有限元法基础ElementandNode单元和节点.PPT

Theory of Elasticity弹性力学 Chapter 8 Two-Dimensional Solution 平面问题的直角坐标求解 13.1 Numerical Methods (数值方法) 13.2 Basics of the Finite Element Method (有限元法基础) 13.3 Approximating Functions for Two-Dimensional Linear Triangular Elements (二维线性三角形单元的近似函数) 13.4 Virtual Work Formulation for Plane Elasticity (平面弹性虚功方程) 13.5 A Simple Example (简单例子) 13.6 FEM Code Application (有限元序程的应用) Vocabulary(词汇) * Chapter Page Content（内容） 13 1 Introduction（概述） Mathematical Preliminaries （数学基础） Stress and Equilibrium（应力与平衡） Displacements and Strains （位移与应变） Material Behavior- Linear Elastic Solids（弹性应力应变关系) Formulation and Solution Strategies（弹性力学问题求解） Two-Dimensional Formulation （平面问题基本理论） Two-Dimensional Solution （平面问题的直角坐标求解） Two-Dimensional Solution （平面问题的极坐标求解） Three-Dimensional Problems（三维空间问题） Bending of Thin Plates （薄板弯曲） Plastic deformation – Introduction（塑性力学基础） Introduction to Finite Element Mechod（有限元方法介绍） Chapter Page 13 2 Introduction to Finite Element Mechod （有限元方法介绍） Chapter Page 13 3 13.1 Numerical Methods  (数值方法) Three numerical methods (三种数值方法) Finite dfifference method (FDM) (有限差分法) Finite element method (FEM) (有限元法) Boundary element method (BEM) (边界元法) Chapter Page 13 4 13.1 Numerical Methods  (数值方法) History of FEM (有限元发展历史) In 1943，Courant proposed a approximative method in his mathematic paper which was similar to FEM (1943年Courant在他的应用数学论文中首先提出了一个与有限单元法类似的近似方法。) In 1960,Clough proposed Finite Element Method (FEM) ( 1960年，Clough提出了有限元法) Clough Chapter Page 13 5 13.2 Basics of the Final Element Method  (有限元法基础) Element and Node (单元和节点) FEM discretizes the domain under study by dividing the region into subdomains called elements. (有限元方法将研究区域离散成许多子域，这些子域叫单元) node (节点) element(单元) Chapter Page 13 6 13.2 Basics of the Final Element Method  (有限元法基础) Typical basic steps (典型基本步骤) 1. Discretize the body into a finite number of element subdomains (离散) 2. Develop approximate so