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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Bibliographic Details
Main Authors:	Garcke Harald, Hüttl Paul, Knopf Patrik
Format:	Article
Language:	English
Published:	De Gruyter 2021-07-01
Series:	Advances in Nonlinear Analysis
Subjects:	shape optimization topology optimization eigenvalue problem linear elasticity multi-phase-field model 35p05 49q10 49r05 74b05 74p05 74p15
Online Access:	https://doi.org/10.1515/anona-2020-0183

id	doaj-819050d9b1d74959816b80dead51fd38
record_format	Article
spelling	doaj-819050d9b1d74959816b80dead51fd382021-10-03T07:42:25ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2021-07-0111115919710.1515/anona-2020-0183Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approachGarcke Harald0Hüttl Paul1Knopf Patrik2Fakulät für Mathematik, Universität Regensburg, 93053Regensburg, GermanyFakulät für Mathematik, Universität Regensburg, 93053Regensburg, GermanyFakulät für Mathematik, Universität Regensburg, 93053Regensburg, GermanyA 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.https://doi.org/10.1515/anona-2020-0183shape optimizationtopology optimizationeigenvalue problemlinear elasticitymulti-phase-field model35p0549q1049r0574b0574p0574p15
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Garcke Harald Hüttl Paul Knopf Patrik
spellingShingle	Garcke Harald Hüttl Paul Knopf Patrik Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach Advances in Nonlinear Analysis shape optimization topology optimization eigenvalue problem linear elasticity multi-phase-field model 35p05 49q10 49r05 74b05 74p05 74p15
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
series	Advances in Nonlinear Analysis
issn	2191-9496 2191-950X
publishDate	2021-07-01
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.
topic	shape optimization topology optimization eigenvalue problem linear elasticity multi-phase-field model 35p05 49q10 49r05 74b05 74p05 74p15
url	https://doi.org/10.1515/anona-2020-0183
work_keys_str_mv	AT garckeharald shapeandtopologyoptimizationinvolvingtheeigenvaluesofanelasticstructureamultiphasefieldapproach AT huttlpaul shapeandtopologyoptimizationinvolvingtheeigenvaluesofanelasticstructureamultiphasefieldapproach AT knopfpatrik shapeandtopologyoptimizationinvolvingtheeigenvaluesofanelasticstructureamultiphasefieldapproach
_version_	1716846275224141824

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

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