Explicit dynamics and buckling simulations with 7-p shell elements and enhanced assumed strain

Abstract

Explicit strategies for shell dynamics are presented using 7-parameter shell elements and the Central Difference scheme. The formulation of the 7-parameter shell element is based on the widely used Enhanced Assumed Strain (EAS), allowing the use of a 3D constitutive law in the shell element without the need to condense the transverse normal stress component in the material law. The 7-parameter shell elements were mainly employed in the context of non-linear quasi-static loading and implicit dynamics for reproducing buckling phenomena. Explicit dynamics is the focus of this work, which proposes different strategies to handle the EAS field. In addition, kinematic constraints at the intersections between shell components are prescribed in terms of velocity. The critical time step size for thin-shell structures modeled with 7-parameter shell elements is increased thanks to the Selective Mass Scaling technique (SMS). The relevance of the proposed approaches is based on the ability to conserve momenta and energy and reproduce complex dynamic buckling phenomena. Numerical applications include classical benchmark tests for assessing the relevance of momentum-energy conserving time integration schemes: the free fly of a toss rule and the three intersecting plates. Buckling phenomena are also investigated for a roof cylindrical shell and a closed cylinder under follower external pressure. The proposed non-linear explicit dynamic strategies are attractive due to their enhanced capability to conserve momenta and energy and efficient prediction of dynamic buckling phenomena.