A triangular finite shell element based on a fully nonlinear shell formulation

Abstract

This work presents a fully nonlinear six- parameter (3 displacements and 3 rotations) shell model for finite deformations together with a triangular shell finite element for the solution of the resulting static boundary value problem. Our approach defines energeti- cally conjugated generalized cross-sectional stresses and strains, incorporating first-order shear deformations for an inextensible shell director (no thickness change). Finite rotations are treated by the Euler-Rodrigues formula in a very convenient way, and alternative parameterizations are also discussed herein. Condensation of the three-dimen- sional finite strain constitutive equations is performed by applying a mathematically consistent plane stress condi- tion, which does not destroy the symmetry of the linear- ized weak form. The results are general and can be easily extended to inelastic shells once a stress integration scheme within a time step is at hand. A special displace- ment-based triangular shell element with 6 nodes is fur- thermore introduced. The element has a nonconforming linear rotation field and a compatible quadratic interpo- lation scheme for the displacements. Locking is not ob- served as the performance of the element is assessed by several numerical examples, which also illustrate the robustness of our formulation. We believe that the com- bination of reliable triangular shell elements with powerful mesh generators is an excellent tool for nonlinear finite element analysis.