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

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.

References in corpus (3)

• High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero
• Phase-Field Methods for Spectral Shape and Topology Optimization
• Structural multiscale topology optimization with stress constraint for additive manufacturing

Cited by in corpus (4)

• Phase field topology optimisation for 4D printing
• Phase-Field Methods for Spectral Shape and Topology Optimization
• Adaptive Computation of Elliptic Eigenvalue Topology Optimization with a Phase-Field Approach
• Overhang penalization in additive manufacturing via phase field structural topology optimization with anisotropic energies