平面三角形单元有限元差分法

The Finite Element Difference Method on Plain Triangular Element

本文基于有限元差分法的构造方法,建立了平面三角形单元的有限元差分法。该方法的计算过程简单、规范,能够形成通用的计算程序。它直接给出连续的应力场,能够通过常应变收敛试验,具有较常规有限元法高得多的计算精度。更重要的是,该方法的构造思路能够推广于人们熟知的任何单元中。

According to the formulation procedures in ref. [1], this paper establishes a finite element-difference method(FEDM for short) on the plain triangular element. The calculation with this method is simple and standard, and can be easily to work out universal programs. It directly obtaines a continuous stress field and is able to pass through patch test, in addition, it provides a much higher computational precision than classical finite element does. Morever, it is more significant that, according to this formulation, every element known intimately in finite element method can be used in forming FEDM.