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.
@article{arxiv.2005.13497,
title = {Shape and Topology Optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach},
author = {Harald Garcke and Paul Hüttl and Patrik Knopf},
journal= {arXiv preprint arXiv:2005.13497},
year = {2021}
}