Investigating nonlinear buckling and post-buckling characteristics of functionally graded porous cylindrical shells under external pressure and thermal conditions

Abstract

This paper investigates the post-buckling behavior of functionally graded porous (FGP) perfect/imperfect cylindrical shells under external pressure in a thermal environment. The properties of these porous cylindrical shells are assumed to be temperature-dependent, determined using the modified rule of mixture and Touloukian formulation. The governing equations are derived from classical shell theory and von Kármán-Donnell’s type of kinematic nonlinearity. The boundary layer theory of shell buckling, which accounts for nonlinear prebuckling deformations, large deflections in the post-buckling range, and initial geometric imperfections, is extended to FGP cylindrical shells. A two-step perturbation approach is employed to solve the post-buckling problem, determining the buckling loads and post-buckling equilibrium paths. Numerical parametric analysis, including three types of porosity distribution, is conducted to examine the effects of shell geometric parameters, material properties, and temperature rise on the post-buckling behavior of the FGP cylindrical shell. Numerical results indicate that the current method effectively and accurately resolves the problem, aligning with literature findings. It is observed that increases in geometric parameters related to length, radius-to-thickness ratio, porosity volume fraction, functionally graded volume fraction index, and temperature lead to a decrease in post-buckling load. Additionally, it is demonstrated that the porosity index significantly influences the post-buckling path of an FGP cylindrical shell.