High–Order Constitutive Equations for Thick Cylindrical Shells

Abstract

A refined two-dimensional theory for thick cylindrical shells and its application in the finite element analysis are 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 stress distributions along the thickness of the shell. Due to the incorporation of the initial curvature effect, stress resultants and stress couples in the proposed refined shell theory are not symmetric. These unsymmetric stress resultants and couples are not convenient for use in the finite element analysis. The effective stress resultants and couples are used to make the stress resultant and couple tensors symmetric. The strain components which correspond to the effective stress resultants and couples are also given here. A coupled strain energy density is proposed which provides the foundation for the C° assumed strain element developed in this paper. A simple and efficient C° quadrilateral shell element is developed by the quasi-conforming element technique. The element stiffness matrix presented here is given explicitly. This C° thick/thin shell element satisfies the rigid body motion, passes the patch test, and exhibits neither shear locking nor spurious kinematic modes. The numerical examples solved here demonstrate that the C° quasi-conforming shell element gives very good results in the analysis of both thick and thin shells.