非均质问题中的无网格边界单元法

介绍了一种不需要内部网格计算非均匀介质问题的边界元算法.该算法是建立在一种能将任何区域积分转换成边界积分的径向积分转换法基础上,首先用对应各向同性问题的基本解来建立以正规化位移表示的非均质问题的积分方程,然后用径向积分转换法将出现在积分方程中的区域积分转换成边界积分,从而形成不需要使用内部网格来计算区域积分的纯边界元算法.与其它无网格法相比,此方法需要很少的内部点,有些问题甚至不需要内部点都能得到满意的结果,因此,可以计算大型的三维非均匀介质工程问题.由于此方法继承了边界元和无网格算法的优点,因而具有广阔的发展前景.

MESHLESS BEM IN NONHOMOGENEOUS PROBLEMS

A boundary element method which can be used to solve nonhomogeneous and nonlinear problems without using internal cells is described. This method is based on a transformation technique,the Radial Integration Method(RIM),which can transform any domain integrals into boundary integrals.Firstly,integral equations expressed in terms of normalized displacements for nonhomogeneous and nonlinear problems are derived using fundamental solutions for corresponding linear isotropic problems,and then the domain integrals appearing in the integral equations are transformed to the boundary using RIM,resulting in a pure boundary element algorithm without need of internal cells to evaluate these domain integrals.Comparing to other meshless methods,this method requires much less internal points.For some problems,even without internal points,satisfactory results can also be achieved.Therefore, large three dimensional nonhomogeneous and nonlinear engineering problems can be solved.Since the method has the advantages of the boundary element method and meshless methods,it has a promising development potential.