Garcke, Harald and Huettl, Paul and Knopf, Patrik (2022) Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach. ADVANCES IN NONLINEAR ANALYSIS, 11 (1). pp. 159-197. ISSN 2191-9496, 2191-950X
Full text not available from this repository. (Request a copy)Abstract
A cost function involving the eigenvalues of an elastic structure is optimized using a phase-field approach, which allows for topology changes and multiple materials. We show continuity and differentiability of simple eigenvalues in the phase-field context. Existence of global minimizers can be shown, for which first order necessary optimality conditions can be obtained in generic situations. Furthermore, a combined eigenvalue and compliance optimization is discussed.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | LEVEL SET METHODS; CONSTRAINTS; LOADS; Shape optimization; topology optimization; eigenvalue problem; linear elasticity; multi-phase-field model |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Feb 2024 06:59 |
| Last Modified: | 07 Feb 2024 06:59 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56579 |
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