边界伸缩法

The Boundary Expanding-Contracting Method

本文提出边界伸缩原理,并在此基础上提出边界伸缩法.不但较好地解决了边界元方法中求解边界附近区域包括边界上解的问题,而且可以方便地利用迭代过程改善求解精度.计算实例表明.本文提出的方法是十分有效的.

The boundary element method (BEM) which is used to solve the elastic problems has more advantages than other numerical methods. Especially, .it can resolve rapidly varying internal stress and strain fields more accurately. However, it often fails in the region near the boundary because of the singularity of the solutions. Though we can increase the boundary meshes more and more, the solutions of stress on the boundary can't be given directly, which has obstructed the applications of the BEM to some extent. In this paper we proposed the boundary expanding-contracting principle and the boundary expanding-contracting method (BECM) based on the principle. With this method, not only the solutions in the region near or on the boundary can be obtained directly, but the iterative processes can also be used conveniently to improve the accuracy of the solutions.