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arXiv · 2005.13497

Shape and Topology Optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach

Harald Garcke·Paul Hüttl·Patrik Knopf
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Abstract

A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and multiple materials. We prove continuity and differentiability of the eigenvalues and we establish the existence of a global minimizer to our optimization problem. We further derive first-order necessary optimality conditions for local minimizers. Moreover, an optimization problem combining eigenvalue and compliance optimization is also discussed.

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Harald Garcke, Paul Hüttl, Patrik Knopf. 2020-05-31. Shape and Topology Optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach. https://doi.org/10.1515/anona-2020-0183

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