On the use of geometrically exact shells in a conserving framework for flexible multibody dynamics

The present work deals with the design of energy–momentum conserving schemes for flexible multibody dynamics. The proposed approach is based on nonlinear finite element methods for the space discretization of flexible bodies. In particular, the focus is on geometrically exact shells relying on Reissner–Mindlin kinematics. It is shown that the equations of motion pertaining to the semi-discrete shell formulation can be written in the form of differential-algebraic equations (DAEs). The DAEs provide a uniform framework for a rotationless description of flexible multibody dynamics. The use of rotational parameters is circumvented throughout the discretization process in space and time. The rotationless description facilitates the straightforward incorporation of geometrically exact shells (and beams) into a multibody framework. In addition to that, the advocated approach makes possible the design of a uniform energy–momentum conserving time-stepping scheme for general multibody systems. Numerical examples demonstrate the excellent numerical stability properties of the present scheme. Moreover, comparison is made with more traditional formulations based on rotational parameters.