Frequency optimization of power-law functionally graded plates via surrogate model

A surrogate based technique to address natural frequency optimization problems of a power-law functionally graded plate was proposed. The natural element method was employed to conduct the direct free vibration analysis based on the first order shear deformation plate theory, which is a kind of meshless method based on the natural neighbor interpolation. Initially, some sample data were selected to construct the gradient index-frequency surrogate model. Later, a nonlinear optimization problem of the fundamental frequency was formulated, and the optimum solution was obtained by using Nelder-Mead simplex method. Several numerical examples were given to validate the efficiency and feasibility of the proposed method. It is observed that the piecewise cubic Hermite interpolating polynomial produces the best surrogate model with few sample data. The surrogate-based method improves the numerical efficiency by eliminating repeated frequency calculations.