Shape and material optimization for buckling behavior of functionally graded toroidal shells

Abstract

For the first time, an investigation on the shape and material optimization for buckling behavior of functionally graded (FG) toroidal shells using differential evolution (DE) algorithm is presented in this paper. For buckling analysis, an analytical approach is used to derive governing equations, then combining with the Galerkin procedure to obtain the critical buckling load. In the optimization problem, the material distribution of functionally graded material is described by interpolated points whose coordinates of these interpolated points are located along the thickness direction of the toroidal shell using Hermite cubic functions. The design variables are volume fraction at the interpolated points. The DE algorithm is employed to find maximum critical buckling loads with ceramic volume fraction constraints. In the section of numerical results, the reliability of the current formulation is validated by several examples. Furthermore, a comprehensive examination of the influences of geometric and material parameters, etc., on the buckling behavior of the FG toroidal shells are performed. Besides, the study sets out to explore current optimal results to its effectiveness and robustness, in particular distributions, in order to examine its impact on critical buckling loads.