Optimal design of a circular plate with rectilinear anisotropy

We investigate the problem of optimization of the basic frequency of free oscillations of a nonorthotropic ring plate with rectilinear anisotropy that is undergoing shear. We introduce a small physical parameter characterizing the anisotropy properties of the plate material. By assuming that the thickness of the plate varies within relatively small limits, we apply the small-parameter method to solve the optimization problem, which allows us to obtain an approximate analytic solution of the problem and an asymptotic estimate of the maximum value of the basic frequency. © 2001 Plenum Publishing Corporation.