三维无限体中两平行平片裂纹相互干扰的超奇异积分方程解法

APPLICATION OF THE HYPERSINGULAR INTEGRAL EQUATIONS METHOD TO THE INTERACTION BETWEEN TWO PARALLEL PLANAR CRACKS IN 3-D ELASTICITY

本文利用三维断裂力学的超奇异积分方程求解理论，对三维无限体中两平行平片裂纹在任意载荷作用下的相互干扰问题作了研究．首先导出了以裂纹面位移间断（位错）为未知函数的超奇异积分方程组，然后为其建立了有限部积分边界无法；在此基础上，讨论了用裂纹面位移间断计算应力强度因子的方法，最后用此计算了两平行平片裂纹的相对位置对裂纹前沿应力强度因子的影响，其数值结果令人满意．

By using the analytic theory of hypersingular integral equations in three-dimensional fracture mechanics,the interactions between two parallel planar cracks under arbitrary loads are investigated.According to the concepts and method of finite-part integrals,a set of hypersingular integral equations is derived, in which the unknown functions are the displacement discontinuities of the crack surfaces.Then a numerical method of combining the finite-part integral method with the boundary element method is proposed.The method for calculating the stress intensity factors by using the displacement discontinuities of crack surfaces is discussed. Finally,several typical examples are calculated and the numerical results are satisfactory.