TY  - JOUR
N2  - 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.
VL  - 328
A1  - Burman, E
A1  - Elfverson, D
A1  - Hansbo, P
A1  - Larson, MG
A1  - Larsson, K
Y1  - 2018/01/01/
SN  - 0045-7825
N1  - © 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.
ID  - discovery1531419
AV  - public
EP  - 261
JF  - Computer Methods in Applied Mechanics and Engineering
UR  - http://doi.org/10.1016/j.cma.2017.09.005
SP  - 242
KW  - CutFEM; Shape optimization; Level-set; Fictitious domain method; Linear elasticity
TI  - Shape optimization using the cut finite element method
ER  -