A simple triangular multilayer Kirchhoff-Love shell element

Resumo

This paper presents a new triangular multi-layer nonlinear shell finite element suitable for simulation with large displacements and rotations. This is a nonconforming element with 6 nodes, a quadratic displacement and a linear rotation field based on Rodrigues incremental rotation parameters, having in total 21 degrees of freedom. The novelty of this element concerns the extension to a multilayer situation of the T6-3iKL element, a kinematical model with properties from Kirchhoff-Love theory, approximating the shell director across the layers as constant and the rotation-continuity between adjacent elements, allowing multiple branches connections in the mesh. These kinematical assumptions make the element extremely simple, without need of artificial parameters such as penalties. The element allows implementation of different material constitutive equations. The model is numerically implemented and displacement results are compared to different references in multiple examples, showing the consistency and robustness of the formulation. It is believed that the multilayer extension conserving all the desirable properties of the T6-3iKL (such as no necessity of penalty, simple kinematic, a relatively small number of DoFs, geometric exact, possibility to use 3D material models, easily connected with multiple branched shells and beams) and including possibly the simplest multilayer model, create a simple yet powerful shell element.