Buckling and near-critical post-buckling of sandwich cylindrical shells with FG-GNP face sheets and an auxetic core under external pressure in a thermal environment: a closed-form approach

This paper presents a closed-form formulation for the linear buckling and near-critical single-mode post-buckling response of sandwich cylindrical shells with functionally graded graphene nanoplatelet (FG-GNP) reinforced face sheets and an auxetic honeycomb core under external pressure and a thermal environment. The shell kinematics follow First-order Shear Deformation Theory (FSDT). Face-sheet properties are obtained from a temperature-dependent Halpin–Tsai scheme combined with a power-law through-thickness gradation, while the auxetic core is represented by equivalent orthotropic constants. A Winkler–Pasternak foundation is included. A single-harmonic Galerkin reduction yields a 5× 5 5 × 5 generalized eigenproblem for both simply supported (SS) and clamped–clamped (CC) boundary conditions; for CC edges, an energy-equivalent axial wavenumber is used to represent end restraint without introducing numerical mode shapes. For the baseline configuration, the minimum critical pressures are approximately 15.86 MPa at (m,n)=(1,10) for SS and 19.96 MPa at (0,11) for CC. Increasing temperature difference reduces pcr p cr , whereas the foundation markedly increases it; larger FG index k (less GNP-rich faces) also decreases pcr p cr . The Koiter single-mode expansion predicts a stable (hardening) post-buckling branch for the cases examined. The model is intended as a fast analytical screening and benchmarking tool under the stated assumptions.