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Shape optimization using the cut finite element method
University College London, United Kingdom.
Umeå universitet, Sweden.ORCID iD: 0000-0002-1710-8494
Jönköping University, School of Engineering, JTH, Product Development. Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.ORCID iD: 0000-0001-7352-1550
Umeå universitet, Sweden.
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2018 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 328, p. 242-261Article in journal (Refereed) Published
Abstract [en]

We present a cut finite element method for shape optimization in the case of linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by moving the level-set along a velocity field using a transport equation. The velocity field is the largest decreasing direction of the shape derivative that satisfies a certain regularity requirement and the computation of the shape derivative is based on a volume formulation. Using the cut finite element method no re-meshing is required when updating the domain and we may also use higher order finite element approximations. To obtain a stable method, stabilization terms are added in the vicinity of the cut elements at the boundary, which provides control of the variation of the solution in the vicinity of the boundary. We implement and illustrate the performance of the method in the two-dimensional case, considering both triangular and quadrilateral meshes as well as finite element spaces of different order.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 328, p. 242-261
Keywords [en]
CutFEM, Shape optimization, Level-set, Fictitious domain method, Linear elasticity
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-37559DOI: 10.1016/j.cma.2017.09.005ISI: 000416218500011Scopus ID: 2-s2.0-85030311574Local ID: JTHProduktuvecklingISOAI: oai:DiVA.org:hj-37559DiVA, id: diva2:1147184
Funder
Swedish Research Council, 2011-4992; 2013-4708Available from: 2017-10-04 Created: 2017-10-05 Last updated: 2018-08-17Bibliographically approved

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Hansbo, Peter

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Elfverson, DanielHansbo, PeterLarsson, Karl
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JTH, Product DevelopmentJTH. Research area Product Development - Simulation and Optimization
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