An energy–momentum conserving scheme for geometrically exact shells with drilling DOFs

Abstract

An energy–momentum conserving temporal integration scheme is presented for a recently proposed geometrically exact shell formulation with drilling degrees of freedom. The scheme is based on a novel idea of defining mixed discrete derivatives for holonomic constraint functions with displacements and rotations. By defining general discrete derivative expressions with unknown terms, the mixed discrete derivatives with second-order accuracy are constructed according to deformation modes to satisfy directionality and orthogonality properties simultaneously, thus preserving conservation laws of total energy and momenta. The analysis of shell structures is conducted using the weak form quadrature elements to ensure exact incorporation of constraints and conservation of total energy after discretization, as well as circumvent shear and membrane locking phenomena. Benchmark numerical examples are presented to demonstrate the validity of the present scheme.