Computational Analysis of Thermal Buckling in Doubly-Curved Shells Reinforced with Origami-Inspired Auxetic Graphene Metamaterials

In this work, a computational modelling and analysis framework is developed to investigate the thermal buckling behavior of doubly-curved composite shells reinforced with graphene-origami (G-Ori) auxetic metamaterials. A semi-analytical formulation based on the First-Order Shear Deformation Theory (FSDT) and the principle of virtual displacements is established, and closed-form solutions are derived via Navier’s method for simply supported boundary conditions. The G-Ori metamaterial reinforcements are treated as programmable constructs whose effective thermo-mechanical properties are obtained via micromechanical homogenization and incorporated into the shell model. A comprehensive parametric study examines the influence of folding geometry, dispersion arrangement, reinforcement weight fraction, curvature parameters, and elastic foundation support on the critical buckling temperature (CBT). The results reveal that, under optimal folding geometry and reinforcement alignment with principal stress trajectories, the CBT can increase by more than 150%. Furthermore, the combined effect of G-Ori reinforcement and elastic foundation substantially enhances thermal buckling resistance. These findings establish design guidelines for architected composite shells in applications such as aerospace thermal skins, morphing structures, and thermally-responsive systems, and illustrate the potential of auxetic graphene metamaterials for multifunctional, lightweight, and thermally robust structural components.