Geometrical and material optimization of the functionally graded doubly-curved shell by metaheuristic optimization algorithms

Abstract

This paper presents the simultaneous geometrical and material optimization of functionally graded doubly-curved shells under static load and free vibration. The weak form of governing equations is derived from third-order shear and normal deformation theory. Bending and free vibration analyses were conducted using the finite element method. The functionally graded material (FGM) is composed of metal and ceramic, and Voigt’s rule of mixtures is applied to capture the characteristics of FGMs throughout the shell thickness direction. In this regard, two multi-objective optimization algorithms (i.e., multi-objective particle swarm optimization and multi-objective cuckoo search optimization algorithms are employed. The objective functions combine minimizing the maximum normalized displacement and mass and maximizing the first dimensionless frequency. The results show that where minimizing the mass of the FG shell structure was considered an objective function, the value of the power index is equal to zero for almost all studied cases.