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.

翻译：细长梁状结构在工程应用中频繁出现，且常通过接头或连接件在离散位置相互作用。当涉及不同梁理论、插值方案和旋转参数化的数值公式时，对此类相互作用的精确建模尤为具有挑战性。本文在有限元离散的几何精确梁理论框架下，提出了一种与具体公式无关的通用梁-梁点耦合方法。耦合约束仅通过截面运动学（即质心位置和方向）进行表述。引入了适用于位置和旋转耦合的广义变形度量，可处理一般耦合构型，包括相对旋转和参考构型中非重合的截面质心。以变分一致的方式推导了耦合条件对平衡方程弱形式的贡献，可直接融入现有梁有限元模型的弱形式中。采用拉格朗日乘子法和罚函数正则化实现约束增强。所提方法满足无应力参考构型下的客观性、对称性和一致性等关键性质。数值算例证明了该方法在耦合不同公式和离散化的梁时的鲁棒性与灵活性，即使相互作用点位于梁单元内部任意位置。