Optimizing frequencies of functionally graded material plates via multi-objective genetic algorithm: Positioning point supporters for maximum performance

Abstract

In the presented study, an approach is introduced for optimizing the vibrational characteristics of aerospace structures that are composed of Functionally Graded Materials (FGM). The focus is placed on the strategic positioning of point supporters to enhance the structural performance under various operational conditions. The effective elasticity properties of the FGMs are determined using the Mori-Tanaka method for homogenization. The deformation behavior of these structures is analyzed by employing the first-order shear deformation theory. Solutions are computed through the 2D Ritz method, which utilizes Chebyshev polynomials, forming the basis for the objective function of a multi-objective genetic algorithm. This algorithm is designed to optimize the positioning and the number of point supporters aimed at targeting specific vibration frequencies. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is utilized to efficiently generate Pareto optimal solutions, which illustrate the trade-offs between conflicting objectives. The validation of the solution method is achieved through comparisons with experimental data, confirming the accuracy and practical relevance of the approach. The application of the optimization framework is extended to various configurations of aerospace structures, including diverse compositions of FGM and different boundary conditions. This methodology is shown not only to enhance the operational performance of aerospace structures but also to contribute to the precise design and manufacturing of components in aircraft and satellites, aligning with the central interests of aerospace engineering.