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

Abstract 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 $$5\times 5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>5</mml:mn> <mml:mo>×</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> 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 $$p_{cr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mi>cr</mml:mi> </mml:mrow> </mml:msub> </mml:math> , whereas the foundation markedly increases it; larger FG index k (less GNP-rich faces) also decreases $$p_{cr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mi>cr</mml:mi> </mml:mrow> </mml:msub> </mml:math> . 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.