基于哈密顿原理的两种材料界面裂纹奇性研究

研究了两种材料组成的弹性体在交界面上含裂纹时的裂纹尖端奇异场。通过变量代换及变分原理，将平面弹性扇形域的方程导向哈密体系，从而可通过分离变量及共轭辛本征函数展开法解析法求解扇形域方程，得到求解双材料界面裂纹尖点奇性的一般表达式，由此为该类问题的求解开辟了一条新途径。

THE INTERFACE CRACK SINGULARITY ANALYSIS OF THE BIMATERIAL BODY BASED ON HAMILTON PRINCIPLE

The stress singularity of the tip of crack at the interface of bimaterial elastic body is considered. The governing equations of plane elasticity for sectorial domain are derived in Hamiltoman form by using variable substitution and variational principle.The methods of separation of variables and conjugate symplectic eigenfunction expansion are developed for solving the equations in sectorial domain.The general formulations of solving the singnlarity of the crack tip at bimaterial interface are put forward.