Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory

•Nonlinear thermal dynamic response.•The S-FGM circular cylindrical shells reinforced by outside stiffeners.•The Reddy's third-order shear deformation shell theory.•The shells are surrounded on elastic foundations and subjected to thermo-mechanical and damping loads.•Taken into account the thermal stress in both the shells and stiffeners.

This paper presents an analytical investigation on nonlinear thermal dynamic behavior of imperfect functionally graded circular cylindrical shells eccentrically reinforced by outside stiffeners and surrounded on elastic foundations using the Reddy's third order shear deformation shell theory in thermal environment. Material properties are graded in the thickness direction according to Sigmoid power law distribution (S-FGM) in terms of the volume fractions of constituents with metal–ceramic–metal layers. The shells are affected by mechanical, damping loads and temperature. The stress function and the Bubnov–Galerkin method are applied. Unlike previous publications, we propose a general formulation for forces and moments which allow the non-linear dynamic of shear deformable eccentrically stiffened shell to be studied taking into account the thermal stress in both the shells and the stiffeners. Numerical results are given for evaluating effects of temperature, material and geometrical properties, elastic foundation and eccentrically outside stiffeners on nonlinear dynamic of the shear deformable S-FGM shells. A good agreement is obtained by comparing the present analysis with other available in the literature.