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An analytical approach for nonlinear thermo-mechanical buckling of functionally graded graphene platelet reinforced composite (FG-GPLRC) circular plates and shallow spherical shells resting on nonlinear elastic medium using the higher-order shear deformation theory (HSDT) and the nonlinearities of von Kármán is established in the present work. Assuming that the structures are axisymmetrically displaced for the central axis and external pressure and thermal loads are applied. The nonlinear elastic medium is used to model the behaviour of hardening or softening medium depending on the positive and negative values of the nonlinear parameter, respectively. By applying the Ritz energy method, the relation expressions of load-deflection are archived to investigate the postbuckling response and critical buckling load of the structures. Special effects on the nonlinear thermo-mechanical behaviour of plates and shells with different medium stiffnesses, different material parameters, and different geometrical dimensions are explored and discussed in numerical results. [ABSTRACT FROM AUTHOR]

The main aim of this research is to establish the algorithm for nonlinear thermo-mechanical buckling of sandwich functionally graded graphene platelet reinforced composite (FG-GPLRC) shallow spherical caps and circular plates with porous core under external pressure and/or uniformly distributed thermal load according to the higher-order shear deformation theory considering the von Karman nonlinearities. Sandwich spherical caps and circular plates are made by the porous core and two FG-GPLRC coatings and are assumed to be rested on an elastic foundation modeled by the Pasternak model. The equilibrium equation system in the form of nonlinear algebra can be approximately obtained using the Ritz energy method. The critical buckling loads and postbuckling curves can be explicitly determined. The effects of material parameters, geometrical parameters, porous core, and elastic foundation on thermo-mechanical buckling of sandwich spherical caps and circular plates with porous core and FG-GPLRC coatings are investigated and discussed in detail in the numerical investigation section. [ABSTRACT FROM AUTHOR]

The buckling and nonlinear postbuckling analysis of toroidal shell segments with auxetic-core layer and Graphene-reinforced polymer coatings under torsional loads is reported in the present research. The functionally graded Graphene-reinforced polymer coatings are considered with three distribution laws, and the auxetic cores are designed in the honeycomb lattice forms. An auxetic homogenization technique is applied to establish the stiffness terms of the auxetic core. The combination of nonlinear von Karman Donnell shell theory and the Stain and McElman approximate is applied to formulate the nonlinear equilibrium equations of shells with the shallow longitudinal curvature considering the two-parameter foundation model. The deflection of shells is assumed to be a three-term form corresponding to the pre-buckling, linear and nonlinear postbuckling behaviors, and the Galerkin method is employed for three terms of defection. The torsion-deflection and torsion-twist angle postbuckling behaviors can be obtained in explicit forms. The numerical examinations validate the large effects of honeycomb lattice auxetic core, the functionally graded Graphene-reinforced polymer coatings, the parameters of shell's geometric and foundation on the nonlinear buckling behaviors of shells. [ABSTRACT FROM AUTHOR]