位移边界条件下正交异性材料界面上的不对称扩展裂纹

根据平面波动方程的函数不变解思想,给出正交异性体反平面运动方程位移的不变解,导出具有任意自相似指数的问题解的一般表示,由此把正交异性体中不对称扩展界面裂纹的位移边界问题化为寻求单一未知函数的问题,此函数只需满足具体问题的边界条件。给出了实例,通过线性叠加,可以求得任意复杂位移边界条件下的解。

DISSYMMETRICAL EXTENSION CRACK AT THE INTERFACE BETWEEN ORTHOTROPIC MEDIA UNDER DISPLACEMENT BOUNDARY CONDITIONS

Based on the idea of functionally invariant solutions to the wave equation, invariant displacement solutions to the anti-plane equation of motion for orthotropic bodies are presented. The general representations of the solutions are derived for problems with arbitrary index of self-similarity. The problem under displacement boundary conditions of dissymmetrical extension crack at the interface between orthotropic media is transformed to a single unknown function, which only need satisfy the specific boundary conditions of a given problem. Examples are given to illustrate the present method, in which the solutions for arbitrary complex displacement boundary conditions are obtained based on linear superposition.