Thermo-mechanical bending and stress analysis of deep GNP-reinforced thick cylindrical shells on an orthotropic Pasternak foundation considering nanoparticle agglomeration

Abstract

In this study, a comprehensive thermo-elastic analysis of a GNP-reinforced deep thick cylindrical shell resting on an orthotropic Pasternak–Winkler elastic foundation is presented. The shell is composed of a polymeric matrix enriched with graphene nanoplatelets (GNPs), whose volume fraction varies through the thickness according to several functional distribution patterns. To accurately represent the three-dimensional mechanical response, a quasi-3D sinusoidal shear deformation theory incorporating the thickness-stretching effect (εₙ ≠ 0) is employed, thereby avoiding any shallow-shell or constant transverse strain assumptions. The orthotropic foundation model, which remains rarely explored in the context of nanocomposite cylindrical shells, allows anisotropic shear interactions to be properly captured. The temperature field across the thickness is obtained analytically by solving the one-dimensional steady-state conduction equation, and temperature-dependent thermo-mechanical properties of both the matrix and the GNPs are fully incorporated. The governing equations are derived via Principle of Virtual Work and solved through a semi-analytical framework combining exact circumferential expansion with a high-order differential quadrature discretization along the axial direction. Axial and radial deflections, together with the through-thickness distributions of von Mises stress, are evaluated for a wide range of parameters. The results demonstrate that increasing the GNP content markedly enhances structural stiffness and reduces deflections, while thermo-mechanical coupling may induce localized increases in von Mises stress. Among all dispersion patterns, the FG-A configuration provides the most uniform stress distribution and is therefore the most effective from a structural integrity standpoint. Foundation characteris- tics—including the Winkler modulus, orthotropic shear stiffnesses, and anisotropy angle—exert a significant influence on both deflection and stress fields. The proposed formulation, which integrates thickness stretching, thermal dependency, orthotropic foundation behavior, and GNP agglomeration effects, offers a high-fidelity thermo-elastic solution applicable to thin, moderately thick, and deep cylindrical shells.