What question did this study set out to answer?

The aim is to formulate a closed-form solution for the buckling and post-buckling behavior of cylindrical shells with FG-GNP face sheets and auxetic cores.

February 19, 2026Continuum Mechanics and Thermodynamics0 citationsOpen Access

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

AÇAhmet ÇalıkBurdur Mehmet Akif Ersoy Üniversitesi

Key Points

The aim is to formulate a closed-form solution for the buckling and post-buckling behavior of cylindrical shells with FG-GNP face sheets and auxetic cores.
Used First-order Shear Deformation Theory (FSDT) for shell kinematics.
Employed a Halpin–Tsai scheme for face-sheet properties depending on temperature.
Included a Winkler–Pasternak foundation in the analysis.
Applied single-harmonic Galerkin method to derive a generalized eigenproblem for different boundary conditions.
Minimum critical pressures were found to be approximately 15.86 MPa for simply supported and 19.96 MPa for clamped–clamped configurations.
Higher temperature differences led to reduced critical pressure values.
Using foundations increased critical pressures notably.
Higher FG index (less GNP content) resulted in lower critical pressures.
Predicted post-buckling behavior was stable with a hardening branch.

Abstract

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 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 p₂ₑ p cr, whereas the foundation markedly increases it; larger FG index k (less GNP-rich faces) also decreases p₂ₑ 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.

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