Geometrically nonlinear analysis of thin shell by a quadrilateral finite element with in-plane rotational degrees of freedom

We present in this research article, the improvements that we made to create a four nodes flat quadrilateral shell element for geometrically nonlinear analysis, based on corotational updated lagrangian formulation. These improvements are initially related to the improvement of the in-plane behaviour by incorporation of the in-plane rotational degrees of freedom known as "drilling degrees of freedom" in the membrane displacements field formulation. In the second phase, a co-rotational spatial local system of axes which adapts well to the problems of quadrilateral elements is adopted, while ensuring simplicity and effectiveness at numerical level. The required goal being mainly to have a robust thin shell element associated with a simplified formulation. The obtained element remains economic, and showing a robust behaviour in delicate situations of tests.