A variationally consistent beam-to-beam point coupling formulation for geometrically exact beam theories
This work addresses a domain-specific problem in engineering applications, such as structural analysis, by providing an incremental improvement in coupling methods for beam theories.
The authors tackled the challenge of accurately modeling interactions between slender beam-like structures at discrete points, such as joints, by proposing a versatile, formulation-independent beam-to-beam point coupling approach within geometrically exact beam theory. The result is a method that ensures objectivity, symmetry, and consistency, demonstrated through numerical examples showing robustness and flexibility in coupling beams with different formulations and discretizations.
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.