An energy-conserving co-rotational procedure for the dynamics of shell structures

The simplest facet-shell formulation involves the combination of the constant-strain membrane triangle with a constant-curvature bending triangle. The paper first describes an alternative co-rotational procedure to the one initially proposed by Peng and Crisfield in 1992. This new formulation introduces a spin matrix which allows a simpler formulation for the consistent tangent stiffness matrix. The paper then moves to the dynamics of the element. To obtain stable solutions, an energy-conserving mid-point time-integration scheme is developed. This scheme exactly conserves the total energy when external forces are constant and when the physical system does not present any damping. The performance of this scheme is compared with other more conventional implicit schemes through a set of numerical examples involving large-scale rotations.