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Configurational variations for the primal and dual problem in elasticity
Author(s) -
Materna D.,
Barthold F.J.
Publication year - 2009
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.200800144
Subject(s) - dual (grammatical number) , minification , calculus of variations , mathematics , residual , hyperelastic material , sensitivity (control systems) , method of mean weighted residuals , elasticity (physics) , mathematical optimization , mathematical analysis , finite element method , algorithm , physics , thermodynamics , art , literature , electronic engineering , galerkin method , engineering
This contribution is concerned with variational methods and configurational variations for the primal and the dual problem in elasticity. The derivations of variational balance laws are based on energy minimization principles for the primal and the dual problem. Variations of the energy of the primal problem with respect to configurational changes lead to the primal material residual. We introduce an energy functional of the dual problem and we investigate configurational variations for this energy, which yield a novel material residual of the dual problem. Furthermore, we propose variational sensitivity relations for the primal and the dual solution due to configurational variations. The explicit formulations of the residuals and the sensitivity relations are derived for a hyperelastic material.