双材料中矩形裂纹问题的超奇异积分方程方法

使用超奇异积分方程方法,对双材料空间中垂直于界面的矩形裂纹Ⅰ型问题进行了研究.首先根据双材料空间的弹性力学基本解,使用边界积分方程方法,在有限部积分的意义下导出了以裂纹面位移间断为未知函数的超奇异积分方程.根据裂纹面上位移函数的分布特性,通过将位移间断函数表示为特征函数和一组多项式乘积的形式,为其建立了数值方法.数值结果表明,该方法不仅具有较好的收敛性和较高的数值计算精度,而且能够精确满足裂纹面上的边界条件.在此基础上,对不同材料组合界面对裂纹前沿应力强度因子的影响进行了分析,取得了较好的数值结果.

Hypersingular integral equation method for a rectangular crack subjected to tension loading in bimaterial

The method of hypersingular integral equation is applied to the calculation of the stress intensity factor at the front of a rectangular crack which is vertical to a bimaterial interface and loaded by interior normal pressure.Based on the fundamental solution of two perfectly bonded elastic halfspaces,and using the boundary integral equation method and the finite-part integral concepts,the problem is reduced to a hypersingular integral equation in which the unknown function is the crack opening displacement discontinuity.In the numerical calculation,the unknown function is approximated by the product of basic density function and polynomials.The results show that the present method yields rapidly converging numerical results of stress intensity factors for various aspect ratios of a rectangular crack near an interface,and the boundary conditions along the crack surface are satisfied well.Finally,numerical solutions for the stress intensity factors of some examples are provided in tables with varying the shape of crack,distance from the interface,and elastic constants,and the effect of bimaterial interface and crack shape on the stress intensity factor is discussed.