Rigorous Analysis of Energy Conservation During Dynamic Deployment of Elastic Thin-Shell Structures

Abstract

This paper studies the dynamic deployment of cylindrical thin-shell structures with open cross section, attached to a rigid base. The structures are elastically folded and then released. Previous experiments have shown that the total energy decreases while a fold moves back and forth along the structure, which was explained in terms of energy losses related to the fold “bouncing” against the boundary. This paper uses a rigorous numerical simulation, based on an in-house isogeometric shell finite element code that simultaneously eliminates shear locking and hourglassing without any intrinsic energy dissipation, to show that the total energy of the system is conserved during deployment. The discrepancy with the previous results is explained by showing that energy transfers from low-frequency, “rigid body” modes, to higher frequency modes.