移动接触下求解二维闭合裂纹的双重迭代边界元法

A double iterative BEM for solving 2D closed crack loaded by a moving contact elastic body

使用子域边界元法对受移动接触弹性体作用下的二维闭合裂纹问题进行了数值计算。由于两弹性体的接触界面和裂纹表面的接触范围的大小和接触状态事先是未知的 ,对此 ,在两个接触表面同时采用迭代的方法进行了求解。在裂纹的每个裂尖上都采用了四分之一的奇异单元以保证裂尖位移场和应力场奇异性的满足。用我们编制的二维裂纹问题程序对一些中心裂纹问题进行了计算 ,计算结果与经典断裂力学的理论值比较吻合。在无摩擦的条件下 ,对一些具有不同角度且受移动接触弹性体作用下的闭合裂纹问题进行了数值计算 。

Using a sub\|region boundary element method, the two\|dimensional closed crack problems loaded by a moving contact elastic body are calculated. Since the extent and nature of the contact interface for two elastic bodies and the crack are all not known in advance, a double iterative contact algorithm is presented. The singular quarter\|point boundary elements on each side of the crack tips are used to guarantee the singularity of displacement and stress field. The BEM program for solution of closed crack problem is developed, some numerical examples are presented, and the results of center crack cases are in good agreement with the analytical solution in classical fracture mechanics. In the condition of non\|friction, some coupling computational results of SIF for closed crack problems, which has different angles and loaded by a moving contact elastic body, is also obtained by numerical computation.