三维有限体中平片裂纹的超奇异积分方程方法——Ⅰ、理论分析

A THEORETICAL ANALYSIS OF THE PLANAR CRACK PROBLEM IN A THREE DIMENSIONAL FINITE BODY BY SOLVING HYPERSINGULAR INTEGRAL EQUATIONS

本文利用单个平片裂纹的基本解,将三维有限体中的平片裂纹问题,归为解一组超奇异积分方程,然后使用主部分析方法,对这组方程的求解作了理论分析,其结果在本文的第Ⅰ部分给出,关于这组方程的数值法求解,则给出于本文的第Ⅱ部分。

In this paper, using the fundamental solution for the planar crack problem, the problem of planar crack in a three dimensional finite body is reduced to the solution of a system of hypersin-gular integral equations. The theoretical analysis for solving this system of equations is presented, as the first part of the authors paper. In the second part, the authors will present the numerical method of solution of the hypersingular integral equations and the result.