Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach

A cost function involving the eigenvalues of an elastic structure is optimized using a phase-field approach, which allows for topology changes and multiple materials.We show continuity and differentiability of simple eigenvalues in the phase-field context. Existence of global minimizers can be shown...

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Auteurs principaux:	Garcke Harald, Hüttl Paul, Knopf Patrik
Format:	article
Langue:	EN
Publié:	De Gruyter 2021
Sujets:	shape optimization topology optimization eigenvalue problem linear elasticity multi-phase-field model 35p05 49q10 49r05 74b05 74p05 74p15 Analysis QA299.6-433
Accès en ligne:	https://doaj.org/article/819050d9b1d74959816b80dead51fd38
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spelling	oai:doaj.org-article:819050d9b1d74959816b80dead51fd382021-12-05T14:10:40ZShape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach2191-94962191-950X10.1515/anona-2020-0183https://doaj.org/article/819050d9b1d74959816b80dead51fd382021-07-01T00:00:00Zhttps://doi.org/10.1515/anona-2020-0183https://doaj.org/toc/2191-9496https://doaj.org/toc/2191-950XA cost function involving the eigenvalues of an elastic structure is optimized using a phase-field approach, which allows for topology changes and multiple materials.We show continuity and differentiability of simple eigenvalues in the phase-field context. Existence of global minimizers can be shown, for which first order necessary optimality conditions can be obtained in generic situations. Furthermore, a combined eigenvalue and compliance optimization is discussed.Garcke HaraldHüttl PaulKnopf PatrikDe Gruyterarticleshape optimizationtopology optimizationeigenvalue problemlinear elasticitymulti-phase-field model35p0549q1049r0574b0574p0574p15AnalysisQA299.6-433ENAdvances in Nonlinear Analysis, Vol 11, Iss 1, Pp 159-197 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	shape optimization topology optimization eigenvalue problem linear elasticity multi-phase-field model 35p05 49q10 49r05 74b05 74p05 74p15 Analysis QA299.6-433
spellingShingle	shape optimization topology optimization eigenvalue problem linear elasticity multi-phase-field model 35p05 49q10 49r05 74b05 74p05 74p15 Analysis QA299.6-433 Garcke Harald Hüttl Paul Knopf Patrik Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
description	A cost function involving the eigenvalues of an elastic structure is optimized using a phase-field approach, which allows for topology changes and multiple materials.We show continuity and differentiability of simple eigenvalues in the phase-field context. Existence of global minimizers can be shown, for which first order necessary optimality conditions can be obtained in generic situations. Furthermore, a combined eigenvalue and compliance optimization is discussed.
format	article
author	Garcke Harald Hüttl Paul Knopf Patrik
author_facet	Garcke Harald Hüttl Paul Knopf Patrik
author_sort	Garcke Harald
title	Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
title_short	Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
title_full	Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
title_fullStr	Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
title_full_unstemmed	Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
title_sort	shape and topology optimization involving the eigenvalues of an elastic structure: a multi-phase-field approach
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/819050d9b1d74959816b80dead51fd38
work_keys_str_mv	AT garckeharald shapeandtopologyoptimizationinvolvingtheeigenvaluesofanelasticstructureamultiphasefieldapproach AT huttlpaul shapeandtopologyoptimizationinvolvingtheeigenvaluesofanelasticstructureamultiphasefieldapproach AT knopfpatrik shapeandtopologyoptimizationinvolvingtheeigenvaluesofanelasticstructureamultiphasefieldapproach
_version_	1718371848807251968

Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach

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