An arbitrary reference configuration (ARC) based nonlinear shell formulation for finite rotation/deformation dynamic analysis

In this paper, we present a generalized shell node based formulation to further develop a general shell element formulation for nonlinear dynamic analysis. The generalized shell node is constructed by several nodal Cartesian coordinate system attached to a rigid body for each element node. There is a master nodal Cartesian coordinate system existing in the generalized shell node to describe the global displacement vector. There are also several attached nodal Cartesian coordinate systems in the generalized shell node which are used for special interpolations for the shell finite element. To utilize finite element analysis to handle finite nodal rotation, the exact nodal rotation is formulated for the shell element. The total Lagrangian formulation, the updated Lagrangian formulation, and the arbitrary reference configuration (ARC) formulation for the application of the generalized shell node along with the application of the forward incremental displacement central difference (FIDCD) time integration method for the resulting semi-discretized equation of motion are described in this paper. The pros/cons are assessed for finite rotation and finte rotation and finite deformation dynamic analysis.