A fully incremental simple triangular multilayer Kirchhoff-Love shell element

Abstract

This paper presents a new triangular multi-layer nonlinear shell finite element with incremental degrees of freedom, suitable for large displacements and rotations. This is a nonconforming element with 6 nodes, quadratic displacement and linear rotation field based on Rodrigues incremental rotation parameters, with a total of 21 DoFs. The novelty of this element is the extension to a multilayer, fully incremental situation of the T6-3iKL element, a kinematical model with properties from Kirchhoff-Love theory, approximating the shell director across layers as constant. The model is numerically implemented, and results are compared to different references in multiple examples, showing the capabilities of the formulation. It is believed that the possibly simplest multilayer extension, combined with fully incremental DoFs, simple kinematic, no necessity of artificial parameters such as penalties, a relatively small number of DoFs, possibility to use various 3D material models, easily connected with multiple branched shells and beams, and geometric exact theory create a simple yet powerful shell element.