Multi-Objective Structural-Vibrational Optimization of Bi-Directional Thermal-Dependent FGM Shells Using PSO-GWO Approach

In this study, an improved multiobjective optimization approach is proposed for optimal structural-vibrational design solution of bi-directional thermal-dependent functionally graded cylindrical shells (FGCS). The first-order shear deformation theory is first applied for the dynamic modeling, and the eigenvalue equations are obtained by the Rayleigh–Ritz method. The obtained results are compared with the literature to verify the accuracy of the analytical method. On this basis, characterization studies are carried out to obtain the important influencing parameters and their value ranges. Subsequently, the numerical experiments are carried out using Design Expert to obtain multivariate polynomials for several objective functions along with the important design variables (fundamental frequency, mass and cost). In order to avoid settling into local optima, a hybrid PSO-GWO technique is used to search for Pareto optimum solutions in space. The results show that the bi-directional graded index ranging from 0 to 1 significantly influences the fundamental frequency of the system. The graded indexes and material distribution are identified as key design variables. The ideal bi-directional graded index and material distribution for functionally graded ceramic shells (FGCS) in a thermal environment are determined. The optimization process aims to balance the conflicting objectives of maximizing frequency while simultaneously minimizing both mass and cost. By addressing these trade-offs, the final design achieves an effective compromise that meets the desired performance goals and economic constraints.