Mixed finite element discretization of intrinsic geometrically exact beams for explicit multibody dynamics

The Reissner-Simo and Hodges models are two equivalent continuous descriptions of finite-strain beam dynamics.

The Reissner-Simo formulation uses displacements and rotations, while the Hodges formulation is intrinsic and avoids both variables.

Although equivalent in theory, the two approaches behave differently after discretization and offer distinct numerical advantages.

In this work, we develop a structure-preserving discretization of the intrinsic formulation.

Because the intrinsic equations involve linear differential operators, both kinematic and dynamic boundary conditions can be imposed naturally using mixed finite elements.

The resulting formulation also enables multibody systems to be assembled without algebraic constraints, avoiding the stiff differential-algebraic equations typically introduced by kinematic constraints.

We demonstrate the approach on different examples, also showing that closed kinematic loops can be modeled without algebraic constraints.

The resulting interconnected systems retain a port-Hamiltonian structure,with all nonlinearities confined to the interconnection operator.

This structure allows exact energy preservation when combined with implicit midpoint time integration.

Furthermore the scheme appear to require less Newton iterations compared to existing energy preserving scheme.