EIGENFREQUENCY MAXIMIZATION OF PLATES BY OPTIMIZATION OF TOPOLOGY USING HOMOGENIZATION AND MATHEMATICAL-PROGRAMMING

A computational scheme is presented for single or multiple eigenfreque ncy maximization of isotropic and composite plates. Eigenvalue maximiz ation 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 t he plate structure possessed a repetitious microstructure and the homo genization theory was used to obtain equivalent elastic moduli. The st ructural eigenvalues and modes were computed via a finite-element anal ysis using a shear-deformable laminated finite element which was also applied to discretize a single-layered isotropic plate. Sequential lin ear programming was employed to perform the optimization task. Numeric al 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 o btained results was verified by discretizing the resultant topology wi th a set of finite elements, computing its eigenvalues and then compar ing them with eigenvalues from a uniform plate having the same volume.