Shape optimization in three-dimensional linear elasticity by the boundary contour method
type: Item
instance of: scholarly article
title: Shape optimization in three-dimensional linear elasticity by the boundary contour method
zbMATH Open document ID: 0978.74058
DOI: 10.1016/S0955-7997(99)00022-3
published in: Engineering Analysis with Boundary Elements
publication date: 2002-01-31T00:00:00Z
review text: A variant of the usual boundary element method (BEM), called the boundary contour method (BCM), has been presented in the literature in recent years. In the three-dimensional BCM, surface integrals on boundary elements of the usual BEM are transformed, through the application of Stokes theorem, into line integrals along the bounding contours of these elements. The BCM employs linear combinations of global weighted shape functions, being defined piecewise on the boundary elements. A useful consequence of this approach is that stresses, at suitable boundary points, can be easily obtained from a post-processing step of the standard BCM. The subject of this paper is the shape optimization in three-dimensional (3D) linear elasticity by the use of BCM. This is achieved by coupling the 3D BCM code with a mathematical programming code based on a successive quadratic programming algorithm. Numerical results are presented for several interesting illustrative examples, like shape optimization of a fillet, optimal shape of an ellipsoidal cavity inside a cube, etc.
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 74S15
zbMATH DE Number: 1452642
zbMATH Keywords: three-dimensional linear elasticity
zbMATH Keywords: quadratic programming algorithm
zbMATH Keywords: ellipsoidal cavity inside cube
zbMATH Keywords: boundary element method
zbMATH Keywords: boundary contour method
zbMATH Keywords: surface integrals
zbMATH Keywords: Stokes theorem
zbMATH Keywords: line integrals
zbMATH Keywords: global weighted shape functions
zbMATH Keywords: post-processing step
zbMATH Keywords: shape optimization
zbMATH Keywords: mathematical programming code
zbMATH Keywords: fillet
author: Xiaolan Shi
author: S. Mukherjee
reviewed by: Ladislav Prášek
describes a project that uses: NLPQL
MaRDI profile type: Publication
cites work: Q3318255
cites work: A Novel Boundary Element Method for Linear Elasticity With No Numerical Integration for Two-Dimensional and Line Integrals for Three-Dimensional Problems
cites work: The Boundary Contour Method for Three-Dimensional Linear Elasticity
cites work: The boundary contour method for two-dimensional linear elasticity with quadratic boundary elements
cites work: The hypersingular boundary contour method for two-dimensional linear elasticity
cites work: Boundary integral equation method for shape optimization of elastic structures
cites work: Shape optimization using the boundary element method with substructuring
cites work: Shape optimization in elasticity and elasto-viscoplasticity by the boundary element method
cites work: Three-dimensional shape optimization using the boundary element method
cites work: General-purpose computer program for shape optimization of engineering structures using the boundary element method
cites work: Q4004365
cites work: Stresses, stress sensitivities and shape optimization in two-dimensional linear elasticity by the Boundary Contour Method
cites work: An integral equation approach to boundary value problems of classical elastostatics
cites work: Problems and methods of optimal structural design. Transl. from the Russian by Vadim Komkov, ed. by Edward J. Haug
cites work: Optimal shape design of three-dimensional MEMS with applications to electrostatic comb drives
cites work: Shape and layout optimization of structural systems and optimality criteria methods
full work available at URL: s0955-7997(99)00022-3
OpenAlex ID: W2016106542
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description: scientific article; zbMATH DE number 1452642