<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$5\times 5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>5</mn> <mo>×</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$p_{cr}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>p</mi> <mrow> <mi mathvariant="italic">cr</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, whereas the foundation markedly increases it; larger FG index <i>k</i> (less GNP-rich faces) also decreases <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$p_{cr}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>p</mi> <mrow> <mi mathvariant="italic">cr</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. 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.</p>

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

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2026年2月17日

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Ahmet Çalık

摘要

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 $5\times 5$ $5 \times 5$ 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 $p_{cr}$ $p_{cr}$ , whereas the foundation markedly increases it; larger FG index k (less GNP-rich faces) also decreases $p_{cr}$ $p_{cr}$ . 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.