Elastic formulation of non-homogenous symmetric shells with arbitrary curvature and variable thickness by first-order shear deformation theory

Elastic analysis of a non-homogenous symmetric shells with arbitrary curvature and variable thickness is considered in the present research. First order Shear Deformation Theory and total potential energy approach is applied for obtaining the governing equations of non-homogenous symmetric shell. As a special case, the governing equations are rewritten for a cylinder with variable thickness. Analytical method for constant thickness and Perturbation method for variable thickness are used for solving the governing equations and obtaining results. The comparison between classical theory and First order Shear Deformation Theory (FSDT) are illustrated with some numerical results. Non-homogenous material, boundary condition effects, non-uniform pressure, arbitrary curvature with variable thickness are some advantages of current work. Functionally graded material is considered as non-homogenous material. Gradation is considered for all mechanical properties along the thickness direction based on a power function. Homogenous material and non-homogenous material by difference in non-homogeneity parameter can be studied with the present research. There is some applications of varying thickness shells in industrial like aerospace engineering. We can reach to optimum design of thickness and also some property like high temperature residence by applying non homogenous material.