A new mixed-dimension coupling method is formulated for members with (bi-symmetric) wide flange cross sections based on the idea of least squares transformations between two sets of point clouds. This coupling method imposes the minimum number of constraint equations required to link the displacement, rotation, and torsion-warping degrees-of-freedom of the dependent node. At the heart of the formulation is the solution of a 4 × 4 eigenvalue problem and the deduction of torsion-warping deformations. The proposed method is implemented and validated for nonlinear finite element analysis and the source code is made publicly available. Examples demonstrate that the proposed coupling method can improve interface stress distributions over alternative methods and is suitable for the coupling of elastic continuum finite elements.

基于两组点云之间最小二乘变换的思想，为具有（双对称）宽翼缘截面的构件制定了一种新的混合维度耦合方法。这种耦合方法施加了链接从属节点的位移、旋转和扭转-翘曲自由度所需的最少约束方程。该公式的核心是解决 4 × 4 特征值问题和推导扭转翘曲变形。所提出的方法已针对非线性有限元分析进行实施和验证，并且源代码已公开。实例表明，所提出的耦合方法可以改善替代方法的界面应力分布，并且适用于弹性连续体有限元的耦合。