双轴载荷作用下源于椭圆孔的分支裂纹的一种边界元分析

A BOUNDARY ELEMENT ANALYSIS OF A PAIR OF BRANCHING CRACKS EMANATING FROM AN ELLIPTICAL HOLE UNDER BIAXIAL LOADS

利用一种边界元方法来研究双轴载荷作用下无限大板中源于椭圆孔的分支裂纹.该边界元方法由Crouch与Starfied建立的常位移不连续单元和笔者提出的裂尖位移不连续单元构成.在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界.文中算例说明本数值方法对计算平面弹性裂纹的应力强度因子是非常有效的.该文对双轴载荷作用下无限大板中源于椭圆孔的分支裂纹的数值结果进一步证实本数值方法对计算复杂裂纹的应力强度因子的有效性,同时该数值结果可以揭示双轴载荷及裂纹体几何对应力强度因子的影响.

This paper investigates stress intensity factors of a pair of branching cracks emanating from an elliptical hole in an infinite elasticity plate under biaxial loads. A boundary element method, which consists of the non singular displacement discontinuity element presented by Crouch and Starfied and the crack tip displacement discontinuity elements proposed by the author, is used to solve the problem. In the boundary element implementation, the left or the right crack tip displacement discontinuity element is placed locally on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundary. Numerical examples are included to show that the present approach is very efficient and accurate for calculating stress intensity factors of plane elasticity crack problems. Complex crack problems in a plane elasticity plate can be treated effectively by this approach, and the inflnence of the elliptical aspect ratio, and the transverse load on stress intensity factors can be examined by this model.