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Saint‐Venant's principle and its connections to shape and topology optimization
Author(s) -
Barbarosie C.,
Toader A.M.
Publication year - 2008
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200710357
Subject(s) - mathematics , shape optimization , topology optimization , ball (mathematics) , scalar (mathematics) , topology (electrical circuits) , mathematical analysis , geometry and topology , geometry , physics , finite element method , combinatorics , thermodynamics
A version of Saint‐Venant's principle is stated and proven for a scalar elliptic equation in a domain of arbitrary shape, loaded only in a small ball. Some links are pointed out to the bubble method in topology optimization: when a small hole is introduced in a given shape, the difference between the perturbed solution and the unperturbed one satisfies the hypotheses of Saint‐Venant's principle. An important tool is the Poincaré‐Wirtinger inequality for functions defined on a sphere; results from spectral geometry are used to determine the constant therein.