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

Abstract

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.

Post-buckling analysis of shell-like structures using an implicit dynamic time integration scheme

“…As in the previous example, the shell behaviour exhibits an unstable phase socalled "snap through phenomena" when tracing the load-deflection path. The static limit load of the spherical shell numerically evaluated using the above properties is 50.489 MN, taken from Boutagouga et al (2010). Figure 10 shows also the load-deflection path after the limit point using the dynamic analysis algorithms with Δt 5 0.05 s.…”

“…The static response of the cylindrical shell presents post-buckling instability beyond the limit point characterised in a high non-linear behaviour so-called “snap back phenomena”. The static limit load of the cylindrical shell numerically evaluated using the above properties is: 5.707 MN , taken from Boutagouga et al. (2010).…”