New preprint on beam-to-beam coupling in geometrically exact beam theories

14 April 2026

In their new paper “A variationally consistent beam-to-beam point coupling formulation for geometrically exact beam theories”, Ivo Steinbrecher, Nora Hagmeyer, Christoph Meier, and Alexander Popp present a formulation-independent approach for coupling beam cross-sections within the framework of geometrically exact beam theory.

The work addresses the challenge of modeling interactions between beams described by different formulations, interpolation schemes, or rotational parametrizations. Instead of relying on nodal coupling or formulation-specific constraints, the proposed method expresses the coupling conditions solely in terms of cross-section kinematics, namely centroid positions and orientations. Based on this, suitable generalized deformation measures for positional and rotational coupling are introduced, enabling consistent modeling of rigid connections for general configurations.

The coupling constraints are derived in a variationally consistent manner and can be incorporated directly into the weak form of existing beam finite element formulations. Constraint enforcement is investigated using both Lagrange multipliers and penalty regularization. Fundamental properties such as objectivity, symmetry, and consistency with a stress-free reference configuration are demonstrated.
The authors shown the performance and flexibility of the proposed approach by several numerical examples.

Steinbrecher, I., Hagmeyer, N., Meier, C., & Popp, A. (2026). A variationally consistent beam-to-beam point coupling formulation for geometrically exact beam theories. Preprint, submitted for publication. arXiv