to understand results.In practice，the finite element method is usually composed of three main steps:1，pre-processing: the user object to be analyzed to establish part of the model，in this model，the geometry of the part being cut into several discrete sub-region - otherwise known as "modules." In some of the modules referred to as "nodes" of the discrete points connected with each other. Some of these nodes are fixed displacement，while the remaining loads are given. Prepare such a model could be extremely time-consuming process is why the commercial competition between the lies: how to use the most friendly graphical inter-face of the "pre-processing module"，to help users complete the tedious work of boring. Some pre-processing module as a computerized drawing and an integral part of the de-ign process，can be pre-existing CAD file grid coverage，which can be easily completed by Finite Element Analysis.2，Analysis: the pre-processing module prepared data into finite element program,andthus constitutes a solution of linear or nonlinear system of algebraic equations thatKij * Uj = FiWhere u and f，respectively，for each node of the displacement and the role of external forces. Matrix form of K depend on the type of problem solving，the module will outline the truss with the linear elastic stress analysis. Business procedures may carry a very large library，the different types of unit s applicable to a wide range of various problems. Finite element method is one of the main advantages of: Many different types of problems are available to deal with the same procedure，the difference is only specified from the cell library for the problem in different cell types.3，post-processing: In the early finite element analysis，users need to carefully study the procedures for computing a large number of figures after，that is，the model set out in the discrete position of the displacement and stress. This method is easy to miss important trends and hot spots，and the latest graphics processing to be use to help the usercom-puting the results of direct observation. Typical post-processing module can display the model across the color line graph of stress for different stress levels，indicating the entire stress field is similar to the images or Photoelasticity moire results.附录C.中文翻译CAE的技术种类有很多，其中包括有限元法,边界元法,有限差法等。
proe有限元分析
proe有限元分析有限元分析（finite element analysis，FEA）是一种广泛应用于工程领域的数值计算方法。
它在解决复杂结构工程问题中发挥着重要的作用。
所谓有限元，是指将连续结构离散成很多个小单元，每个小单元被称为有限元。
有限元分析就是通过有限元的集合来近似连续结构，从而求解问题的方法。
有限元分析的基本思想是将复杂的物理问题转化为数学模型，然后利用数值计算的方法进行求解。
它的核心是将结构分成许多小单元，每个小单元内的位移和应力都可以通过简单的方程求解。
这些小单元的集合构成了整个结构，通过求解每个小单元之间的相互作用，得到整个结构的力学行为。
有限元分析可分为离散、连续两个步骤。
首先，将连续结构划分为若干有限元，每个有限元内部满足一定的形状函数，这些函数表示位移场在该有限元内的分布。
然后，在每个有限元内，根据位移场和边界条件，得到各个单元上的线性方程。
由此可得到整个结构的刚度矩阵和载荷向量。
最后，通过求解线性方程，得到位移和应力的数值解。
有限元分析的主要优点是可以处理各种不规则的结构和复杂的边界条件。
它可以有效地模拟结构的力学行为，并得到精确的数值解。
因此，在工程领域应用广泛，可用于分析和设计各种结构，包括建筑、桥梁、飞机、汽车等。
有限元分析的应用范围非常广泛。
例如，在工程设计中，可以使用有限元分析来评估结构的承载能力，确定合适的材料和尺寸。
在机械设计中，可以利用有限元分析来优化零件的形状和布局，减少材料的使用量和减轻结构的重量。
在热传导和流体力学领域，有限元分析可以用于模拟热传导和流体流动的过程，预测结构的温度和流场分布。
当然，有限元分析也存在一些局限性。
对于大型结构和复杂问题，计算量非常大，需要高性能计算设备和较长的计算时间。
另外，在分析过程中需要合理选择有限元的类型和网格划分，否则会对结果产生较大的误差。
此外，有限元分析只是一种数值解法，结果还需要通过实验验证。
总之，有限元分析是一种强大的工程分析工具，通过将连续结构离散化，可以有效地模拟结构的力学行为。
ADAMS有限元分析
ADAMS有限元分析1. 简介ADAMS（Automatic Dynamic Analysis of Mechanical Systems，机械系统动力学的自动化分析）是一种在机械工程领域广泛使用的有限元分析软件。
它可以模拟机械系统的动力学行为，帮助工程师在设计过程中评估系统的性能和可靠性。
ADAMS通过利用有限元方法和动力学模型，可以模拟复杂机械系统的运动、振动、应力和变形等物理效应，并提供全面的分析结果。
2. 工作原理ADAMS的分析过程基于有限元方法和动力学模型。
有限元方法是一种常用的数值计算方法，将连续体划分为大量的小单元，通过计算每个单元的相互作用，得到整个系统的响应。
动力学模型是一种描述物体在力的作用下随时间演化的模型，用于分析物体的力学行为。
在ADAMS中，用户首先需要建立机械系统的几何模型。
这可以通过绘制各个零件的几何形状或导入CAD模型来实现。
然后，用户需要给每个零件分配材料属性和初始条件，以便ADAMS能够正确计算物体的应力和变形。
接下来，用户需要定义系统的边界条件和加载条件，以模拟实际工作环境中的力和约束。
ADAMS会根据用户提供的信息自动生成有限元网格，并根据动力学模型进行求解。
求解过程中，ADAMS会考虑材料的力学性质、物体的自由度、力的作用点和作用方向等因素，计算出物体在给定时间内的运动状态、应力分布和变形情况。
3. 功能与应用ADAMS提供了丰富的功能和工具，适用于各种机械系统的分析和设计。
以下是ADAMS的主要功能和应用：3.1 动态仿真ADAMS可以模拟机械系统在不同加载条件下的动态响应。
用户可以通过改变加载条件、调整系统参数和观察运动轨迹等方式，评估系统的动态性能、优化设计和改进操作。
3.2 振动分析ADAMS可以对机械系统的振动特性进行分析。
用户可以计算系统的固有频率、模态形式和振动衰减情况，以评估系统的结构稳定性和振动抑制。
3.3 应力分析ADAMS可以计算机械系统中零件和结构的应力分布。
机器人机构优化设计有限元分析毕业论文中英文资料对照外文翻译文献综述
机器人机构优化设计有限元分析中英文资料对照外文翻译文献综述FEM Optimization for Robot StructureAbstractIn optimal design for robot structures, design models need to he modified and computed repeatedly. Because modifying usually can not automatically be run, it consumes a lot of time. This paper gives a method that uses APDL language of ANSYS 5.5 software to generate an optimal control program, which mike optimal procedure run automatically and optimal efficiency be improved.1）IntroductionIndustrial robot is a kind of machine, which is controlled by computers. Because efficiency and maneuverability are higher than traditional machines, industrial robot is used extensively in industry. For the sake of efficiency and maneuverability, reducing mass and increasing stiffness is more important than traditional machines, in structure design of industrial robot.A lot of methods are used in optimization design of structure. Finite element method is a much effective method. In general, modeling and modifying are manual, which is feasible when model is simple. When model is complicated, optimization time is longer. In the longer optimization time, calculation time is usually very little, a majority of time is used for modeling and modifying. It is key of improving efficiency of structure optimization how to reduce modeling and modifying time.APDL language is an interactive development tool, which is based on ANSYS and is offered to program users. APDL language has typical function of some large computer languages. For example, parameter definition similar to constant and variable definition, branch and loop control, and macro call similar to function and subroutine call, etc. Besides these, it possesses powerful capability of mathematical calculation. The capability of mathematical calculation includes arithmetic calculation, comparison, rounding, and trigonometric function, exponential function and hyperbola function of standard FORTRAN language, etc. By means of APDL language, the data can be read and then calculated, which is in database of ANSYS program, and running process of ANSYS program can be controlled.Fig. 1 shows the main framework of a parallel robot with three bars. When the length of three bars are changed, conjunct end of three bars can follow a given track, where robot hand is installed. Core of top beam is triangle, owing to three bars used in the design, which is showed in Fig.2. Use of three bars makes top beam nonsymmetrical along the plane that is defined by two columns. According to a qualitative analysis from Fig.1, Stiffness values along z-axis are different at three joint locations on the top beam and stiffness at the location between bar 1 and top beam is lowest, which is confirmed by computing results of finite element, too. According to design goal, stiffness difference at three joint locations must he within a given tolerance. In consistent of stiffness will have influence on the motion accuracy of the manipulator under high load, so it is necessary to find the accurate location of top beam along x-axis.To the questions presented above, the general solution is to change the location of the top beam many times, compare the results and eventually find a proper position, The model will be modified according to the last calculating result each time. It is difficult to avoid mistakes if the iterative process is controlled manually and the iterative time is too long. The outer wall and inner rib shapes of the top beam will be changed after the model is modified. To find the appropriate location of top beam, the model needs to be modified repetitiously.Fig. 1 Solution of Original DesignThis paper gives an optimization solution to the position optimization question of the top beam by APDL language of ANSYS program. After the analysis model first founded, the optimization control program can be formed by means of modeling instruction in the log file. The later iterative optimization process can be finished by the optimization control program and do not need manual control. The time spent in modifying the model can be decreased to the ignorable extent. The efficiency of the optimization process is greatly improved.2）Construction of model for analysisThe structure shown in Fig. 1 consists of three parts: two columns, one beam and three driving bars. The columns and beam are joined by the bolts on the first horizontal rib located on top of the columns as shown in Fig.1. Because the driving bars are substituted by equivalentforces on the joint positions, their structure is ignored in the model.The core of the top beam is three joints and a hole with special purpose, which can not be changed. The other parts of the beam may be changed if needed. For the convenience of modeling, the core of the beam is formed into one component. In the process of optimization, only the core position of beam along x axis is changed, that is to say, shape of beam core is not changed. It should be noticed that, in the rest of beam, only shape is changed but the topology is not changed and which can automatically be performed by the control program.Fig.1, six bolts join the beam and two columns. The joint surface can not bear the pull stress in the non-bolt joint positions, in which it is better to set contact elements. When the model includes contact elements, nonlinear iterative calculation will be needed in the process of solution and the computing time will quickly increase. The trial computing result not including contact element shows that the outside of beam bears pulling stress and the inner of beam bears the press stress. Considering the primary analysis object is the joint position stiffness between the top beam and the three driving bars, contact elements may not used, hut constructs the geometry model of joint surface as Fig.2 showing. The upper surface and the undersurface share one key point in bolt-joint positions and the upper surface and the under surface separately possess own key points in no bolt positions. When meshed, one node will be created at shared key point, where columns and beam are joined, and two nodes will be created at non shared key point, where column and beam are separated. On right surface of left column and left surface of right column, according to trial computing result, the structure bears press stress. Therefore, the columns and beam will share all key points, not but at bolts. This can not only omit contact element but also show the characteristic of bolt joining. The joining between the bottoms of the columns and the base are treated as full constraint. Because the main aim of analysis is the stiffness of the top beam, it can be assumed that the joint positions hear the same as load between beam and the three driving bars. The structure is the thin wall cast and simulated by shell element . The thickness of the outside wall of the structure and the rib are not equal, so two groups of real constant should he set. For the convenience of modeling, the two columns are alsoset into another component. The components can create an assembly. In this way, the joint positions between the beam core and columns could he easily selected, in the modifying the model and modifying process can automatically be performed. Analysis model is showed Fig.1. Because model and load are symmetric, computing model is only half. So the total of elements is decreased to 8927 and the total of nodes is decreased to 4341. All elements are triangle.3.）Optimization solutionThe optimization process is essentially a computing and modifying process. The original design is used as initial condition of the iterative process. The ending condition of the process is that stiffness differences of the joint locations between three driving bars and top beam are less than given tolerance or iterative times exceed expected value. Considering the speciality of the question, it is foreseen that the location is existent where stiffness values are equal. If iterative is not convergent, the cause cannot be otherwise than inappropriate displacement increment or deficient iterative times. In order to make the iterative process convergent quickly and efficiently, this paper uses the bisection searching method changing step length to modify the top beam displacement. This method is a little complex but the requirement on the initial condition is relatively mild.The flow chart of optimization as follows:1. Read the beam model data in initial position from backup file;2. Modify the position of beam;3. Solve;4. Read the deform of nodes where beam and three bars are joined;5. Check whether the convergent conditions are satisfied, if not, then continue to modify the beam displacement and return to 3, otherwise, exit the iteration procedure.6. Save the results and then exit.The program's primary control codes and their function commentaries are given in it, of which the detailed modeling instructions are omitted. For the convenience of comparing with the control flow, the necessary notes are added.the flag of the batch file in ANSYSBATCH RESUME, robbak.db, 0read original data from the backupfile robbak,.db/PREP7 enter preprocessordelete the joint part between beam core and columnsmove the core of the beam by one :step lengthapply load and constraint on the geometry meshing thejoint position between beam core and columns FINISH exit the preprocessorISOLU enter solverSOLVE solveFINISH exit the solverPOST1 enter the postprocessor*GET ,front,NODE,2013,U,Z read the deformation of first joint node on beam*GET,back,NODE, 1441 ,U,Z read the deformation of second joint node on beam intoparameter hacklastdif-1 the absolute of initial difference between front and hacklast timeflag=- 1 the feasibility flag of the optimizationstep=0.05 the initial displacement from initial position to the currentposition*D0,1,1,10,1 the iteration procedure begin, the cycle variable is I andits value range is 1-10 and step length is 1dif=abs(front-back) the absolute of the difference between front and hack inthe current result*IF,dif,LE,l .OE-6,THEN check whether the absolute difference dif satisfies therequest or noflag=l yes, set flag equal to 1*EXIT exit the iterative calculation*ELSEIF,dif,GE,lastdif,THEN check whether the dif value becomes great or not flag=2yes, set flag 2 modify step length by bisection methodperform the next iterative calculation, use the lastposition as the current position and modified last steplength as the current step lengthELSE if the absolute of difference value is not less thanexpected value and become small gradually, continue tomove top beam read the initial condition from back upfile enter the preprocessorMEN, ,P51X, , , step,, , ,1 move the core of the beam by one step length modify thejoint positions between beam core and column applyload and constraint meshingFINISH exit preprocessorISOLU enter solverSOLVE solveFINISH exit the solver/POST1 exit the postprocessor*GET,front,NODE,201 3,U,Z read the deformation of first joint node to parameter front *GET,back,NODE, 144 1,U,Z read the deformation of second joint node to parameter back lastdif-dif update the value of last dif*ENDIF the end of the if-else*ENDDO the end of the DO cycleMost of the control program above is copied from log file, which is long. The total of lines is up to about 1000 lines. Many codes such as modeling and post-process codes are used repeatedly. To make the program construct clear, these instructions can he made into macros, which are called by main program. This can efficiently reduce the length of the main program. In addition, modeling instructions from log file includes lots of special instructions that are only used under graphic mode but useless under hatch mode. Deleting and modifying these instructions when under batch mode in ANSYS can reduce the length of the file, too.In the program above, the deformation at given position is read from node deformation. In meshing, in order to avoid generating had elements, triangle mesh is used. In optimization, the shape of joint position between columns and beam continually is changed. This makes total of elements different after meshing each time and then element numbering different, too. Data read from database according to node numbering might not he data to want. Therefore, beam core first needs to he meshed, then saved. When read next time, its numbering is the same as last time.Evaluating whether the final result is a feasible result or not needs to check the flag value. If only the flag value is I, the result is feasible, otherwise the most proper position is not found. The total displacement of top beam is saved in parameter step. If the result is feasible, the step value is the distance from initial position to the most proper position. The sum of iterative is saved in parameter 1. According to the final value of I, feasibility of analysis result and correctness of initial condition can he evaluated.4）Optimization resultsThe sum of iterative in optimization is seven, and it takes about 2 hour and 37 minutes to find optimal position. Fig.3 shows the deformation contour of the half-construct. In Fig.3, the deformations in three joints between beam and the three driving bars is the same as level, and the corresponding deformation range is between -0.133E-04 and -0.1 15E-O4m, the requirement of the same stiffness is reached. At this time, the position of beam core along x-axis as shown in Fig. 1 has moved -0.71E-01m compared with the original designed positionBecause the speed of computer reading instruction is much faster than modifying model manually, the time modifying model can be ignored. The time necessary foroptimization mostly depends on the time of solution. Compared with the optimization procedure manually modifying model, the efficiency is improved and mistake operating in modeling is avoided.5）ConclusionThe analyzing result reveals that the optimization method given in this paper is effective and reaches the expected goal. The first advantage of this method is that manual mistakes do not easily occur in optimization procedure. Secondly, it is pretty universal and the control codes given in this paper may he transplanted to use in similar structure optimization design without large modification. The disadvantage is that the topology structure of the optimization object can not be changed. The more the workload of modifying the model, the more the advantages of this method are shown. In addition, the topology optimization function provided in ANSYS is usedto solve the optimization problem that needs to change the topology structure.The better optimization results can he achieved if the method in this paper combined with it.中文译文：机器人机构优化设计有限元分析摘要机器人结构最优化设计，设计模型需要反复的修正和计算。
有限元分析概述
如何处理
发展过程（续）：
• 3. 有限元方法的使用现状
有限元分析可以获取几乎任意复杂工程结构的各种机械性 能信息。国际上有90%的机械参评和装备都要采用有限元 方法进行分析，进而进行设计修改和优化。
例如：1990年10月波音公司在计算机上对新型客机B-777进行“无纸设计”，仅用 了三年半的时间，1994年4月第一架B-777便试飞成功。
有限元分析概述
第1节 什么是有限元
➢ 有限元分析源于力学
英文：finite element analysis (FEA) finite element method (FEM)
➢ 已经学过的相关力学：
理论力学、材料力学
➢ 理力、材力与有限元有何联 系？
20世纪理论和应用力学十大进展
序号
名称
得票数
1
有限元方法
384
2
断裂力学
343
3
生物力学的创立 337
4
稳定性、分岔和混沌 理论
337
5
边界层理论
323
6 塑性力学和位错理论 312
7
湍流统计理论
259
8
奇异பைடு நூலகம்动理论
222
9
力学的公理化体系 199
10
克服声障、热障的力 学理论
196
各力学学科分支的联系
• 科学研究的目的：定量获取所研究对象的所有信息 • 定量化一般流程：
高层建筑 深圳某民用住宅转换层抗震分析
4. 若干有限元分析的成功案例（续）
电子行业 冲击和跌落问题
热传导和热 应力问题：
显示器玻壳强度分析
4. 若干有限元分析的成功案例（续）
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本科生毕业设计 (论文)
外文翻译
原文标题INTRODUCTION TO THE FINITE ELEMENT
METHOD
译文标题对于有限元分析的介绍
作者所在系别机械工程系
作者所在专业机械设计制造及其自动化
作者所在班级
作者姓名
作者学号
指导教师姓名
指导教师职称
完成时间
注：1. 指导教师对译文进行评阅时应注意以下几个方面：①翻译的外文文献与毕业设计（论文）的主题是否高度相关，并作为外文参考文献列入毕业设计（论文）的参考文献；②翻译的外文文献字数是否达到规定数量（3 000字以上）；③译文语言是否准确、通顺、具有参考价值。
2. 外文原文应以附件的方式置于译文之后。
共 5 页第11 页。