摘要
该文提出了一种计算效率较高的分析不同材料界面应力奇异性的一维杂交有限元方法。为了推导该方法,首先列出了用于求解不同材料界面裂纹奇异应力场特征解的基本方程和边界条件,然后利用加权残量方法(weighted residual method),得到上述基本方程和边界条件的弱形式,该弱形式的基本变量为位移和应力。运用Galerkin有限元方法的思想及上述弱形式,最后得到了一个一维杂交有限元方法,该一维杂交有限元方法只需对扇形区域在角度方向上离散,其总体方程为一个二次特征矩阵方程。数值算例表明:该方法可以准确而高效地计算不同材料界面奇异应力场的特征解。
A one-dimensional hybrid finite element method for the analysis of stress singularities at bi-material interfaces is developed in the paper. The governing equations and boundary conditions for interfacial crack eigenproblems are reviewed firstly. The weak form of the governing equations and boundary conditions is obtained by the weighted residual method. Displacement and stress are independent variables of the weak form. By virtue of Galerldn finite element formulation and the weak form, a one-dimensional hybrid finite element method that only discretizes the domain circumferentially is formulated. The resulting global equation is a second-order characteristic matrix equation. Validity and efficiency of the method are verified by numerical examples.
出处
《工程力学》
EI
CSCD
北大核心
2009年第2期21-26,共6页
Engineering Mechanics
基金
教育部留学回国人员科研启动基金项目(3047040220)
华南理工大学自然基金项目
关键词
杂交有限元
裂纹
奇异性
断裂
界面
hybrid finite element
crack
singularity
fracture
bi-material interface
