断裂力学中统一的第二类边界积分方程

The Unified Second Kind Boundary Integral Equation in Fracture Mechanics

利用Ｂｅｔｔｉ互等定理，由第一基本解（单位力基本解）导出了第二基本解（单位位移不连续基本解）的一般表达式，在此基础上建立了断裂力学中统一的第二类边界积分方程。最后，经过退化处理给出了目前有关文献中发表的第二基本解及第二类边界积分方程的各种具体表式。本文的研究结果为求解三维及平面、反平面多裂纹问题提供了理论基础。

At first, the general second foundamental solution is derived from the first one by using Betti's reciprocal theorem. Then the unified second kind boundary integral equation is proposed. Finally, degenerating the present results, the expressions of the second foundamental solution and the second kind boundary integral equation in the related literature are given. The present work provides a theoretical basis for solving the problem of threedimensional and plane anti-plane multi-cracks.