Non-linear analysis of shells of revolution with ring elements

This paper presents a ring element for the static analysis of shells of revolution of arbitrary shape under arbitrarily distributed loads, based on a displacement formulation that includes geometric and physical non-linearity. The trial functions for the displacement field in the circumferential direction of the shell involve harmonic series, so that the dependence in the circumferential direction is removed from the formulation. For this element, the derivation of the internal resisting force vector and of the tangent stiffness matrix is presented. Furthermore, the concept of ring elements is extended to a spring ring element for modelling uplift between a shell of revolution and the supporting ground. After the presentation of element theory, the use of these ring elements is demonstrated with two application studies.