切向载荷下内嵌椭圆片裂纹问题的解法

Solutions of the Embedded Elliptical Crack Problem under Shear Loading

利用微分积分方程方法研究三维无限弹性体内嵌平片裂纹问题首先建立平片裂纹问题中裂纹面上的载荷和裂纹扩张位移所满足的微分积分方程，对椭圆片裂纹问题进行研究，如果作用在椭圆片裂纹面上的载荷是幂函数形式，则其裂纹扩张位移有闭合形式解其中关键步骤是作者利用了首创的一种特殊极坐标体系计算得到了一系列的微分积分结果，再利用待定系数法得出了各种载荷下的线性方程组，解之后可得其裂纹扩张位移解答。

Stress intensity factors of an embedded elliptical crack in three-dimensional elasticity are studied in this paper by using differential-integral equations. We first established the differential-integral equations which contain the traction applied on the crack face and the crack opening displacement at the crack boundary. It is found that if the traction applied on the crack face takes the form of power function,the crack opening displacement can be evaluated in a closed form and stress intensity factors can be found immediately. The key procedure is to solve the differential-integral equations by a particular polar coordinate developed by the present authors.