裂纹扩展过程模拟的无网格MSLS方法

SIMULATION OF CRACK GROWTH BY THE MSLS METHOD

采用一种新提出的无网格MSLS方法来进行裂纹扩展过程的模拟分析,该方法的插值函数具有Kronecker delta属性,能够方便准确地施加本质边界条件,且其计算和求导过程相对滑动最小二乘(MLS)插值更为简单,克服了其它无网格方法的一些主要困难,适合于裂纹扩展等网格畸变和网格移动等问题的分析模拟。该文中采用围线积分法计算裂纹的应力强度因子,用最大周向应力理论来建立复合裂纹的断裂准则,数值算例表明了该文理论和方法的正确性与可行性。

A newly proposed Meshless Shepard and Least Square （MSLS） interpolation has been employed for the simulation of crack growth. The MSLS shape function possesses the much desired Kronecker delta property. Thus the essential boundary conditions can be treated as easily as they are in Finite Element Method （FEM）. The construction and derivation of the MSLS interpolation are also simpler than that of the Moving Least Square （MLS） approximation. This MSLS method overcomes the main difficulties of other meshless methods and is well-suited for the analysis of crack propagations. In this work, the contour integral method has been used to compute the mixed-mode stress intensity factors. The crack propagation angle is determined by the criterion of maximum stress in the tangential direction. Several numerical examples are presented to verify the validity and accuracy of the present method.