Investigation of nonlinear buckling of FGM shells using a high-order finite continuation approach

Abstract

This study investigates the buckling behavior of cylindrical shells composed of Functionally Graded Materials (FGMs) when subjected to axial compression, challenging conventional assumptions regarding the influence of Poisson’s effect in homogeneous materials. To address this, we utilize a numerical approach employing the Asymptotic Numerical Method (ANM). Contrary to the expected linear pre-buckling behavior associated with a zero Poisson’s ratio, our findings reveal significant non-linearity in the response of FGM structures, emphasizing the influence of additional non-linear factors inherent in the behavior of advanced composites. Through an extensive numerical analysis conducted using a customized Matlab code, we examine the buckling and post-buckling characteristics of FGM shells with varying surface compositions, particularly focusing on configurations incorporating ${\mathrm{Al}}_2{O}_3$ and $\mathrm{Al}$ on the upper surface. To elucidate our findings, we present numerical examples comparing two FGM scenarios (${\mathrm{Al}}_2{O}_3/\mathrm{Al}$ and $\mathrm{Al}/{\mathrm{Al}}_2{O}_3$) in terms of critical buckling and FGM distribution. Additionally, we validate our results by employing the commercial software Abaqus with Riks-based finite element method and Newton–Raphson solver.