Blank, Luise and Garcke, Harald and Farshbaf-Shaker, M. Hassan and Styles, Vanessa (2014) RELATING PHASE FIELD AND SHARP INTERFACE APPROACHES TO STRUCTURAL TOPOLOGY OPTIMIZATION. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 20 (4). pp. 1025-1058. ISSN 1292-8119, 1262-3377
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSION; SYSTEMS; STRESS; MOTION; TRANSITIONS; MODELS; Structural topology optimization; linear elasticity; phase-field method; first order conditions; matched asymptotic expansions; shape calculus; numerical simulations |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 13 Aug 2019 10:26 |
| Last Modified: | 13 Aug 2019 10:26 |
| URI: | https://pred.uni-regensburg.de/id/eprint/9508 |
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