Non-linear buckling analysis of FGM toroidal shell segments filled inside by an elastic medium under external pressure loads including temperature effects

The analytical approach is presented to investigate non-linear buckling analysis and post-buckling behavior of FGM toroidal shell segments filled inside by an elastic medium under external pressure loads including temperature effects. The governing equations of non-linear buckling of FGM toroidal shell segments are derived based on the classical thin shell theory with the geometrical nonlinearity in von Karman–Donnell sense, Stein and McElman assumption and elastic medium modeled by Pasternak's two-parameter elastic foundation. The static critical buckling loads and the post-buckling pressure–deflection curves in two cases: movable and immovable boundary conditions including temperature effects are obtained by using the Galerkin's method. In the paper, the results are also compared with the solutions published in the literature for the specific cases. Effects of geometrical and material parameters, elastic foundation and temperature on the nonlinear buckling behavior of shells are shown in obtained results.