Structural topology optimization for repeated eigenvalues with the adjoint sensitivity analysis

Abstract

The sensitivity analysis of the eigenvectors corresponding to multiple eigenvalues is a challenging problem. The main difficulty is that for given multiple eigenvalues, the eigenvector derivatives can only be computed for a specific eigenvector basis, the so-called adjacent eigenvector basis. These adjacent eigenvectors depend on individual variables, which makes the eigenvector derivative calculation very elaborate and expensive from a computational perspective for problems. We present a new method avoiding passing through adjacent eigenvectors in the calculation of the partial derivatives of any prescribed eigenvector basis. Some examples, including one in the topology optimization, are provided to validate the present approach. The present paper is based on our research [1]. ? 2019 Proceedings of the International Congress on Acoustics. All rights reserved.