Thermo-Mechanical Post-Buckling Analysis of 3D Graphene Foam Shallow Spherical Shells and Circular Plates Stiffened by a Spider-Web Stiffener System: A Stress Function Approach

Abstract

This study focuses on analyzing the nonlinear postbuckling response of shallow spherical shells and circular plates resting on a nonlinear elastic foundation and subjected to combined mechanical and thermal loads. The spherical shell or circular plate is made of 3D graphene foam material and is stiffened by a spider-web stiffener system, which is also composed of 3D graphene foam. The fundamental formulations and governing equations are derived based on Donnell’s shell theory, incorporating von Kármán geometric nonlinearity. The stiffness components of the stiffened plate/shell structures are determined using the extended stiffener-smearing technique. By employing the stress function approach and the Ritz energy method, analytical expressions for the load-deflection relationship are obtained. Numerical examples are then carried out to investigate the postbuckling behavior of the stiffened shallow spherical shells and circular plates under the influence of material, geometric, and foundation parameters.