三维体内含垂直于双材料界面混合型裂纹的超奇异积分解法

利用双材料位移基本解和Somigliana公式,将三维体内含垂直于双材料界面混合型裂纹问题归结为求解一组超奇异积分方程。使用主部分析法,通过对裂纹前沿应力奇性的分析,得到用裂纹面位移间断表示的应力强度因子的计算公式,进而利用超奇异积分方程未知解的理论分析结果和有限部积分理论,给出了超奇异积分方程的数值求解方法。最后,对典型算例的应力强度因子做了计算,并讨论了应力强度因子数值结果的收敛性及其随各参数变化的规律。

Application of the hyper-singular integral equation method to a three-dimensional mixed-mode crack perpendicular to the bi-materiai interface

Using the fundamental displacement solutions and Somigliana's formula,a mixed-mode three-dimensional crack perpendicular to the interface of different materials is reduced to solve a set of hyper-singular integral equations.The singularity of the singular stress field around the crack front termina-ting at the interface is analyzed by the main-part analysis method of hyper-singular integral equations,and the formulae to evaluate the stress intensity factors expressed with the displacement discontinuities are obtained.Then a numerical method for the hyper-singular integral equations is proposed by using the finite-part integral concepts and the analytical results of the displacement discontinuities near the crack front.Finally,numerical solutions of some typical examples are given.The convergence of stress inten-sity factors is discussed.