TABLE OF CONTENTS The fundamental difference between plate and shell elements lies in the fact that, in the latter, coupling between membrane and bending actions occurs because of shell curvature. The development of an effective curved-shell element is then complicated by the necessity to incorporate the effects of curvature into the element behavior requiring analytical description of the shell geometry as well as high-order representation of displacements.
Problems relating to the geometry representation of the shell surface are reduced somewhat by formulating the curved element in terms of a shallow shell theory. The necessary mathematical manipulations are then performed in a base reference plane, and it is sufficient to assume constant geometric curvature over the element. This, however, introduces geometric discontinuities into the approximation of the shell surface because adjacent elements are portions of different parabolic surfaces that will not match exactly. To ensure that shallow shell finite element approximations converge to the deep shell solution, it is essential that the shallowness assumption be enforced relative to a local base plane, rather than to the global horizontal plane. Regardless of whether or not the shallowness assumption is used, a proper description of the rigid-body modes in elements based on curvilinear shell theory is possible only with the inclusion of transcendental functions in the assumed displacement expressions. This violates interelement compatibility. Alternatively, one may use higher-order polynomials for the displacement fields, which leads to the introduction of additional nodal degrees of freedom, namely, second-order derivatives. The introduction of second-order derivatives complicates...
