有限元分析系统的发展现状与展望外文翻译

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有限元分析系统的发展现状与展望

有限元分析系统的发展现状与展望作者：谢小丽来源：《电脑知识与技术》2016年第18期摘要：随着我国科技的飞速发展，人们更是在不断的创建更快速，更简便，规模更大的建筑物以及更加精密的设备。

但创建这些东西的时候，都需要工程师在设计的时候要精确的预测出产品的技术性能，动力强度，流场，磁场等等的技术参数进行分析和计算。

随着以计算机技术为基础不断发展起来的有限元分析方法，不仅逐渐的解决了一些工程计算上的一些复杂的分析计算，而且相关的研究人员更是研究了许多新技术来不断的为我国做出了不可估量的贡献。

关键词：有限元分析；现状；发展局势中图分类号：TP311 文献标识码：A 文章编号：1009-3044（2016）18-0242-011 有限元分析系统的发展现状1）如今，在我们的生活中，从自行车到飞机，所有的设计都离不开有限元的系统分析计算。

随着科技的不断发展，以往的线性理论已经逐渐的不能满足现在的社会发展要求。

比如在建筑行业中，高层建筑的出现，工作人员就必须要考虑结构的大位移等等的几个非线性问题。

航天工程出现的高温部件存在的热应力问题，工作人员也必要考虑到材料的非线性问题。

所以现在我国的发展状况如果只是采用线性理论来解决问题，是远远不够的。

我们只能不断的发展更好的技术来解决现在的困境。

众所周知，非线性的计算的过程是非常复杂的，它一般会涉及许多复杂的数学问题以及一些运用技巧，相关的工作人员也很难在很短的时间掌握要点。

2）随着数值分析系统的不断改进和完善，尤其是计算机的运算速度上表现得尤其突出。

在现在的工程站上，想要求解一个包含10方程的模型时间只需要10分钟，而如果用手工的方式，则需要几周的时间才可以得出结果。

所以，我们在这方面做出的成绩还是比较优秀的。

3）现如今，CAD软件的无缝集成工艺已经成为我国有限元分析的另一个特点，也就是CAD软件的集成使用。

也就是说，在CAD软件造成零件的设计以后，再自动的生成有限元网络，然后进行分析计算。

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 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, 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 consistsof 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 optionsfor different 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 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, 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, thedisplacement 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 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 (suchas 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 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 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 toapproximate 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 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。

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。

有限元的发展历史和趋势

有限元的发展历史和趋势
有限元法（Finite-Element Method，以下简称FEM）是现代工程和
科学研究中一种常用的方法，它可以大大提高计算的效率，减轻计算工作，帮助计算者迅速解决复杂的数学问题。

1960年，Timoshenko和Gere在《力学原理》一书中首次提出了有限
元分析的概念，这成为有限元技术的开端。

他们认为，由许多有限尺寸的
单元组成的实体可以被视为由有限多边形尺寸的单元组成，这就被称为有
限元分析，成为20世纪70年代结构力学计算的基础。

随着计算资源的发展，解决复杂结构和场问题的能力也发生了巨大变化。

尤其是在80年代，由于计算的速度和计算量的大幅度增加，有限元
法被广泛应用于航空航天、电力、原子能、汽车等领域，扮演着越来越重
要的角色。

此外，它还用于求解许多复杂的场问题，从而获得了巨大进展。

随着信息技术的发展，芯片技术和并行计算的应用使有限元法取得了
新的发展，目前已经应用于许多领域，比如：土木工程、流体力学、医学
工程、声学、生物工程、材料科学等领域。

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。

有限元分析方法在活塞研究中的应用现状与发展趋势

Internal Combustion Engine &Parts0引言柴油机是目前国内外广泛使用的动力设备之一，在生产、生活各方面都起着十分重要的作用，但由于近年以来，国际竞争的加剧以及国际环境的恶化，由此对于柴油机的各方面性能提出了新的要求和指标。

活塞作为柴油机上工作条件最为恶劣的零部件之一，是影响柴油机整机性能的重点所在，于是便出现了围绕活塞的性能而展开的一系列研究。

随着近代以来，电子计算机技术的迅猛发展，运用计算机分析软件对于机械零部件进行分析运算，已经趋于成熟，并且应用广泛，现已深入到分析各类机械的零部件[1]。

运用大型的有限元分析软件，就机械负载、热能负荷、温度场等综合作用下活塞的应变情况，以及燃烧室的不同类型和位置对活塞性能的影响等进行分析，然后利用计算结果改善活塞的结构设计，进而研制结构合理、性能优良的活塞，业已成为现今国内外研究活塞的主要方向。

目前国内关于柴油机活塞方面的研究还处于初步探索阶段，而国外对于活塞方面的研究则较为成熟，而且许多研究技术和研究专利都被国外垄断，因此，就活塞的各方面性能进行有限元分析，对于完善我国柴油机发展领域、提高我国柴油机设计研发水平和打破国外在柴油机活塞技术上的垄断地位具有十分重要的作用和意义。

本文就目前关于柴油机活塞在有限分析方面所取得的一些成果和存在的一些缺陷进行对比分析，旨在探索出一条更为有效的分析活塞的研究道路，从而进一步拓宽活塞的各方面性能研究，弥补活塞研究现状中的不足。

1活塞的研究现状在柴油机运转过程中，活塞长期承受着周期交变的机械负荷和热负荷的作用，因此，活塞是柴油机零部件中最易出现故障的零部件之一。

活塞对柴油机的使用寿命、动力性能、稳定程度、经济状况等都起着举足轻重的作用。

目前国外对于柴油机活塞的研究较为完备，研究情况可以追溯到几十年前，如美国、德国、日本等都在活塞方面进行了深入而细致的研究，先后研制出了满足不同用途的多种柴油机活塞，使得活塞的结构也发生了巨大变化。

利用有限元模型对钻机进行动态分析的研究外文文献翻译、中英文翻译

Studies in dynamic design of drilling machine using updated finite element modelsAbstractThe aim of the present work is to develop updated FE models of a drilling machine using analytical and experimental results. These updated FE models have been used to predict the effect of structural dynamic modifications on vibration characteristics of the drilling machine. Two studies have been carried out on the machine. In the first study, modal tests have been carried out on a drilling machine using instrumented impact hammer. Modal identification has been done using global method of modal identification. For analytical FE modeling of the machine, a computer program has been developed. The results obtained using FEM, have been correlated with the experimental ones using mode shape comparison and MAC values. Analytical FE model has been updated, with the help of a program, which has been developed using direct methods of model updating. In the second study, modal testing has been carried out using random noise generator and modal exciter. Global method has been used for modal identification. Analytical FE modeling has been done using I-DEAS software. Correlation of FE results with the experimental ones has been carried out using FEMtools software. Updating of the analytical FE model has also been done using the above software, based on an indirect technique viz. sensitivity based parameter estimation technique. The updated FE models, obtained from both the studies have been used for structural dynamic modifications (SDM), for the purpose of dynamic design and the results of SDM predictions are seen to be reasonably satisfactory.Article Outline1. Introduction2. Modal testing and identification3. Finite element formulation of drilling machine4. Comparison of analytical FE and experimental results (model correlation)5. Finite element model updating6. SDM studies using updated models for dynamic design7. ConclusionsReferences1. IntroductionDynamic design aims at obtaining desired dynamic characteristics in machines and structures, which may include shifting of natural frequencies, desired mode shapes and vibratory response. The ultimate objectives are to have a quieter and more comfortable environment, higher reliability and better quality of product. The conventional dynamic design is basically hit and trial method in which we try to achieve desired dynamic characteristics by making several prototypes. The disadvantage of this technique is that actual design cycle takes a lot of time and therefore it is not cost effective. However, model updating based dynamic design saves design cycle time as well as reduces the cost involved. Various tools used for updating based dynamic design are: experimental modal analysis (EMA) including modal testing and modal identification, model updating and structural dynamic modification.Ewins [1]and Maia and Silva [2]have explained the basic concepts of modal testing, which is an experimental approach to obtain mathematical model of a structure. In a modal test, the structure under test is excited either by an impact hammer or by a modal exciter, and the response of the structure is recorded at several experimental points, in the form of frequency response functions (FRFs), using a dual channel FFT analyzer. The experimental modal model gives information about the natural frequencies, corresponding mode shapes and modal damping factor and is useful for model updating. The model updating techniques helps us to bring analytical finite element models closer to real systems. In model updating an initial analytical FE model constructed for analyzing the dynamics of a structure is refined or updated using test data measured on actual structure such that the updated model describes the dynamic properties of the structure more correctly. The inaccuracies in FEM, when applied to dynamic problems are due to uncertainties in boundary conditions and structural damping etc.Friswell and Mottershead [3] have discussed the finite element model updating in structural dynamics. Baruch and Bar-Itzhack and Baruch [4] and [5] considered analytical mass matrix to be exact and developed a direct method for updating using test data. Berman and Nagy [6]developed a method of model updating, which uses measured modes and natural frequencies to improve analytical mass and stiffness matrices. Structural dynamic modification (SDM) techniques [7]and [8]are the methods by whichdynamic behaviour of the structure is improved by predicting the modified behaviour brought about by adding modifications like those of lumped masses, rigid links, dampers etc. Thus the dynamic design using updated model is expected to be helpful in order to predict accurately and quickly, the effect of possible modifications on the dynamic characteristics of the structure at computer level itself, thus saving time and cost.Sestieri [7]has discussed SDM application to machine tools and engines. Kundra [8]gave the method of structural dynamic modification via models. Modak [9] has discussed SDM predictions using updated FE model for an F-structure. He used constrained nonlinear optimization method for updating of a machine tool using stiffness parameters at the boundary [10]. The present paper deals with the FE model updating using direct as well as indirect method, and to use this updated FE model for dynamic design based on SDM predictions of a machine tool viz. a drilling machine. Two different studies are reported using different techniques for analytical and experimental analysis and for updating. Various objectives with which the present research work has been carried out are• To develop updated FE models of a complex structure like that of a drilling machine and to use these updated models to predict the effect of various modifications on modal properties of the machine.• To see whether hammer excitation yields good results for fairly complex structures like drilling machine or not, and to compare these results with those obtained from modal exciter.• To analyze the results of SDM predictions obtained using the updated models derived in the studies.2. Modal testing and identificationIn the two studies mentioned earlier, different techniques have been used, for modal testing and identification. In the first study, impact hammer is used to excite the drilling machine structure, at various points as shown in Fig. 1 and Fig. 2. Response is taken at a fixed point with the help of an accelerometer.(12K)Fig. 1. Experimental setup (Study 1).(4K)Fig. 2. Hammer excitation locations.In the present study, the drilling machine is excited at 30 locations and therefore, 30 FRFs are obtained. These FRFs are recorded in the form of inertance. The experimental FRFs, thus obtained are transferred to computer. Modal identification or modal parameter extraction consists of curve fitting a theoretical expression for an individual FRF to the actual measured data obtained. The experimental FRFs are analyzed by GRF-M method using modal analysis software ICATS [11] to obtain modal parameters of the drilling machine. In the second study, the machine tool structure has been excited at the base at point 28, referring to Fig. 2, using modal exciter and response has been measured at various points using piezoelectric accelerometers. The modal identification of the FRFs, thus measured has been carried out using global method GRF-M method in ICATS software.Table 1compares the experimental natural frequencies obtained from both the methods, which shows minor differences in the two modal frequenciesTable 1.Mode110.29 Hz8.67 HZ0.95311.20 Hz8.79 Hz0.946Mode 265.14 Hz47.34 HZ0.90163.37 Hz44.40 Hz0.9063. Finite element formulation of drilling machineSeveral books have given the basic concepts of finite element analysis, some of them are: Zienkiewicz [12] and Bathe [13].The drilling machine structure is very complicated with different mountings and accessories. Therefore exact modeling and analysis of the actual structure is difficult and it takes more computational effort. However for analytical FE analysis, simplified model of drilling machines has been considered. In study 1, the finite element modelling has been done using a program developed in MATLAB. Beam elements have been used for the analysis. The joints and boundary conditions are considered to be rigid and influence of structural damping on modal model parameters, is ignored. The relevant data used for the drilling machine is given below:25 mm pillar type, height = 1.655 m, mass density = 7800 kg/m3, Young’s modulus= 200 Gpa, number of nodes = 30, number of elements = 29, number of nodes per element = 2, degrees of freedom per node = 3.Fig. 3shows the structure of the drilling machine with the node numbers given for study 1.(7K)Fig. 3. Drilling machine structure for FE analysis.The eigenvalues and eigenvectors have been calculated. The analytical FE model of the structure consists of 90 ×90-size mass and stiffness matrices (30 ×3, 30 nodes and 3 d.o.f. per node). But by experiment only 30 coordinates can be measured. Therefore FE model has been reduced using Guyan [14] reduction method with the help of a program developed in MATLAB.In study 2, the finite element modelling has been done using I-DEAS software. The model has been made using beam mesh. Although the FE model has been simplified but the beam elements has rotational degree of freedom, which cannot be measured experimentally. Therefore the FE model needs to be reduced. The FE model has been reduced using model reduction utilityin FEMtools software. Fig. 4 and Fig. 5 shows the mode shape animation for the first and second mode respectively, using I-DEAS software.(31K)Fig. 4. Mode shape animation (first mode).(23K)Fig. 5. Mode shape animation (second mode).4. Comparison of analytical FE and experimental results (model correlation)The first stage of any reconciliation exercise is to determine how closely the experimental and analytical models correspond. If we are unable to obtain a satisfactory degree of correlation between the initial analytical FE model and the test data, then it is extremely unlikely that any form of model updating will succeed. Thus, a successful correlation is crucial for the success of model updating. Table 1gives the comparison between experimental and analytical natural frequencies. There are differences between analytical FE model predictions and experimental results. Thus the FE models need to be updated. However, the differences between the corresponding results of both studies are minor.Apart from natural frequency comparison (as given in Table 1), another method of model correlation is mode shape comparison. To compare the mode shapes, we plot the deformed shapes of the structure for a particular mode, using experimental as well as analytical model. These mode shapes are plotted side-by-side for quick comparison. Mode shape corresponding to second mode is shown in Fig. 6, using ICATS software. It shows a fairlygood level of correlation between the experimental and analytical FE model.(87K)Fig. 6. Mode shape comparison.Several researchers have developed techniques for quantifying the comparison between measured and predicted mode shapes. As an alternative to the graphical approach, Model Assurance Criterion i.e. MAC, [15]) is a widely used technique to estimate the degree of correlation between mode shape vectors. This provides a measure of the least squares deviation or ‘scatter’ of the points from the straight-line correlation. The MAC between a measured and analytical mode is:(1)wherem andarepresents measured or experimental and analytical modeshapes respectively. MAC is a scalar quantity whose value is between 0 and 1. A value of MAC close to 1 shows a good degree of correlation between experimental and analytical FE model. We can see in Table 1 that the MAC numbers are close to 1, though somewhat lower for the second mode. Table 1 also shows that the results obtained from both the studies are quite close to each other.5. Finite element model updatingModel updating can be defined as “the process of correcting the numerical values of individual parameters in a analytical FE model using data obtained from an associated experimental model such that the updated model correctly describes the dynamic properties of the subject structure”.Various model updating methods can be classified into two major groups: • Direct matrix methods• Indirect or iterative methodsDirect methods are capable of reproducing measured data exactly, but they provide no opportunity for the user to select parameters for updating. Here parameter means any physically realizable quantity like Young’s modulus, Poisson’s ratio, mass density etc. When using the direct methods, the entire stiffness and mass matrices are updated in a single(non-iterative) solution step. Consequently any physical meaning, which the initial finite element model might have possessed, is lost in the updating process.Techniques like the indirect methods, allow the updating parameters to be selected. So, considerable physical insight is required if the model is to be improved, not only in its ability to reproduce test results, but also in interpreting the parameters physically. Methods in this second group are iterative and, as such, considerably more expensive of computer effort.Two studies have been carried out for model updating and computer programs for the same were developed in the present work using MATLAB. In the first study, two direct methods are applied to update the analytical FE model of the drilling machine structure.Baruch and Bar-ltzhack [4] and Baruch [5] considered the mass matrix of the analytical model to be exact. The measured eigenvectors are corrected by using the relation:(2)The stiffness matrices of the analytical FE model after updating is given as:K=K a-K a T M a+M a T K a+M a T K a T M a+M aΛT M a(3)uBerman and Nagy [6] used a method similar to that of Baruch. They update mass and stiffness matrices while the mass matrix is updated to ensure the orthogonality of the exact FE model modes. The mass matrix is updated as:(4)(5) The stiffness matrix is updated using following equation:(6) The updated mass matrix obtained will be symmetric and stiffness matrix will be close to that of exact stiffness matrix. Results obtained fromBaruch and Berman–Nagy model updating methods are tabulatedin Table 2. It is clear from Table 2, that the updated model reproduces the measured frequencies. After updating, MAC values have been calculated again using Eq. It can be observed that updated MAC values show some improvement over the initial MAC values.Table 2.Comparison of experimental and updated FE frequencies and MAC valuesModenumberStudy 1Study 2Measured frequency Baruch method Berman method MeasuredfrequencySensitivitymethodUpdatedfrequencyMACUpdatedfrequencyMACUpdatedfrequencyMACMod e 18.67 Hz8.67 Hz0.9258.67 Hz0.9348.79 Hz8.79 Hz0.947Mod e 247.34 Hz47.34 Hz0.96647.34 Hz0.94744.40 Hz44.43 Hz0.913The results after updating have been tabulated in Table 2. It clearly shows that after updating, the updated FE model closely represents the actual machine tool structure. It also shows that MAC values have also been improved after updating.6. SDM studies using updated models for dynamic designStructural dynamic modification (SDM) techniques are methods by which dynamic characteristics of the structure can be improved by adding the modifications like changing mass, spring, damping etc. The mass modification has been considered here for predicting dynamic characteristics using updated FE model.A mass modification on drilling machine is introduced in the form of a lumped mass of 14.3 kg at the top of the vertical pillar, i.e. node 20 as in Fig. 3. The modal test for the mass modified machine is carried out by Modak [10], using impact hammer for excitation. The FRFs are analyzed in ICATS in order to obtain an experimental estimate of the altered dynamic characteristics of the drilling machine, as given in Table 3.Table 3.Comparison of measured and predicted frequencies, after mass modification, using updated FE modelMode no.MeasuredfrequenciesSDM prediction using updated FE modelBaruch’s method Berman and Nagy’s method Sensitivity method18.37 Hz8.34 Hz8.17 Hz8.40 Hz246.05 Hz47.15 Hz46.96 Hz43.20 HzThe effect of the same mass modification on the dynamic characteristics of the drilling machine has also been predicted by updated FE model. Table 3 gives a comparison of the predictions based on the updated FE models obtained by direct methods of Baruch, Berman and Nagy and by indirectmethod based on sensitivity analysis, with that of the measured modified characteristics.It is seen from the Table 3 that the updated FE model predictions of the natural frequencies are quite close to the measured value of natural frequencies. This shows the capability of the updated FE model to accurately predict the effect of structural modifications on the dynamic properties of the structure. Now, this updated FE model has been further used to predict, at computer level, the effect of various mass modifications on the structural dynamics of the drilling machine, for the purpose of dynamic design.The mass modification can bring about significant changes in the natural frequencies of a structure. For predicting the effect of modifications using updated FE model, modification at node 20 and node 25, on the drilling machine has been considered. The effects on FRFs due to these modifications have been shown in Fig. 8and Fig. 9respectively. The values of the first two natural frequencies have been predicted using updated FE models and MODIFY module of ICATS software and are shown in Table 4and Table 5.(33K)Fig. 8. Regenerated FRF due to mass modification at node 20.(29K)Fig. 9. Regenerated FRF due to mass modification at node 25.Table 4.Predicted natural frequencies after mass modification using 20 kg at node 20 (PanelA), predicted natural frequencies after mass modification using 40 kg at node 20 (PanelB)Comparisons of SDM predictions using updated FE modelBaruch method Berman method Sensitivity method ICATS MODIFY Measured Frequencies Panel AMass modification of 20 kg8.22 Hz7.99 Hz8.3 Hz8.2 Hz8.3 Hz47.08 Hz46.83 Hz42.87 Hz47.1 Hz42.8 HzPanel BMass modification of 40 kg7.83 Hz7.45 Hz7.76 Hz7.75 Hz7.8 Hz46.86 Hz46.44 Hz41.27 Hz46.6 Hz41.3 HzTable 5.Predicted natural frequencies after mass modification using 20 kg at node 25 (PanelA), predicted natural frequencies after mass modification using 40 kg at node 25 (PanelB)Comparisons of SDM predictions using updated FE modelBaruch method Berman method Sensitivity method ICATS MODIFY Measured frequenciesPanel AMass modification of 20kg8.34 Hz8.44 Hz8.41 Hz8.35 Hz8.4 Hz 42.24 Hz43.74 Hz41.67 Hz42.2 Hz41.6 HzComparisons of SDM predictions using updated FE modelBaruch method Berman method Sensitivity method ICATS MODIFY Measured frequenciesPanel BMass modification of 40kg8.03 Hz8.21 Hz8.04 Hz8.1 Hz8.1 Hz38.89 Hz41.02 Hz39.67 Hz39.15 Hz39.5 Hz7. ConclusionsComparison of results obtained from experimental modal analysis and FE models of a drilling machine, indicate that its finite element models need to be updated. This is necessary in order to predict dynamic behavior of the complex structure with an acceptable accuracy.An experimentation involving modal testing has been carried out on the drilling machine using impact hammer as well as modal exciter. It has been observed that both impact hammer and modal exciter yield good results for fairly complex structures like drilling machine.Analytical FE model has been updated in the light of experimental data using direct as well as indirect methods. Both the methods give results, which are fairly close when used for predicting results of SDM attaching additional mass on the machine at different locations. The predicted results have been validated by comparison with measured results and are seen to be fairly accurate in particular for the indirect method using sensitivity analysis.References[1]D.J. Ewins, Modal Testing: Theory and Practice, John Willey and Sons, New York (2000).[2] N.M.M. Maia and J.M.M. Silva, Theoretical and Experimental Modal Analysis, John Willey and Sons, New York (1997).[3]M.I. Friswell and J.E. Mottershead, Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers, Dordrecht (1995).[4] M. Baruch and I.Y. Bar-ltzhack, Optimal weighted orthogonalization of measured modes, AIAA Journal16 (1978), pp. 346–351.[5] M. Baruch, Optimisation procedure to correct stiffness and flexibility matrices using vibration test data, AIAA Journal16 (1978), pp. 1208–1210.[6]A. Berman and E.J. Nagy, Improvement of a large analytical model using test data, AIAA Journal21 (1983), pp. 1168–1173.[7] A. Sestieri, SDM application to machine tools and engines, Sadhana 25 (2000), pp. 305–317.[8] T.K. Kundra, Structural dynamic modification via model, Sadhana25 (2000), pp. 261–276.[9]S.V. Modak, Studies in Finite Element Model Updating and Application to Dynamic Design, Ph.D. Thesis, Department of Mechanical Engineering, IIT Delhi, 2001.[10]S.V. Modak, T.K. Kundra, B.C. Nakra, Dynamic design of machine tool structures using an updated model Pro. IMAC- XX, 2002, pp. 1489–1494.[11] ICATS Reference Manual, Imperial College, London, 1996.[12]O.C. Zienkiewicz, The Finite Element Method in Engineering Science, McGraw-Hill Publishing Company, London (1977).[13] K.J. Bathe and E.J. Wilson, Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ (1982).[14] R.J. Guyan, Reduction of stiffness and mass matrices, AIAA Journal 3 (1965), p. 380.[15]R.L. Allemang, BD.L. Rown. A correlation coefficient for modal vector analysis, Proc. 1st IMAC, 1982, pp. 110–116.[16] FEMtools Manual Version 2.0, Dynamic design solutions, 2000.Corresponding author. Steam Turbine Engineering, TCGT Division, Bharat Heavy Electricals Limited, Hyderabad-502032, India译文利用有限元模型对钻机进行动态分析的研究摘要现在的工作的目的是使用分析和实验的结果发展和改进钻机的有限元分析模型，这种有限元分析已经用在监测将钻机的工作特性修改后对钻机动态的结构的影响；对钻机将有两个研究就进行。

有限元的发展历史现状及应用前景

有限元的发展历史现状及应用前景有限元分析的发展趋势“有限元”这个名词第一次出现，到今天有限元在工程上得到广泛应用，经历了三十多年的发展历史，理论和算法都已经日趋完善。

有限元的核心思想是结构的离散化，就是将实际结构假想地离散为有限数目的规则单元组合体，实际结构的物理性能可以通过对离散体进行分析，得出满足工程精度的近似结果来替代对实际结构的分析，这样可以解决很多实际工程需要解决而理论分析又无法解决的复杂问题。

近年来随着计算机技术的普及和计算速度的不断提高，有限元分析在工程设计和分析中得到了越来越广泛的重视，已经成为解决复杂的工程分析计算问题的有效途径，现在从汽车到航天飞机几乎所有的设计制造都已离不开有限元分析计算，其在机械制造、材料加工、航空航天、汽车、土木建筑、电子电器，国防军工，船舶，铁道，石化，能源，科学研究等各个领域的广泛使用已使设计水平发生了质的飞跃，主要表现在以下几个方面：增加产品和工程的可靠性；在产品的设计阶段发现潜在的问题经过分析计算，采用优化设计方案，降低原材料成本缩短产品投向市场的时间模拟试验方案，减少试验次数，从而减少试验经费国际上早在60年代初就开始投入大量的人力和物力开发有限元分析程序，但真正的CAE软件是诞生于70年代初期，而近15年则是CAE软件商品化的发展阶段，CAE开发商为满足市场需求和适应计算机硬、软件技术的迅速发展，在大力推销其软件产品的同时，对软件的功能、性能，用户界面和前、后处理能力，都进行了大幅度的改进与扩充。

这就使得目前市场上知名的CAE软件，在功能、性能、易用性、可靠性以及对运行环境的适应性方面，基本上满足了用户的当前需求，从而帮助用户解决了成千上万个工程实际问题，同时也为科学技术的发展和工程应用做出了不可磨灭的贡献。

目前流行的CAE分析软件主要有NASTRAN、 ADINA 、ANSYS、ABAQUS、MARC、MAGSOFT、COSMOS等。

MSC-NASTRAN软件因为和NASA的特殊关系，在航空航天领域有着很高的地位，它以最早期的主要用于航空航天方面的线性有限元分析系统为基础，兼并了PDA公司的PATRAN，又在以冲击、接触为特长的DYNA3D的基础上组织开发了DYTRAN。

有限元的发展历史和趋势

有限元的发展历史和趋势摘要1965年，“有限元”这个名词第一次在我国出现,到今天有限元在工程上得到广泛应用,经历了三十多年的发展历史,理论和算法都已经日趋完善。

有限元法(Finite Element Method,简写为FEM)是求解微分方程的一种非常有效的数值计算方法,用这种方法进行波动数值模拟受到越来越多的重视。

有限元法起源于固体力学,并逐步扩展到热传导、计算流体力学、电磁学等不同领域,已经成为数学物理中很重要的数值计算方法。

关键词有限元数值发展趋势前言有限元方法在数值计算方法中具有极为重要的地位，有限元方法在应用中不仅本身具有很大的潜力，而且，结合其它理论和方法还有广阔的发展前景。

1有限元的发展历程有限元法的发展历程可以分为提出(1943)、发展(1944一1960)和完善(1961-二十世纪九十年代)三个阶段。

有限元法是受内外动力的综合作用而产生的。

1943年，柯朗发表的数学论文《平衡和振动问题的变分解法》和阿格瑞斯在工程学中取得的重大突破标志着有限元法的诞生。

有限元法早期(1944一1960)发展阶段中，得出了有限元法的原始代数表达形式，开始了对单元划分、单元类型选择的研究，并且在解的收敛性研究上取得了很大突破。

1960年，克劳夫第一次提出了“有限元法”这个名称，标志着有限元法早期发展阶段的结束。

有限元法完善阶段(1961一二十世纪九十年代)的发展有国外和国内两条线索。

在国外的发展表现为: 第一，建立了严格的数学和工程学基础;第二，应用范围扩展到了结构力学以外的领域;第三，收敛性得到了进一步研究，形成了系统的误差估计理论;第四，发展起了相应的商业软件包。

在国内，我国数学家冯康在特定的环境中独立于西方提出了有限元法。

1965年，他发表论文《基于变分原理的差分格式》，标志着有限元法在我国的诞生。

冯康的这篇文章不但提出了有限元法，而且初步发展了有限元法。

他得出了有限元法在特定条件下的表达式，独创了“冯氏大定理”并且初步证明了有限元法解的收敛性。

有限元分析软件外文翻译

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。

有限元模态分析现状与发展趋势_龙英

有限元模态分析现状与发展趋势龙英1，滕召金2，赵福水2（1.湖南现代物流职业技术学院，湖南长沙410131；2.湖南农业大学，湖南长沙410128；3.三一机电技术学校，湖南长沙410131）摘要：模态分析技术开始于20世纪30年代，经过70多年的发展，模态分析已经成为振动工程中一个重要的分支。

最终目标是识别出系统的模态参数，为结构系统的振动特性分析、振动故障诊断和预报以及结构动力特性的优化设计提供依据。

阐述了国内外有限元模态分析现状与发展趋势，并对当今国际上有限元模态分析和软件开发的特征进行了分析。

关键词：有限元；模态分析；发展趋势中图分类号：TH113文献标识码：A 文章编号：1007-8320（2009）04-0027-02The present status and development trends of finite element modal analysisLONG Ying 1，TENG Zhao-jin 2，ZHAO Fu-shui 2（1.Hunan Modern Logisties College ，Changsha ，Hunan 410128，China ；2.Hunan agricultural University ，Changsha ，Hunan 410128，China ；3.Sanyi Electrical and Technical School ，Changsha ，Hunan 410131，China ）Abstract ：Modal analysis began in the 1930’，after 70years of development ，modal analysis of vibration en -gineering has become an important branch.The ultimate goal is to identify the modal parameters of the system ，provide the basis for the vibration characteristics analysis and optimal design structural system ，fault diagnosis and prediction of vibration and dynamic characteristics of the structure.Describing the status quo and develop -ment trend of today ’s international finite element modal ，analyzing characteristics of software development.Key words ：finite element ；modal analysis ；development trend收稿日期：2009-04-12作者简介：龙英（1980-），女，研究方向：机械工程。

有限元的发展历史现状及应用前景

有限元分析的发展趋势“有限元”这个名词第一次出现，到今天有限元在工程上得到广泛应用，经历了三十多年的发展历史，理论和算法都已经日趋完善。

近年来随着计算机技术的普及和计算速度的不断提高，有限元分析在工程设计和分析中得到了越来越广泛的重视，已经成为解决复杂的工程分析计算问题的有效途径，现在从汽车到航天飞机几乎所有的设计制造都已离不开有限元分析计算，其在机械制造、材料加工、航空航天、汽车、土木建筑、电子电器，国防军工，船舶，铁道，石化，能源，科学研究等各个领域的广泛使用已使设计水平发生了质的飞跃，主要表现在以下几个方面： 增加产品和工程的可靠性； 在产品的设计阶段发现潜在的问题 经过分析计算，采用优化设计方案，降低原材料成本 缩短产品投向市场的时间 模拟试验方案，减少试验次数，从而减少试验经费 国际上早在60年代初就开始投入大量的人力和物力开发有限元分析程序，但真正的CAE软件是诞生于70年代初期，而近15年则是CAE软件商品化的发展阶段，CAE开发商为满足市场需求和适应计算机硬、软件技术的迅速发展，在大力推销其软件产品的同时，对软件的功能、性能，用户界面和前、后处理能力，都进行了大幅度的改进与扩充。

计算机辅助设计(CAD)外文翻译

附录：英文资料及翻译计算机辅助设计（CAD）计算机辅助设计系统基本上是一种设计工具，计算机是用来分析所设计的产品的各个方面。

CAD系统支持各种阶段的设计过程—设计构想、初步设计及最终设计。

设计者然后可在各种环境条件，比如温度的变化或不同机械压力下检验产品的状况。

尽管CAD系统并非一定要包含计算机绘图，但能将设计的产品显示在屏幕上是CAD系统的最有价值的特征之一。

物体的图形通常显示在阴极线管屏幕上（CRT）。

计算机图形功能使设计者可用多种办法研究物体：将物体在计算机屏幕上旋转、将其分成几段、将物体局部放大以仔细研究以及在运动程序的帮助下研究机构的运动。

大多数CAD系统使用互动式图形系统。

互交式图形系统使用户可直接和计算机通过交互作用以对图形进行调整及修改。

对CAD系统来说，交互式图形系统就算不是必要的，也已经是很有价值的工具。

许多CAD系统的最终产品是在与计算机连接的绘图仪中产生的图形。

在CAD 图形中，最难解决的问题之一是消去那些被挡住的线。

计算机生成的图形是线框图线。

由于计算机定义物体时没有考虑图的透视效果，它显示出物体的所有面，而不考虑这些面是在朝向观测者的一面还是位于通常人眼无法看到的背面。

可使用多种不同办法在计算机屏幕上生成图形。

一种办法是采用几何模板形式，这种办法是用基本形状和基本的元素创建图形，元素的长度及半径可以修改。

例如，圆柱是一个基本元素，在已显示的零件上去掉一个规定半径和长度的圆柱就可以生成一个孔。

但是每次变化都保留零件所有的几何特征。

另外，CAD系统使用成组技术设计零件。

成组技术是在功能、结构相同或加工方法相似的工件基础上采用分组编码的一种加工方法。

采用成组技术可使工厂减少所用零件得数量，并使零件在工厂中的制造、运输效率更高。

最近的CAD系统使用了压力有限元分析法。

在用这种方法时，待分析物体用很多有压力及弯曲特征的小元素组成的模型表示。

这种分析办法要求同时分解许多方程，用计算机执行一项任务，物体的弯曲可以通过生成动画的方式显示在计算机屏幕上。

有限元方法及国内外研究现状

现代机械设计理论与方法有限元方法学院：机械工程学院日期：2012年12月8日目录摘要 (3)关键词 (3)Abstract (3)Key Words (3)1 有限元方法的国内外研究现状及应用实例 (3)1.1 有限元的发展趋势 (3)1.2 有限元的应用实例 (3)2 有限元方法的分析过程 (4)2.1 有限元分析的三个阶段 (4)2.2 有限元分析的七个步骤 (5)2.3 有限元软件的分析过程 (6)3 参考文献 (8)有限元方法摘要：有限元方法法的基本概念是用较简单的问题代替复杂问题后再求解。

有限元法的基本思想是先化整为零﹑再积零为整，也就是把一个连续体分割成有限个单元；即把一个结构看成由若干通过节点相连的单元组成的整体，先进行单元分析，然后再把这些单元组合起来代表原来的结构进行整体分析。

关键词：有限元方法；单元；节点Finite Element MethodAbstract：The basic concepts of the finite element method is solving complex problems with a simple question instead.The basic idea of the finite element method is dismembered, and then plot the parts into a whole, that is divided a continuum into a finite number of unit; that is to regard a structure as a whole connected by many nodes，first to analysis unit，then analysis the overall combined by these units，which represents the original structure.Key Words：finite element method；unit；node1 有限元方法的国内外研究现状及应用实例“有限单元法”这一名称是克拉夫（Clough）在1960年首先引用的。

有限元的发展现状与新趋势

一、有限元法基本思想有限元法的基本思想是将结构离散化，用有限个简单的单元来表示复杂的对象，单元之间通过有限个节点相互连接，然后根据平衡和变形协调条件综合求解。

由于单元的数目是有限的，节点的数目也是有限的，所以称为有限元法(FEM，Finite Element Method)。

有限单元方法是迄今为止最为有效的数值计算方法之一，它对科学与工程技术的提供巨大支撑。

二、有限元法的孕育过程及诞生和发展▪在17世纪，牛顿和莱布尼茨发明了积分法，证明了该运算具有整体对局部的可加性。

▪在18世纪，著名数学家高斯提出了加权余值法及线性代数方程组的解法。

另一位数学家Lagrange提出泛函分析。

泛函分析是将偏微分方程改写为积分表达式的另一途经。

▪在19世纪末及20世纪初，数学家瑞雷和里兹首先提出可对全定义域运用位移函数来表达其上的未知函数。

▪1915年，数学家伽辽金提出了选择位移函数中形函数的伽辽金法方法被广泛地用于有限元。

▪1943年，数学家库朗德第一次提出了可在定义域内分片地使用位移函数来表达其上的未知函数。

这实际上就是有限元的做法。

▪20世纪50年代，飞机设计师们发现无法用传统的力学方法分析飞机的应力、应变等问题。

波音公司的一个技术小组，首先将连续体的机翼离散为三角形板块的集合来进行应力分析，经过一番波折后获得成功。

(Clough教授参与研究。

)▪20世纪50年代，大型电子计算机投入了解算大型代数方程组的工作，这为实现有限元技术准备好了物质条件。

▪1960年，美国加州大学伯克利分校的R.W.Clough教授在论文中提出了“有限单元”，这样的名词。

值得骄傲的是我国南京大学冯康教授在此前后独立地在论文中提出了“有限单元”。

三、有限元法计算方法及软件有限元计算方法作为一种技术更多的与FEM软件的发展紧密的结合起来。

方法不断更新，优胜劣汰，传承和发展。

在传统有限元分析的数值计算方法之中，有直接计算法(DirectSolver)与迭代法(Iterative 所谓快速解法)两种。

有限元分析的发展趋势

有限元分析的发展趋势摘要：1965年“有限元”这个名词第一次出现，到今天有限元在工程上得到广泛应用，经历了三十多年的发展历史，理论和算法都已经日趋完善。

关键词：有限元分析结构计算结构设计Abstract: The 1965 "finite" appeared for the first time this term, and today is widely used finite element in engineering, after more than 30 years of history, theory and algorithms have been improved. Finite element discretization of the core idea is to structure, is the actual structure of the supposed discrete combination unit for a limited number of rules, the actual structure to analyse the physical properties can be felt through a discrete body of drawn precision engineering approximation as an alternative to the analysis of actual structures, this would solve a lot of theoretical analysis and practical engineering needed to address complex problems that cannot be resolved.Key words: finite element analysis structural calculation physical design1 有限元的发展历程有限元法的发展历程可以分为提出(1943)、发展(1944一1960)和完善(1961-二十世纪九十年代)三个阶段。

有限元分析英文文献

The Basics of FEA Procedure有限元分析程序的基本知识2.1IntroductionThis 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。

2.2Overview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 mechanical behavior 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。

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Finite element analysis system development present situation and forecastAlong with modern science and technology development, the people unceasingly are making the faster transportation vehicle, the large-scale building, the greater span bridge, the high efficiency power set and the preciser mechanical device. All these request engineer to be able precisely to forecast in the design stage the product and the project technical performance, needs to be static, technical parameter and so on dynamic strength to the structure as well as temperature field, flow field, electromagnetic field and transfusion carries on the analysis computation. For example analysis computation high-rise construction and great span bridge when earthquake receives the influence, has a look whether can have the destructive accident; The analysis calculates the nuclear reactor the temperature field, the determination heat transfer and the cooling system are whether reasonable; Analyzes in the new leaf blade the hydrodynamics parameter, enhances its operating efficiency. The sell may sum up as the solution physics question control partial differential equations often is not impossible.In recent years the finite element analysis which develops in the computer technology and under the numerical analysis method support(FEA, Finite Element Analysis) the side principle for solves these complex project analysis estimation problems to provide the effective way. Our country in " 95 " Plan period vigorously promotes the CAD technology, mechanical profession large and middle scalene terries CAD popular rate from " 85 " End 20% enhances that present 70%.With enterprise application of CAD, engineering and technical personnel has gradually get rid drawing board, and will join the main energy how to optimize the design, engineering and improving the quality of products, computer-aided engineering analysis (CAE. Computer Aided Engineering) method and software will be the key technical elements .ln engineering practice, finite element analysis software and CAD system integration design standards should be a qualitative leap, mainly in the following aspects :The increase design function, reduces the design cost;Reduces design and the analysis cycle period;Increase product and project reliability;Uses the optimized design, reduces the material the consumption or the cost;Discovers the latent question in advance before the product facture or the project construction;Simulates each kind of experimental plan, reduces the experimental time and the funds;Carries on the machine accident to analyze, search accident cause factor.In vigorously promotes the CAD technology today, from the bicycle to the aerospace craft, all designs manufacture all will not be able to leave the finite eleme nt analysis computation, FEA obtains the more and more widespread value in the engineering design and the analysis. The next chart is the American San Francisco bay bridge earthquake responds the computation the finite element analysis model. The development direction and on significant progress international early20th century in the end of the 50's, at the beginning of the 60's has the formidable function on the investment massive manpower and the physical resource development the finite element analysis procedure. What is most famous was (NASA) entrusts US by American country Space Agency in 1965 to calculate the NASTRAN finite element analysis system which the scientific company and the Bell aerospace system company developed.This system development until now had several dozens editions, is in the present world the scale is biggest, the function strongest finite element analysis system. From at that time to the present, the world each place development facility and the university also developed one batch of scales smaller but to use nimble, the price is lower special-purpose or general finite element analysis software, mainly had German ASKA, England's PAFEC, France's company's the and so on SYSTUS, US'S ABQUS, ADINA, ANSYS, BERSAFE, BOSOR, COSMOS, ELAS, MARC and STARDYNE product. Now on the international FEA method and the software development presents below some tendency characteristics:1.develops from the pure structure mechanics computation to solves many physicalfields question finite element analysis method most early is comes from the structure matrix analysis development, gradually promotes to the board, the shell and the entity and so on the continual body solid mechanics analysis, the practice proved this is one extremely effective numerical analysis method. Moreover the or etically also already proved, so long as uses in to be separated solution object theunit enough to be small, the obtained solution may enough approach to the precise value.Therefore the recent years finite element method has developed question the and so on hydromechanics, temperature field, electricity conduction, magnetic field, transfusion and sound field solution computation, recently developed solves several inter disciplinary studies. the questions. For example when the air current flows a very high iron tower to have the distortion, but the tower distortion in turn affects to the air current flows. This needs to use the solid mechanics and the hydrodynamics finite element analysis finally overlapping iteration solves, namely so-called " Flows solid coupling " Question.2 Progresses from the solution linear project question to the analysis non-linear problem along with the science and technology development, the linear theory already by far could not satisfy the design there quest. For example in construction profession high-rise construction and great span hanging bridge appearance, request consideration geometry non-linear problem and so on structure big displacement and big strain; Astronautics and power engineering high temperature part existence thermal deformation and thermal load, also must consider the material the non-linear problem; Such as the plastic, the rubber and the compound material and so on each kind of new material appearance ,only depends on the question which the linear computation theory is insufficient to solve meets, only has uses the non-linear finite element algorithm to be able to solve. It is well known, the non-linear value computation is very complex, it involves to the very many special mathematics question and the operation skill, thanks the general engineering technical personnel to grasp very much. Has spent massive specialty and so on manpower and investment development such as MARC, ABQUS and ADINA for this recent years overseas some companies to solution non-linear problem finite element analysis software, and widely applies to the project practice. These software common characteristics are have the highly effective non-linear solution as well as rich and the practical non-linear material. Definitely.3 The enhancement visible pretag e modelling and the post positioned data processing function early time finite element analysis software research key lies in infers new high efficiency solution method and the high accuracy unit. Along with the numerical analysis method gradually consummation, the computer operating speed rapid development, the entire computing system uses in to solve the operation inparticular the time more and more few, but the data preparation and the operation result performance question day by day is actually prominent. On the present project workstation, solves to contain 100,000 equations the finite lement models only to need to use several dozens minutes. But if establishes this model with the manual way, then the rehandling massive computed result must use several week-long time. May not exaggerate said, engineer calculates a project question when the analysis has 80% above the energy all to spend in the data preparation and the result analysis. Therefore the present nearly all shangye finite element software all has the function very strong pretage modeling and the post positioned data processing module. Is emphasizing " Visible " Today ,very many procedures have all established to user extremely friendly GUI (Graphics User Interface), enables the user direct-viewing fast to carry on the grid automatic division by the visible graphic mode, the production finite element analysis needs the data, and the massive computed result will reorganize the distortion chart, the equivalentd is tribution cloud chart according to the request, will be advantageous for the extreme value search and needs the data to tabulate the output.4 With the CAD software seamless integration now the finite element analysis system another characteristic is and the general CAD software integrated use namely, after uses CAD software to complete the part and the components modeling design, automatically produces the finite element grid and carries on the computation, if analyzes the result does not conform to the design requirement then recarries on the modeling and the computation, until satisfaction, thus enormously raised the design level and the efficiency.The complex project analysis question today, which engineer may quickly solves in integrated CAD and in the FEA software environment in before is unable to deal with. Therefore now all shangye finite element system business all has developed and famous CAD software (for example Pro/ENGINEER, Unigraphics, SolidEdge, SolidWorks, IDEAS, Bentley and AutoCAD and so on) connection.5 Basically in Wintel platform development early time finite element analysis software all is in the large and middle scale computers(mainly is Mainframe) on the development and the movement, after wards also developed take the project workstation (EWS, Engineering WorkStation) as the platform, their common characteristic all uses the UNIX operating system.. The PC machine appearance caused the computer the application to have he fundamental change, engineer hadlonged for completed the complex project analysis on the desk the dream to become the reality. But early PC machine uses 16 CPU and the DOS operating system, in the memory public block data is restricted, at that time there fore calculated the model the scale not to be able to surpass 10,000 steps equations. Microsoft the Windows operating system and 32 Intel Pentium processor promoting for used in the finite element analysis PC machine to provide essential software and the hardware supports the platform. Therefore on the current international famous finite element procedure research and the development organization all in abundance move theirs software the value to the Wintel platform in. Next cava logged version environment and the SGI workstation simultaneously calculates the solution time with ADINA the V7.3 in PC machine Windows on the NT which 4 projects examples needed. May see the newest upscale PC machine solution ability already and center low-grade EWS is equally matched.In order to will develop on the large and middle scale computers and EWS the finite element procedure will move the value to PE machine on, frequently will need to use Hummingbird Corporation simulation software Exceed. Does this the result quite is troublesome, moreover cannot fully use the PC machine software and hardware resources. Therefore recently some companies, for example IDEAS, ADINA and R&D starts in the Windows platform to develop the finite element procedure, is called as " Native Windows" The edition, meanwhile has the finite element routine package which in on Linux operating system environment develops in PC machine.The domestic development situation and the prospect in 1979 US'S SAP5linear structure was static, the mechanical analysis procedure transplants successfully to the domestic introduction, raised the application general finite element procedure to analyze the computation project question the high tide. This high tide continuously continued to 1981 the ADINA non-linear structure analysis procedure introduction, many continuously was unable the project difficult problem which solved all to be easily solved for a while. Everybody also starts to realize indeed is engineer carries on then is computation to the finite element analysis procedure using the compute r the important tool。