弹性力学中Fredholm积分方程组解法的表达通式及其讨论

本文采用覆盖域的概念,给出受外力作用的任意形状弹性体采用Fredhikm积分方程组解法的统一表达式,而且就含洞的无限大体且远场应力不为零,边界上有集中力作用等特殊情况进行讨论并给出相应的表达式,对边界上作用力和覆盖域边界上作用力之间在合力和合力矩上的关系也作了讨论,文中给出的算例表明,对于一些简单情况可以求得解析解。而对于需要采用数值解的问题,本文工作具有精度高、收敛快的优点。

GENERAL EXPRESSION OF FREDHOLM INTEGRAL EQUATIONS METHOD ON ELASTIC MECHANICS AND ITS DISCUSSION

In the paper, the concept of covering domain is used to develop a general expression for the Fredholm Integral Equations Method, by which the elasticity problems of arbitrary shaped body loaded by external forces cann be solved. Some special expressions are given for the body which is infinite and has no zero stresses at distance, or which is subjected to some concentrated forces on the boundary. The relationships between the loaded forces and the solution are also discussed. The examples given in the paper show that some analytical solution may be got for the simple problems. When the numerical solutions are needed, the method proves excellent in higher precision and faster convergence.