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

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Garcke, Harald ; Hüttl, Paul ; Knopf, Patrik
License: Creative Commons Attribution 4.0
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Date of publication of this fulltext: 02 Aug 2021 15:50


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.

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