Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
Garcke, Harald, Hüttl, Paul, Knopf, Patrik
2021University of Regensburg Publication Server (University of Regensburg)21 citationsOpen Access PDF
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.
Topics & Concepts
Eigenvalues and eigenvectorsTopology optimizationMathematicsDifferentiable functionShape optimizationTopology (electrical circuits)Field (mathematics)Optimization problemMathematical optimizationPhase (matter)Mathematical analysisApplied mathematicsPure mathematicsPhysicsFinite element methodCombinatoricsStructural engineeringEngineeringQuantum mechanicsTopology Optimization in EngineeringAdvanced Numerical Analysis TechniquesAdvanced Mathematical Modeling in Engineering