Open Access
International Journal of Applied Mathematics and Computer Science, volume 17, issue 3, pages 413-430
A Level Set Method in Shape and Topology Optimization for Variational Inequalities
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Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre lés Nancy Cedex, France
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Publication type: Journal Article
Publication date: 2007-10-01
Q2
Q2
SJR: 0.505
CiteScore: 4.1
Impact factor: 1.6
ISSN: 1641876X, 20838492
Computer Science (miscellaneous)
Applied Mathematics
Engineering (miscellaneous)
Abstract
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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Fulmanski P. et al. A Level Set Method in Shape and Topology Optimization for Variational Inequalities // International Journal of Applied Mathematics and Computer Science. 2007. Vol. 17. No. 3. pp. 413-430.
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Fulmanski P., Laurain A., Scheid J., Sokołowski J. A Level Set Method in Shape and Topology Optimization for Variational Inequalities // International Journal of Applied Mathematics and Computer Science. 2007. Vol. 17. No. 3. pp. 413-430.
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RIS
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TY - JOUR
DO - 10.2478/v10006-007-0034-z
UR - https://doi.org/10.2478/v10006-007-0034-z
TI - A Level Set Method in Shape and Topology Optimization for Variational Inequalities
T2 - International Journal of Applied Mathematics and Computer Science
AU - Fulmanski, Piotr
AU - Laurain, Antoine
AU - Scheid, Jean-François
AU - Sokołowski, Jan
PY - 2007
DA - 2007/10/01
PB - Walter de Gruyter
SP - 413-430
IS - 3
VL - 17
SN - 1641-876X
SN - 2083-8492
ER -
Cite this
BibTex (up to 50 authors)
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@article{2007_Fulmanski,
author = {Piotr Fulmanski and Antoine Laurain and Jean-François Scheid and Jan Sokołowski},
title = {A Level Set Method in Shape and Topology Optimization for Variational Inequalities},
journal = {International Journal of Applied Mathematics and Computer Science},
year = {2007},
volume = {17},
publisher = {Walter de Gruyter},
month = {oct},
url = {https://doi.org/10.2478/v10006-007-0034-z},
number = {3},
pages = {413--430},
doi = {10.2478/v10006-007-0034-z}
}
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Fulmanski, Piotr, et al. “A Level Set Method in Shape and Topology Optimization for Variational Inequalities.” International Journal of Applied Mathematics and Computer Science, vol. 17, no. 3, Oct. 2007, pp. 413-430. https://doi.org/10.2478/v10006-007-0034-z.