Analysis of thin-walled structural elements via 3D standard BEM with generic substructuring

Abstract

This paper is concerned with the application of standard 3D Boundary Element Methods to solve thin-walled structural elements (needle-like/shell-like solids). A subregion-by-subregion data structure, incorporating iterative solvers and discontinuous boundary elements, is presented. To efficiently and accurately evaluate the quasi-singular integrals, special quadrature methods are applied. In addition, structured matrix-vector products, designed to avoid the excessive number of conditional tests during solver iterations, are proposed. Numerical results for complex thinwalled BE models are validated by comparison with FEM calculations and previously published BEM analyses. KeywordsThe boundary element method · Thin-walled structural elements · Singular and quasi-singular quadratures · Subregion-by-subregion storage formats · Structured matrix-vector products

Constructing efficient substructure-based preconditioners for BEM systems of equations

“…In previous works [21,22,[24][25][26][27][28], several numerical quadratures have been investigated. One has concluded that the numerical integration strategy proposed in Ref.…”

“…To accelerate the solver iterations, structured matrix-vector products (SMVP) [21,28] are employed. Herein, the matrix columns of a given subregion are grouped into three separate blocks: one associated with interfaces G ij for which i 4j, a second associated with the outer boundary G ii , at which boundary values are prescribed, and one associated with interfaces G ij for ioj.…”

Boundary-element parallel-computing algorithm for the microstructural analysis of general composites

“…This was demonstrated in Araújo et al [40], where continuous boundary elements are used to model 3D frequency-dependent elastodynamic problems. Discontinuous boundary elements avoid this issue, but require special integration algorithms for the quasi-singular integrals [38,12,41]. This approach has been adopted herein.…”

“…To avoid these difficulties, the direct application of 3D standard boundary-element formulations has been employed to model general composites and thin-domain problems [11][12][13]. Besides advantages as high accuracy, fulfillment of radiation conditions, and easier mesh generation, the boundary-element method (BEM) also presents the following interesting characteristic: it is derived from the exact integral representation of the problem response and does not require any interelement compatibility (in the FE sense) for assuring solution convergence.…”

“…This allows more flexibility for generating boundary-element models as long as the integrals involved are accurately evaluated. Indeed, this is the basis of discontinuous boundary elements, very useful for the BE subregion-by-subregion (BE-SBS) algorithm [12], considered in this work for the microstructural modeling of composites and development of the parallel code.…”