Burman, E;
Elfverson, D;
Hansbo, P;
Larson, MG;
Larsson, K;
(2018)
Shape optimization using the cut finite element method.
Computer Methods in Applied Mechanics and Engineering
, 328
pp. 242-261.
10.1016/j.cma.2017.09.005.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | Shape optimization using the cut finite element method |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.cma.2017.09.005 |
| Publisher version: | http://doi.org/10.1016/j.cma.2017.09.005 |
| Language: | English |
| Additional information: | © 2017 Elsevier B.V. All rights reserved. This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | CutFEM; Shape optimization; Level-set; Fictitious domain method; Linear elasticity |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1531419 |
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