弹性半空间中矩形平片裂纹问题分析

通过使用超奇异积分方程方法,对弹性半空间中与自由边界面垂直的I型三维矩形平片裂纹问题进行了研究.首先根据弹性半空间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导出了以裂纹面位移间断为未知函数的超奇异积分方程.通过将位移间断函数近似地表示为特征函数与一组多项式之积的形式,建立了数值计算方法.通过对几个典型数值算例的计算,分析了自由边界面对裂纹前沿应力强度因子的影响.

Analysis of a Rectangular Planar Crack in a Halfspace Elasticity

In this paper a hypersingular integral equation method is applied to calculate the model I stress intensity factor along a rectangular planar crack vertical to free boundary surface in a halfspace elasticity.Based on the fundamental solution of a halfspace elasticity,the boundary integral equation method is used to reduce the problem to a hypersingular integral equation in which the unknown function is the crack opening displacement discontinuity.In solving the hypersingular integral equation,the unknown function is approximated by the product of a fundamental density function and a polynomial.The calculation shows that the present method gives the smooth variation of stress intensity factors along the crack front.Finally,some numerical examples are given in this paper,and the effect of the free boundary surface on the stress intensity factors is investigated in detail.