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

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.

Keywords

• shape optimization
• topology optimization
• eigenvalue problem
• linear elasticity
• multi-phase-field model
• 35p05
• 49q10
• 49r05
• 74b05
• 74p05
• 74p15