A variationally consistent beam-to-beam point coupling formulation for geometrically exact beam theories

2026-04-02

AI Summary

This work addresses the challenge of modeling point-wise coupling between beam structures formulated under different geometrically exact beam theories, interpolation schemes, and rotation parameterizations. A formulation-independent, general point-coupling method is proposed, built upon a variational-consistent weak-form constraint derived from cross-sectional kinematics—specifically, centroid position and orientation. The approach introduces universal coupling deformation measures for both position and rotation, accommodating arbitrary relative rotations and non-coincident centroid configurations while preserving objectivity, symmetry, and consistency with a stress-free reference configuration. Constraints are enforced via Lagrange multipliers and penalty methods. Numerical examples demonstrate that the method exhibits excellent robustness and flexibility when coupling heterogeneous beam elements and handling arbitrary internal coupling locations.

Abstract

Slender beam-like structures frequently occur in engineering applications and often interact at discrete locations through joints or connectors. Accurate modeling of such interactions is particularly challenging when different numerical formulations are involved in terms of underlying beam theory, interpolation schemes, and rotation parametrization. In this work, a versatile formulation-independent beam-to-beam point coupling approach is proposed within the framework of the geometrically exact beam theory discretized by the finite element method. The coupling constraints are expressed solely in terms of cross-section kinematics, namely centroid positions and orientations. Suitable generalized deformation measures for positional and rotational coupling are introduced, allowing for general coupling configurations, including relative rotations and non-coincident cross-section centroids in the reference configuration. The contribution of the coupling conditions to the weak form of the balance equations is derived in a variationally consistent manner and can be incorporated directly into the weak form of existing beam finite element models. Constraint enforcement is formulated using a Lagrange multiplier method and a penalty regularization. The proposed approach satisfies key properties such as objectivity, symmetry, and consistency with an stress-free reference configuration. Numerical examples demonstrate the robustness and flexibility of the method for coupling beams with different formulations and discretizations, even when the interaction points are located at arbitrary positions within beam elements.

Problem

• beam-to-beam coupling
• geometrically exact beam theory
• point interaction
• multi-formulation coupling
• cross-section kinematics

Innovation

• geometrically exact beam
• point coupling
• variational consistency
• Lagrange multipliers
• cross-section kinematics