On the modeling of shells in multibody dynamics

Abstract. Energy preserving/decaying schemes are presented for the simulation of the nonlinear multi-body systems involving shell components. The proposed schemes are designed to meet four specific require-ments: unconditional nonlinear stability of the scheme, a rigorous treatment of both geometric and material nonlinearities, exact satisfaction of the constraints, and the presence of high frequency numerical dissipa-tion. The kinematic nonlinearities associated with arbitrarily large displacements and rotations of shells are treated in a rigorous manner, and the material nonlinearities can be handled when the constitutive laws stem from the existence of a strain energy density function. The efficiency and robustness of the proposed ap-proach is illustrated with specific numerical examples that also demonstrate the need for integration schemes possessing high frequency numerical dissipation. Key words, multibody dynamics, geometrically exact shell, time integration, energy decaying scheme Subject classification. Applied and Numerical Mathematics 1. Introduction and Motivation. Thi