article

A Level Set Method in Shape and Topology Optimization for Variational Inequalities

Authors:

Piotr Fulmański,

Antoine Laurain,

Jean-Francois Scheid,

Jan SokołowskiAuthors Info & Claims

International Journal of Applied Mathematics and Computer Science, Volume 17, Issue 3

Pages 413 - 430

https://doi.org/10.2478/v10006-007-0034-z

Published: 01 October 2007 Publication History

A Level Set Method in Shape and Topology Optimization for Variational Inequalities

The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.

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Cited By

Laurain A(2018)A level set-based structural optimization code using FEniCSStructural and Multidisciplinary Optimization10.1007/s00158-018-1950-258:3(1311-1334)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1007/s00158-018-1950-2
Dambrine MLaurain A(2016)A first order approach for worst-case shape optimization of the compliance for a mixture in the low contrast regimeStructural and Multidisciplinary Optimization10.1007/s00158-015-1384-z54:2(215-231)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1007/s00158-015-1384-z
Giusti SSokołowski JStebel J(2015)On Topological Derivatives for Contact Problems in ElasticityJournal of Optimization Theory and Applications10.1007/s10957-014-0594-7165:1(279-294)Online publication date: 1-Apr-2015
https://dl.acm.org/doi/10.1007/s10957-014-0594-7
Show More Cited By

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Published In

cover image International Journal of Applied Mathematics and Computer Science

International Journal of Applied Mathematics and Computer Science Volume 17, Issue 3

Scientific Computation for Fluid Mechanics and Hyperbolic Systems (special issue), Jan Sokołowski and Eric Sonnendrücker (Eds.)

Oct 2007

134 pages

ISSN:1641-876X

EISSN:2083-8492

Issue’s Table of Contents

This content is open access.

Publisher

Walter de Gruyter & Co.

United States

Publication History

Published: 01 October 2007

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Cited By

Laurain A(2018)A level set-based structural optimization code using FEniCSStructural and Multidisciplinary Optimization10.1007/s00158-018-1950-258:3(1311-1334)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1007/s00158-018-1950-2
Dambrine MLaurain A(2016)A first order approach for worst-case shape optimization of the compliance for a mixture in the low contrast regimeStructural and Multidisciplinary Optimization10.1007/s00158-015-1384-z54:2(215-231)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1007/s00158-015-1384-z
Giusti SSokołowski JStebel J(2015)On Topological Derivatives for Contact Problems in ElasticityJournal of Optimization Theory and Applications10.1007/s10957-014-0594-7165:1(279-294)Online publication date: 1-Apr-2015
https://dl.acm.org/doi/10.1007/s10957-014-0594-7
Szulc KŻochowski A(2015)Application of topological derivative to accelerate genetic algorithm in shape optimization of coupled modelsStructural and Multidisciplinary Optimization10.1007/s00158-014-1126-751:1(183-192)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1007/s00158-014-1126-7
Dijk NMaute KLangelaar MKeulen F(2013)Level-set methods for structural topology optimizationStructural and Multidisciplinary Optimization10.1007/s00158-013-0912-y48:3(437-472)Online publication date: 1-Sep-2013
https://dl.acm.org/doi/10.1007/s00158-013-0912-y
Myźliński A(2012)Topology optimization of quasistatic contact problemsInternational Journal of Applied Mathematics and Computer Science10.5555/3063131.306314822:2(269-280)Online publication date: 1-Jun-2012
https://dl.acm.org/doi/10.5555/3063131.3063148
Fulmanski PLaurain AScheid JSokołowski J(2008)Level set method with topological derivatives in shape optimizationInternational Journal of Computer Mathematics10.1080/0020716080203335085:10(1491-1514)Online publication date: 1-Oct-2008
https://dl.acm.org/doi/10.1080/00207160802033350

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