New preprint on space-time finite elements for geometrically exact beams

In their new preprint “A space-time finite element formulation for geometrically exact shear-deformable beams”, Ivo Steinbrecher and Alexander Humer present a finite element formulation for the transient analysis of geometrically exact beams in which space and time are discretized simultaneously within a unified space-time framework.

The proposed formulation is based on a mixed approach in which translational and angular velocities are introduced as independent fields.

Finite rotations are represented by nodal rotation vectors and interpolated objectively on the space-time surface.

The resulting formulation can be applied to generally curved beam structures and supports geometric kinks and rigid joints.

A particular advantage of the space-time approach is its ability to represent time-dependent material domains directly through the geometry of the space-time surface.

This enables problems involving non-material boundaries to be treated without modifying the underlying beam formulation.

Several numerical examples demonstrate the properties and capabilities of the formulation.

The results show convergence to solutions obtained with classical time-stepping approaches, confirm the objectivity of the formulation, and illustrate the role of time-upwind stabilization in suppressing spurious oscillations.

The examples further demonstrate the treatment of rigidly connected beam segments and axially moving continua.

Ivo Steinbrecher and Alexander Humer. A space-time finite element formulation for geometrically exact shear-deformable beams. https://arxiv.org/abs/2610.03285