Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
Harald Garcke, Paul Hüttl, Patrik Knopf
Abstract
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 eigenvectorsMathematicsDifferentiable functionTopology optimizationTopology (electrical circuits)Simple (philosophy)Mathematical analysisFunction (biology)Shape optimizationApplied mathematicsOrder (exchange)Optimization problemSpectrum of a matrixMathematical optimizationTopology Optimization in EngineeringNumerical methods in inverse problemsAdvanced Mathematical Modeling in Engineering