摘要:
根据[1～2]中提出的离散型固体力学及其变分原理的基础上,本文形成四种类型的元素的边界积分变分定理.当进行断裂分析时,可用它们计算沿裂纹边界法线方向的能量释解率;在有孔洞时,当在孔洞边界存在或不存在外力作用的情况下,可用它们计算沿孔洞边界法线方向的能量改变量;当进行离散分析时,也可以用来建立离散方程.以便求解待解函数值.并且由本文分析可知,在[3]中提出的J积分形式是不确切的.
Abstract:
Based on the solid mechanics of the discrete form and its variational principles pro-posed by Niu[1,2], this paper puts forward four kinds of the boundary integral-variational theorems of an aroitrary element. In the course of the fracture analysis,they can be used to compute the energy release rate along the normal direction of the crack boundary.When there is the hole in the solid, and there are the given surface forces on the hole boundary or there are not any given surface forces on the hole boundary, they can be used to compute the variation of the energy along the normal direction of the hole boundary. In the course of the discrete analysis, they can be used to establish the discrete equations,so that the values of the unknown functions are solved. At the same time, from this paper we know that the J-integral proposed by Rice[3] represents an integral to be independent of a path imperfectly.
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