A new approach for nonlinear dynamic buckling of S-FGM toroidal shell segments with axial and circumferential stiffeners

This paper presents an analytical approach to study the nonlinear dynamic buckling of sigmoid functionally graded material (S-FGM) toroidal shell segments surrounded by elastic foundations subjected to axial compression. Shells are reinforced by closely spaced rings and stringers. The nonlinear dynamic buckling analysis is based on the classical shell theory with von Kármán–Donnell-type of geometrical nonlinearity. By using the Galerkin method, the closed-form expression of the deflection–time curves is obtained. Numerical solutions are presented in tabular and graphical forms to investigate the deflection–time curves of FGM shells surrounded by elastic foundations. Finally, the influences of geometrical parameters, volume fraction index, elastic foundations, and the effectiveness of stiffeners on the nonlinear dynamic buckling of the S-FGM toroidal shell segments are discussed. The present results are compared with the available data for a special case.