Boundary discretization based on the residual energy using the SGBEM

Abstract

The paper has as objective the estimation of the error in the structural analysis performed by using the displacement approach of the Symmetric Galerkin Boundary Element Method (SGBEM) and suggests a strategy able to reduce this error through an appropriate change of the boundary discretization. The body, characterized by a domain X and a boundary C , is embedded inside a complementary unlimited domain X1nX bounded by a boundary C+. In such new condition it is possible to perform a separate valuation of the strain energies in the two subdomains through the computation of the work, defined generalized, obtained as the product among nodal and weighted quantities on the actual boundary C and on the complementary boundary C+. In order to reduce the error in the analysis phases, the scattered energy has been computed as generalized work in each boundary element of C+ and an adequate node number has been introduced inside the boundary elements where this generalized work is higher. This strategy, made in a recursive way, has shown effectiveness whether in the convergence proofs of some mechanical and kinematical quantities or in computing the percentage error obtained as ratio between the scattered work in X1nX and the total work, both expressed in terms of generalized quantities.