Issue |
ESAIM: COCV
Volume 20, Number 4, October-December 2014
|
|
---|---|---|
Page(s) | 1025 - 1058 | |
DOI | https://doi.org/10.1051/cocv/2014006 | |
Published online | 05 August 2014 |
Relating phase field and sharp interface approaches to structural topology optimization
1
Fakultät für Mathematik, Universität Regensburg,
93040
Regensburg,
Germany
luise.blank@mathematik.uni-regensburg.de;
harald.garcke@mathematik.uni-regensburg.de
2
Weierstrass Institute for Applied Analysis and
Stochastics, Mohrenstrasse
39, 10117
Berlin,
Germany
Hassan.Farshbaf-Shaker@wias-berlin.de
3
Department of Mathematics, University of Sussex,
Brighton, BN1 9QH, UK
v.styles@sussex.ac.uk
Received:
8
March
2013
Revised:
10
January
2014
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.
Mathematics Subject Classification: 49Q10 / 74P10 / 49Q20 / 74P05 / 65M60
Key words: Structural topology optimization / linear elasticity / phase-field method / first order conditions / matched asymptotic expansions / shape calculus / numerical simulations
© EDP Sciences, SMAI, 2014
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.