Eigenfrequency Maximization of Plates by Optimization of Topology Using Homogenization and Mathematical Programming

Abstract

A computational scheme is presented for single or multiple eigenfrequency maximization of isotropic and composite plates. Eigenvalue maximization was achieved by means of an optimization process which sought to redistribute the material of the plate structure in an optimal way so that a bound on the total volume was satisfied. It was assumed that the plate structure possessed a repetitious microstructure and the homogenization theory was used to obtain equivalent elastic moduli. The structural eigenvalues and modes were computed via a finite-element analysis using a shear-deformable laminated finite element which was also applied to discretize a single-layered isotropic plate. Sequential linear programming was employed to perform the optimization task. Numerical examples are presented for clamped and simply supported plates for which the natural frequencies were extremized independently as well as simultaneously. For isotropic clamped plates, the optimality of the obtained results was verified by discretizing the resultant topology with a set of finite elements, computing its eigenvalues and then comparing them with eigenvalues from a uniform plate having the same volume.