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

A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, optimized. This allows us to handle topology changes and multiple materials. We prove continuity differentiability we establish existence global minimizer our optimization problem. further derive first-order necessary optimality conditions for local minimizers. Moreover, problem combining eigenvalue compliance also discussed.