可压或不可压固体结构非线性断裂有限元分析

可压或不可压固体结构非线性断裂有限元分析 A FINITE ELEMENT METHOD FOR NONLINEAR FRACTURE ANALYSIS OF COMPRESSIBLE OR INCOMPRESSIBLE SOLIDS 叶碧泉 Ye Biquan 1 first-author Departmert of Mathematics Wuhan University Wuhan Hubei Departmert of Mathematics Wuhan University Wuhan Hubei Depaitmeit of Mathematics, Wuhan University Depaitmeit of Mathematics, Wuhan University 本文采用弹-塑性分析中的全量迭代法计算了带裂纹体的应力、应变场,以及作为非线性断裂判据的J积分和裂纹张开位移δ;考虑到材料的可压或不可压性,我们采用了简化积分的办法,克服了常规有限单元法计算单元刚度矩阵时所遇到的困难。 In this paper, we use Newton-Raphson method to analysis elasto-plasticity fracture problems The stress and strain fields at the tip of the crack as well as J-integral have Calculated （J Cam be thought of as the amplitude of the crack tip singularity fields）. As poisson’s ratio μ egn or approaches 0.5, regular finite element method become inappliable In order to overcome the difficulty, we transform siffne-ss matrix into K 1 +αK 2 （as μ→0.5, α→∞）, and then, use regular Gauss in-tegral for K 1 and reduced integral for K 2 . This method not only can be app-lied to two dimensions but also to three dimensions. J积分 裂纹张开位移 非线性有限元分析 简化积分 J-integral The crack opening displacement Nonlinear finite element analysis Reduced integral. 国家自然科学基金(61672102) 1988-02-01 2021-04-01 2