弹性半空间中平片裂纹问题的超奇异积分方程方法  

HYPERSINGULAR INTEGRAL EQUATION METHOD FOR A PLANAR CRACK PROBLEM IN A HALFSPACE ELASTICITY

作　　者：刘建秀[1] 乐金朝[1,2] 乐金朝 

机构地区：[1]郑州轻工业学院机械工程系,郑州450002 [2]郑州工业大学水利工程系,郑州450002

出　　处：《机械强度》1999年第3期208-211,共4页Journal of Mechanical Strength

基　　金：河南省自然科学基金

摘　　要：使用边界积分方程方法，在有限部积分的意义下，将弹性半空间中垂直于自由边界面的平片裂纹问题归结为一组以裂纹面位移间断为未知函数的超奇异积分方程，根据有限部积分原理为其建立了数值方法，并给出了用裂纹面位移间断计算应力强度因子的公式。通过对圆形、椭圆形和矩形等典型的平片裂纹问题的计算。In this paper, the boundary integral equation method is used to study a halfspace elasticity with an embedded planar crack subjected to arbitrary loads. As the crack is perpendicular to the free boundary, 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 surface. 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 field along the crack front, numerical formulas of stress intensity factors by using the displacement discontinuities near the crack front are given. Finally, the stress intensity factor solutions of some typical planar crack problems (such as circular, elliptic and rectangular) are calculated, and the effect of the boundary on the stress intensity factors is investigated in detail.

关 键 词：平片裂纹 超奇异积分方程 弹性半空间 

分 类 号：O346.1[理学—固体力学]