文档介绍：Chapter 6 Finite Element Method for Plane Stress and Plane Strain Problems
第六章有限单元法解平面问题
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弹性力学第六章有限元
References 参考书
徐芝纶,弹性力学简明教程第六章。高等教育出版社。
华东水利学院, 弹性力学问题的有限单元法,水利电力出版社。
卓家寿, 弹性力学中的有限元法,高等教育出版社。
. Zienkiewicz, The Finite Element Method,Third Edition, , Z66
. Rockey and so on ,The Finite Element Method, Second Edition, , R682-2
徐汉忠第一版2000/7
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弹性力学第六章有限元
Introduction-1 导引-1
The finite element method is an extension of the analysis techniques (matrix method) of ordinary framed structures.
有限元法是刚架结构分析技术的扩充。
The finite element method was pioneered in the aircraft industry where there was an urgent need for accurate analysis plex airframes.
有限元法首先应用于飞机工业。
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弹性力学第六章有限元
Introduction-2
The availability of automatic puters from 1950 onwards contributed to the rapid development of matrix methods during this period.
从 1950以后数字计算机的出现使矩阵位移法迅速发展。
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弹性力学第六章有限元
Introduction-3
The finite element method was developed rapidly from 1960 onwards and known in China from 1970 onwards.
从 1960以后有限元法迅速发展。 1970以后传入我国。
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弹性力学第六章有限元
Introduction-4
In a continuum structure , a corresponding natural subdivision does not exist so that the continuum has to be artificially divided into a number of elements before the matrix method of analysis can be applied.
连续结构不存在自然的单元,须人为划分为单元
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弹性力学第六章有限元
Introduction-5
The artificial elements, which are termed ‘finite elements’ or discrete elements, are usually chosen to be either rectangular or triangular in shape.
单元通常取为三角形或矩形。
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弹性力学第六章有限元
Fundamental quantities and fundamental equations expressed by matrix 基本量和基本方程的矩程表示
Body force 体力: {p}=[X Y]T
Surface force 面力: {p}=[X Y]T
Displacement 位移: {f}=[u v]T
Strain 应变: {}=[x y rxy ]T
Stress 应力: {}= [x y xy ]T
Geometrical equations
Physical equations
virtual work equations
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弹性力学第六章有限元
Geometrical Equation 几何方程
x u/x /x 0 u
{}= y