A Refined two-dimensional theory for thick cylindrical shells

Abstract

A higher order two-dimensional theory for thick cylindrical shells is presented in this paper. The shell equations given here do not only incorporate the effect of transverse shear deformations but also account for the initial curvature as well as the radial stress. The proposed theory presents a very good approximation for the shell constitutive equations and the nonlinear distributions of the in-plane stresses across the thickness of the shell. The latter is very important in the thick shells analysis. The formulation is based on: 1.(1) assumed out-of-plane stress components which satisfy the given traction boundary conditions:2.(2) three-dimensional elasticity equations with an integral form of the equilibrium equations: and3.(3) stress resultants and stress couples acting on the middle surface of the shell, average displacements along the normal at a point on the middle surface, and average rotations of the normal.The proposed shell equations can be conveniently used in the finite element analysis. An application of this theory to the finite element analysis of circular arches is given in this paper. A more convenient form of the proposed shell equations for finite element analysis and its application to cylindrical shells will be presented in a follow-up paper.