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Shape optimization using the cut finite element method
University College London, UK, Department of Mathematics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)ORCID iD: 0000-0002-1710-8494
Jönköping University, School of Engineering, JTH, Product Development.ORCID iD: 0000-0001-7352-1550
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK. (UMIT)
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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
Lausanne: Elsevier, 2018. Vol. 328, p. 242-261
Keyword [en]
CutFEM, Shape optimization, Level-set, Fictitious domain method, Linear elasticity
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-140281DOI: 10.1016/j.cma.2017.09.005ISI: 000416218500011OAI: oai:DiVA.org:umu-140281DiVA, id: diva2:1146834
Funder
Swedish Foundation for Strategic Research , AM13-0029Swedish Research Council, 2011-4992Swedish Research Council, 2013-4708eSSENCE - An eScience Collaboration
Available from: 2017-10-04 Created: 2017-10-04 Last updated: 2018-06-09Bibliographically approved

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Elfverson, DanielHansbo, PeterLarson, MatsLarsson, Karl

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