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On the Stability of Sizing Optimization Problems for a Class of Nonlinearly Elastic Materials

On the Stability of Sizing Optimization Problems for a Class of Nonlinearly Elastic Materials In this work we deal with a stability aspect of sizing optimization problems for a class of nonlinearly elastic materials, where the underlying state problem is nonlinear in both the displacements and the stresses. In [14] it is shown under which conditions there exists a unique solution of discrete design problems for a body made of the considered nonlinear material, if the nonlinear state problem is solved exactly. In numerical examples the nonlinear state problem has to be solved iteratively, and therefore it can be solved only up to some small error \eps . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

On the Stability of Sizing Optimization Problems for a Class of Nonlinearly Elastic Materials

Stangl, C.
Applied Mathematics and Optimization , Volume 44 (3) – Jan 1, 2001
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Publisher
Springer Journals
Copyright
Copyright © Inc. by 2001 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-001-0023-9
Publisher site
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Abstract

In this work we deal with a stability aspect of sizing optimization problems for a class of nonlinearly elastic materials, where the underlying state problem is nonlinear in both the displacements and the stresses. In [14] it is shown under which conditions there exists a unique solution of discrete design problems for a body made of the considered nonlinear material, if the nonlinear state problem is solved exactly. In numerical examples the nonlinear state problem has to be solved iteratively, and therefore it can be solved only up to some small error \eps .

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Jan 1, 2001

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