A new implementation of BEM by an expanding element interpolation method

Abstract

A new implementation of boundary element method (BEM) by an expanding element interpolation method is presented in this paper. The expanding element is achieved by collocating virtual nodes along the perimeter of the traditional discontinuous element. With the virtual nodes, both continuous and discontinuous fields on the domain boundary can be accurately approximated, and the interpolation accuracy increases by two orders compared with the original discontinuous element. The boundary integral equations are built up for the inner nodes of the traditional discontinuous elements, only (taking these nodes as source points), while the virtual nodes are used for connecting the shape functions at the source points, thus the size of the final system of linear equations will not increase. The expanding element inherits the advantages of both the continuous and discontinuous elements while overcomes their disadvantages. Successful numerical examples with different boundary conditions have demonstrated that our new implementation is very encouraging and promising.

The boundary element method for elasticity problems with concentrated loads based on displacement singular elements

“…The boundary element method [1 -6] has been applied in many areas [7][8][9][10][11][12] because of its high accuracy and boundary-only discretization. Compared with the finite element method (FEM), BEM can obtain very high accuracy with much fewer elements on the boundary.…”

Boundary Element Analysis of Thin-Walled Structures Using an Expanding Element Interpolation Method

“…Accurate and efficient analysis of super thin structures is of crucial importance in engineering applications [1], [2]. The boundary element method (BEM) [3]- [9] has become recently an attractive alternative for problems in computational mechanics, and has been widely used to solve the problems of computational mechanics. Compared with the FEM, the BEM is a boundary method.…”