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Article

Title: Shape optimization of elasto-plastic bodies (English)
Author: Dimitrovová, Zuzana
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
Volume: 46
Issue: 2
Year: 2001
Pages: 81-101
Summary lang: English
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Category: math
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Summary: Existence of an optimal shape of a deformable body made from a physically nonlinear material obeying a specific nonlinear generalized Hooke’s law (in fact, the so called deformation theory of plasticity is invoked in this case) is proved. Approximation of the problem by finite elements is also discussed. (English)
Keyword: mixed boundary value problem
Keyword: deformation theory of plasticity
Keyword: shape optimization
Keyword: cost functional
Keyword: finite elements
MSC: 46E35
MSC: 46N10
MSC: 49N10
MSC: 49Q10
MSC: 65N30
MSC: 74C05
MSC: 74P10
idZBL: Zbl 1061.49027
idMR: MR1818080
DOI: 10.1023/A:1013731705302
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Date available: 2009-09-22T18:06:02Z
Last updated: 2015-05-19
Stable URL: http://hdl.handle.net/10338.dmlcz/134459
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Reference: [r6] J. Haslinger, P. Neittaanmäki: Finite Element Approximation for Optimal Shape Design: Theory and Applications.John Wiley & Sons, Chichester, 1988. MR 0982710
Reference: [r1] I. Hlaváček, J. Nečas: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier, Amsterdam-Oxford-New York, 1981. MR 0600655
Reference: [r7] J. Nečas, I.  Hlaváček: Solution of Signorini’s contact problem in the deformation theory of plasticity by secant modules method.Apl. Mat. 28 (1983), 199–214. MR 0701739
Reference: [r8] I. Hlaváček: Reliable solution of problems in the deformation theory of plasticity with respect to uncertain material function.Appl. Math. 41 (1996), 447–466. MR 1415251
Reference: [r5] J. Haslinger, R. Mäkinen: Shape optimization of elasto-plastic bodies under plane strains: sensitivity analysis and numerical implementation.Struct. Optim. 4 (1992), 133–141. 10.1007/BF01742734
Reference: [r2] K. Washizu: Variational Methods in Elasticity and Plasticity.Pergamon Press, Oxford, 1968. Zbl 0164.26001, MR 0391679
Reference: [r3] I. Hlaváček: Inequalities of Korn’s type, uniform with respect to a class of domains.Appl. Math. 34 (1989), 105–112. MR 0990298
Reference: [r4] D. Begis, R.  Glowinski: Application de la méthode des éléments finis à l’approximation d’un problème de domaine optimal: Méthodes de résolution des problèmes approchés.Appl. Math. Optim. 2 (1975), 130–169. MR 0443372, 10.1007/BF01447854
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