含圆形嵌体弹性平面中径向裂纹问题的超奇异积分方程方法

根据含圆形嵌体平面问题在极坐标下的弹性力学基本解,使用Betti互换定理,在有限部积分意义下将问题归结为两个以裂纹岸位移间断为基本未知量、对于Ⅰ型和Ⅱ型问题相互独立的超奇异积分方程,对含圆形嵌体弹性平面中的径向裂纹问题进行了研究.根据有限部积分原理,建立了问题的数值算法.计算结果表明,嵌体半径、裂纹位置及材料剪切弹性模量等都对裂纹应力强度因子具有较为明显的影响.

Hyper-singular equation method for radial crack in elastic plane with a circular inclusion

A radial crack in an elastic plane with a circular inclusion is investigated by use of a hyper-singular integral equation method.Based on the fundamental solution of a plane with a circular inclusion under a polar co-ordinate,and using Betti's reciprocal theorem and the finite-part integral concepts,two independent hyper-singular integral equations for the crack problems of model I and model II are derived,in which the unknown functions is displacement discontinuities on the crack surface.Then,a numerical method for the solution of the hyper-singular integral equations are proposed,and the crack displacement discontinuities are approximated by products of a series of the second type of Chebyshev's polynomials and a basic density function,which exactly express the singularities of stress near the crack tips.The numerical solutions for the stress intensity factors of some examples are given.From the numerical results,it is shown that the stress intensity factors of a crack are greatly varied with the radius of a circular inclusion,the position of crack and the shear elastic module of a circular inclusion.