Blank, Luise and Garcke, Harald and Hecht, Claudia and Rupprecht, Christoph (2016) SHARP INTERFACE LIMIT FOR A PHASE FIELD MODEL IN STRUCTURAL OPTIMIZATION. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 54 (3). pp. 1558-1584. ISSN 0363-0129, 1095-7138
Full text not available from this repository. (Request a copy)Abstract
We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness, and we derive optimality conditions with minimal regularity assumptions. We relate the diffuse interface problem to a perimeter penalized sharp interface shape optimization problem in the sense of Gamma-convergence of the reduced objective functional. Additionally, the convergence of the equations of the first variation can be shown. The limit equations can also be derived directly from the problem in the sharp interface setting. Numerical computations demonstrate that the approach can be applied for complex structural optimization problems.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | LEVEL-SET METHOD; TOPOLOGY OPTIMIZATION; SHAPE; SENSITIVITY; LOADS; shape and topology optimization; linear elasticity; sensitivity analysis; optimality conditions; Gamma-convergence; phase field method; diffuse interface; numerical simulations |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Mar 2019 06:40 |
| Last Modified: | 14 Mar 2019 06:40 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2638 |
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