Nonlinear Kirchhoff-Love Shell Finite Element: Two Simple Triangular Shell Element

Resumo

Shells are one of the most important models in solid mechanics since many structures in engineering
may be associated with it: metal sheets-based products, slabs, thin-walled pressure vessels, and other objects with
one of its dimensions considerably smaller than others. Shell models may be adaptable to finite element usage, but
some particularities must be watched it, such as locking behaviours.

This work aims to study and develop a nonlinear formulation for shells models using a special simple trian-
gular shell element, which is a new displacement-based triangular shell element with 6 nodes. Moreover, the shear

locking and membrane locking behaviour are not observed at the performance of this new element.
In formulation of shell models, we consider finite strains, large displacements, and rotations. Rotation field
is re-parameterized in terms of the Rodrigues rotation vector, resulting in a simpler update of rotational variables.
The Kirchhoff-Love kinematical assumption and an initial plane reference configuration for the shell is considered
here.
A computational implementation is done with several numerical examples using the new element developed
here. Furthermore, a comparison with numerical examples using the well-known element T6-3i (Campello et al.
[1]), a six parameter (3 displacements and 3 rotations) element, is done with the aim to also illustrate the robustness
of our formulation.