发布时间 : 星期四 文章吐血分享：研究生非线性有限元（双语）作业更新完毕开始阅读a0c27296d4d8d15abe234ed3
摘 要 摘 要
对于大多数工程问题的数值求解，有限元方法已经成为一种有效的求解工具，其所涉及和应用的领域及其广泛，不仅包括汽车、飞机、建筑、桥梁等的结构变形和应力分析，还包含热流、热体流、磁通量、渗流等流动问题的场分析。随着计算机技术和CAD技术的发展，许多复杂问题的求解通过计算机的建模分析已经很容易就能实现了。有限元的基本过程是：将被研究物体的复杂几何区域离散为简单的限单元，而单元内的材料性质和控制方程通过单元节点的未知量来进行表达，再通过单元集成、载荷和约束条件的处理，得到方程组，求解该方程组就可以得到该物体行为的近似表达式。本文根据平面应变问题的特点，采用四节点四边形单元，对所研究问题的截面进行离散和单元划分，通过设定形函数，列出问题的载荷矩阵以及相应的刚度矩阵，借助于MATLAB工具及其相应程序，编辑输入文件，从而得出问题的近似解。此外，本文还针对所研究的问题，运用ANSYS有限元分析软件，对其进行有限元分析，通过建立几何模型，划分网格，施加载荷和约束设定求解模式，得出比较精确的求解办法。基于编程计算结果和软件分析结果，本文对以上两种求解过程以及对应的求解结果进行了对比和分析，从而进一步加强了对有限元求解问题过程的理解和掌握。
关键词：有限元分析；四节点；四边形单元；平面应变；
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非线性有限元分析 Abstract
For most of the numerical solution of engineering problems, finite element method has become an effective tool for solving, which involves a wide application area, including not only structural deformation and stress analysis for automobiles, airplanes, buildings, bridges and other, but also field analysis of heat, hot body float, flux, seepage flow. With the development of computer technology and CAD technology, many complex issues solution has been easily achieved through computer modeling analysis. The basic process of finite element is as follow: discrete the complex geometry area of the object being studied into the simple finite element zone, material properties and control equations in the element are expressed via the unknown quantity for the node. The equations are obtained through integration units, loads, and constraints treatment, solving the equations，we can get the approximate expression of the body act. Based on the characteristics of plane strain problem, we use the four-node quadrilateral element to discrete and mesh the sections of problem under study, by setting the shape function and listing loading matrix and the corresponding stiffness matrix of problem, by means of MATLAB tools and corresponding
program, we edit the input file so as to arrive approximate solution. Additionally, for the research question, in this article, we also use ANSYS, finite element analysis software,
analysis the problem, by establishing the geometric model, meshing, applying loads and constraints and setting the solving mode to obtain more precise way to the solution. Based on the programming results and analysis results by software, the two solution process and the corresponding results above were compared solving and analyzed in the paper, thus, we can understand and master the further finite element problem solving process.
Keywords: finite element analysis; four nodes; quadrilateral element; plane strain;
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目 录 目 录
摘 要 ................................................................................................................................................ 1 Abstract ............................................................................................................................................ II 第一章 MATLAB的编程求解 ....................................................................................................... 1
1.1 MATLAB简介 ................................................................................................................... 1 1.2 四边形单元求解原理 ........................................................................................................ 1
1.2.1 形状函数 ................................................................................................................. 1 1.2.2 刚度矩阵 ................................................................................................................. 2 1.2.3 载荷矩阵 ................................................................................................................. 3 1.3 求解题目及建模 ................................................................................................................ 4 1.4利用QUAD程序求解 ....................................................................................................... 5 第二章 ANSYS的分析求解 ........................................................................................................... 9
2.1 ANSYS软件简介 ............................................................................................................... 9 2.2 ANSYS软件的优势 ........................................................................................................... 9 2.3 问题求解过程 .................................................................................................................... 9
2.3.1建立几何模型 .......................................................................................................... 9 2.3.2 网格划分 ............................................................................................................... 10 2.3.3施加载荷和约束 .................................................................................................... 11 2.3.4选定求解类型及求解模式 .................................................................................... 12 2.3.5查看结果 ................................................................................................................ 12
总 结 .............................................................................................................................................. 14 致 谢 .............................................................................................................................................. 15 参考文献......................................................................................................................................... 16
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