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

## Palavras-chave:

Triangular Shell Element, Nonlinear Shell Formulation, Finite Rotations, Large Strains## 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.