Closed form coefficients in the symmetric boundary element approach

Abstract

In the area of the structural analysis, the problems connected to the use of the symmetric Galerkin Boundary Element Method (SGBEM) must be investigated especially in the mathematical and computational difficulties that are present in computing the solving system coefficients. Indeed, any coefficient is made by double integrals including often fundamental solutions having a high degree of singularity. Therefore, the related computation proves to be difficult in the solution. This paper suggests a simple computation technique of the coefficients obtained in closed form. Using a particular matrix, called ‘progenitor’ matrix [Panzeca T, Cucco F, Terravecchia S. Symmetric boundary element method versus finite element method. Comp Method Appl Mech Eng 2002;191:3347–67.], it is possible to derive the solving algebraic system made up of a coefficient matrix and of a known term vector. The latter matrices and vectors, arranged in the sub-structure approach, permitted to develop a versatile computation code, called KARNAK.sGbem [Cucco F, Panzeca T, Terravecchia S. The program KARNAK SGBEM release 1.0. Palermo; 2002. Available from: http://www.bemsoft.it.].