A quadrature element formulation of an energy–momentum conserving algorithm for dynamic analysis of geometrically exact beams

• A new scheme for dynamic analysis of geometrically exact beams is presented.
• Weak form quadrature elements, along with Simo’s conserving algorithm, are used.
• Computational efficiency is enhanced and locking problems are circumvented.
• Strain objectivity and conservation of energy are exactly preserved in the scheme.

A weak form quadrature element formulation of geometrically exact beams is established and employed for dynamic analysis along with the energy and momentum conserving algorithm. In addition to its high computational efficiency and circumvention of shear locking problems, the formulation also ideally preserves strain objectivity and conservation of energy, which are violated in some finite element formulations for rotation interpolations. Several benchmark examples are presented to demonstrate the effectiveness of the formulation.