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REVIEW ARTICLES

Symmetric Galerkin Boundary Element Methods

[+] Author and Article Information
Marc Bonnet

Laboratoire de Mécanique des Solides, CNRS UMR 7649, Ecole Polytechnique, 91128 Palaiseau Cedex, France

Giulio Maier

Department of Structural Engineering, Technical University (Politecnico), 20133 Milan, Italy

Castrenze Polizzotto

Department of Structural and Geotechnical Engineering, University of Palermo, 90128 Palermo, Italy

Appl. Mech. Rev 51(11), 669-704 (Nov 01, 1998) (36 pages) doi:10.1115/1.3098983 History: Online April 20, 2009

Abstract

This review article concerns a methodology for solving numerically, for engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form. The discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager’s sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions; some quadratic forms have a clear energy meaning; variational properties characterize the solutions and other results, invalid in traditional boundary element methods enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, and computer implementations. Areas and aspects which at present require further research are identified, and comparative assessments are attempted with respect to traditional boundary integral-elements. This article includes 176 references.

Copyright © 1998 by American Society of Mechanical Engineers
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