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。