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\ud 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\ud 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

Displacement approach with external variables only for multi-domain analysis via symmetric BEM

“…The regularity conditions written at the interfaces between the bem-es and a subsequent condensation process lead to a solving equation system having reduced dimensions due to the presence of only the nodal displacements of the free boundary. This strategy has been implemented inside the Karnak.sGbem calculus code (Panzeca et al, 2002a) and some applications show the effectiveness of the response compared to the analytical solutions, when the latter are applicable, or to the single domain formulation with the symmetric BEM.…”

“…The load vector coefficients are obtained in closed form too. A particular strategy made it possible to set up a software, called Karnak.sGbem (Panzeca et al, 2002a), able to give solutions to plane structural system having any geometry and subdivisible into bem-es having different material characteristics and different thicknesses. These systems may be subjected to inplane external actions, like boundary and volume forces or imposed displacements of the constraints and inelastic actions.…”

“…Both the strategies shown in the Sections 3 and 4 have been implemented within the Karnak.sGbem (Panzeca et al, 2002a) calculus code. It is necessary to point out that both the displacement methods shown in this paper, i.e.…”

“…The method proposed was implemented within the Karnak.sGbem (Panzeca et al, 2002a) calculus code. This algorithm allows one to perform an elastic analysis for plates having any shape, made up of homogeneous material and having constant thickness for each bem-e, subjected to boundary forces, to imposed displacements, and to domain actions like body forces and inelastic strains, both transferred on the boundary of the bem-e according to a strategy developed by Panzeca et al (2004).…”

Shear deformable plate by SGBEM: Indirect “progenitor matrix” approach

“…In Eq. ( 53) the rows of weighted displacements and tractions 2   W 0 and 1   P 0 , not verified by solution, are available for further post-analysis steps such as: improvement of discretization on the boundary through the evaluation of weighted residuals or energy considerations [28]; energy evaluation in the body domain and in the unlimited domain [29].…”