静、动态基本解及奇异积分的探讨

Fundamental Solution and Singular Integral

本文首先讨论了弹性力学中动力基本解和静力基本解的关系,得到了对于空间问题令频率ω→0可以从动力基本解退化到静力基本解,对于平面问题则不能从动力基本解退化为静力基本解的结论;其次求得了边界单元法中的奇异积分的解析表达式,从而证明了不管奇点是否位于角点、奇异积分在Cauchy主值意义下总是存在的问题.文中还给出了数值验证结果.

In this paper , the relation between the elastodynamic and static fundamental solutions is discussed . On this basis a conclusion is made that if the frequency ω approaches to zero the elastodynamic fundamental solution will become the static foundamental solution for three dimensional problems , but not for two dimensional problems . An analytic expression of singlar integral is also presented