Configurational variations for the primal and dual problem in elasticity

被引：4

作者：

Materna, Daniel ^{[1
]}

Barthold, Franz-Joseph ^{[1
]}

机构：

[1] Dortmund Univ Technol, Chair Numer Methods & Informat Proc, D-44227 Dortmund, Germany

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2009年 / 89卷 / 08期

关键词：

Variational principles; energy minimization; configurational mechanics; variational sensitivity analysis; MATERIAL FORCES; STRUCTURAL OPTIMIZATION; SENSITIVITY-ANALYSIS; MECHANICS;

D O I：

10.1002/zamm.200800144

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim

引用

页码：666 / 676

页数：11

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