Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity

摘要

The coupling of Finite Element Method (FEM) with a Boundary Element method (BEM) is a desirable result that exploits the advantages of each. This paper examines the efficient symmetric coupling of a Symmetric Galerkin Multi-zone Curved Boundary Element Analysis method with a Finite Element Method for 2-D elastic problems. Existing collocation based multi-zone boundary element methods are not symmetric. Thus, when they are coupled with FEM, it is very difficult to achieve symmetry, increasing the computational work to solve the problem. This paper uses a fully Symmetric curved Multi-zone Galerkin Boundary Element Approach that is coupled to an FEM in a completely symmetric fashion. The symmetry is achieved by symmetrically converting the boundary zones into equivalent 'macro finite elements', that are symmetric, so that symmetry in the coupling is retained. This computationally efficient and fast approach can be used to solve a wide range of problems, although only 2-D elastic problems are shown. Three elasticity problems, including one from the FEM-BEM literature that explore the efficacy of the approach are presented.