Analytical approach on the nonlinear pressure buckling analysis of helically stiffened FG‐GRC toroidal shell segments with generalised meridional curvature

Abstract A new solution for nonlinear pressure buckling problems of helically stiffened functionally graded graphene‐reinforced composite (FG‐GRC) toroidal shell segments with generalised meridional curvature in thermal environment is presented in this paper using an approximated technique for the nonlinear form of stress function. The FG‐GRC toroidal shell segments stiffened by orthogonal and helical FG‐GRC stiffeners and under external pressure are established and analysed. The anisotropic beam theory is used to model the FG‐GRC stiffener behaviour, and it is combined with the coordinate transformation technique to obtain the smeared helical FG‐GRC stiffener model, considering the thermal stresses of both shells and stiffeners. Due to the complex meridional curvature, for the first time, an approximate technique is developed to determine the stress function in a nonlinear form. Three‐term deflection form, Donnell's shell theory with the nonlinearly approximated stress function, Pasternak elastic foundation, and the energy method are combined to analyse the nonlinear buckling behaviour of shells. Investigated results indicate the remarkably beneficial effects of helical FG‐GRC stiffeners, geometrical and material properties, and foundation on the nonlinear buckling behaviour of the considered shells.