Post-buckling analysis of functionally graded doubly curved shallow shells reinforced by FGM stiffeners with temperature-dependent material and stiffener properties based on TSDT

Based on the third order shear deformation shells theory (TSDT) with von Kármán geometrical nonlinearity taking into account initial imperfection and smeared stiffener technique, this paper presents post-buckling analyses for imperfect functionally graded stiffened doubly curved shallow shells resting on elastic foundations under mechanical load, thermal load and thermo-mechanical load by an analytical method. Shells are reinforced by stiffeners system in which material properties of the stiffeners are assumed to be continuously graded in the thickness direction. The material properties are assumed to be temperature- dependent. Two cases of uniform rising temperature and nonlinearly changing of temperature across the thickness are considered. The expressions of thermal parameters are found in the analytical form. Applying Galerkin method, explicit expressions to determine the critical buckling load and the post-buckling mechanical and thermal load-deflection curves are obtained. In the case of temperature-dependent material properties, an iterative algorithm has been presented. The effects of thermal element, FGM stiffeners, geometrical and material parameters, initial imperfection, and foundation are investigated.