The probabilistic dynamic stability analysis of fluid-filled porous cylindrical shells reinforced with graphene platelets

Abstract

The aim of the current paper is the probabilistic dynamic stability analysis of graphene-reinforced functionally graded porous cylindrical shells under dynamic axial loads. For this purpose, various sources of uncertainty including the material and geometrical properties of the cylinder and loading are considered. By combining a Lagrangian solution method and a semi-analytical method, some formulations are developed for determining the dynamic buckling loads of the cylindrical shells. In order to model the fluid–reservoir interaction, a semi-analytical boundary solution is used. The functionally graded porous shells reinforced with graphene platelets (FGP-GPL) are modeled with three porosity distributions and three GPL dispersions in the shell thickness based on the Halpin–Tsai formulation. The kinetic equilibrium equations of the shells are derived based on Sanders’ nonlinear theory and the higher order shear theory. Moreover, in order to solve the nonlinear dynamic equations of motion, the Newton–Raphson and the Newmark methods are combined. Finally, the results are presented in terms of the probabilistic density functions (PDFs) and cumulative density functions (CDFs) of the buckling loads. In addition, a parametric study is conducted for the effects of the different material and physical conditions on the probabilistic dynamic buckling loads of the composite cylinders. As a result, in the probabilistic dynamic stability analysis of the composite shells, the distributions of the different buckling loads may have overlaps with each other. This phenomenon indicates that in probabilistic cases, the first buckling mode of a structure is not necessarily always the dominant failure mode.