无单元Galerkin法和边界元耦合法

无网格方法与有限元法或边界元法耦合是无网格方法处理边界条件的方法之一,在无网格方法中研究无网格方法与有限元法或边界元法耦合的研究显得非常重要.本文在无单元Galerkin法和边界元法的基础上,基于无单元Galerkin法子域和边界元法子域的界面上位移连续和面力平衡条件,提出了一种新的无单元Galerkin法和边界元法的直接耦合方法,对弹性力学问题详细推导了在整个求解域上的耦合公式.与以往的耦合法相比,这种方法简单直观,不需要增加新的耦合区域,也不需要建立新的逼近函数来保证界面位移的连续性.算例结果表明,该方法具有较好的计算精度.

Coupling of Element Free Galerkin Method and Boundary Element Method

The coupling of meshless method with finite element or boundary element method is one of the methods to apply the boundary conditions in meshless method.Based on element-free Galerkin method and boundary element method,and considering the conditions of displacement and traction on the interface between element-free Galerkin sub-domain and boundary element sub-domain,a new direct coupling of element-free Galerkin method and boundary element method was proposed.The corresponding formulae of EFG-BEM for elasticity were obtained in detail.Comparing with other coupling methods,the coupling method in this paper is a direct method,no new sub-domain needed near the interface,and no approximation function needed to ensure continuous displacement on the interface.A numerical example was given and show the method has high precision.