双材料平面多裂纹问题的超奇异积分方程方法

基于双材料平面问题的弹性力学基本解，使用边界积分方程方法，在有限部积分的意义下，将双材料平面单侧多裂纹问题归结为1组以裂纹面位移间断为未知函数的超奇异积分方程组，根据有限部积分原理为其建立了数值算法，并给出了相应的应力强度因子计算公式。通过对均质平面中共线双裂纹问题和双材料平面中存在2个垂直于界面裂纹问题的数值计算，分析了裂纹之间以及裂纹与界面之间的相互影响。数值结果表明，超奇异积分方程方法能够有效求解双材料中多个裂纹的相互作用问题。

HYPERSINGULAR INTEGRAL EQUATION METHOD OF MULTIPLE CRACKS IN BIMATERIAL PLANE

Based on the fundamental solution of elasticity for two-half elasticity plane,the boundary integral equation method is extended to study the fracture problem in bimaterial plane with multiple cracks subjected to arbitrary loads. As the cracks lie in one side of the bimaterial plane,the problem is reduced with finite-part integral conceptions to a set of hypersingular integral equations,in which the unknown functions are the displacement discontinuities on the crack surfaces. According to the finite-part integral principles,a numerical method for the hypersingular integral equations is established. Then,based on the analytic results of the singular stress fields near the crack tip,a set of numerical formulas for stress intensity factors are proposed. Finally,solutions for stress intensity factors are given for conditions such as those with two collinear cracks in a finite plane and two cracks which are perpendicular to the interface in bimaterial plane. The interaction of cracks and the effects of the interface on stress intensity factors are investigated in detail. The numerical results show that the hypersingular integral equation method works effectively in solving the multiple cracks problem in bimaterial plane.