Shear-deformable axisymmetric conical shell element with 6-DOF and convergence of O(h⁴)

According to Hughes, finite element researchers are turning away, more and more, from Poisson-Kirchhoff type elements to elements based on theories which accommodate transverse shear strains and require only C0-continuity. For axisymmetric shells, the conical element with two nodal circles and having 3 DOF (u, w and β) at each node is found to be very popular among industrial users. The earliest shear-deformable or C0-formulation for this element was developed by Zienkiewicz et al. Their formulation was based on a linear interpolation for u, w and β. The shear-locking inherent in such low-order interpolation was overcome by reduced integration for the shear stiffness. Tessler, who pioneered the concept of interdependent variable interpolation strategy for C0 elements, developed a conical element with interdependent quadratic and linear interpolations for w and β, respectively, and an independent linear interpolation for u. The rate of convergence of the above element dictated by the degree of interpolation polynomial for w is O(h2). In this article it is shown that with the same number of degrees of freedom for the conical element, it is possible to achieve a cubic interpolation for w and thus obtain a rate of convergence of O(h4) for the element. This is done by introducing at the interpolation stage an additional rotational DOF in the middle of the cone which is eliminated by static condensation at the end. The performance of the element is verified by applying it to typical problems. © 1994.