Influence of material and internal support on natural frequencies of thin-walled cylindrical tanks

This paper presents closed-form formulations of higher order shear deformation theory (HSDT) to analyse the functionally graded plates (FGPs) acted upon a thermo-mechanical load for simply supported (SS) conditions. This theory assumes nullity conditions for transverse stress on bottom and top face of the FGPs.  Moreover, it considers the influence of both stresses and strains in the axial and transversal direction. In these improvements, an accurate parabolic variation is assumed in the thickness direction for transverse shear strains. Therefore, this theory omits the use of correction factor for accurately estimating the shear stress. The physical properties of the FGPs are considered to change along the thickness using a power law. The equilibrium relations and  constraints on all edges are attained by considering the virtual work. Numerical evaluations are attained based on Navier’s approach. The exactness and consistency of the developed theory are ascertained with numerical results for deflections and stresses of SS FGPs; and it is deemed that numerical solutions for thermo-mechanical load will utilize as a reference in the future.