A new partitioned component mode synthesis via variable condensation

In dual assembly component mode synthesis, interconnecting forces between substructures are represented by Lagrange multipliers that are augmented to the displacement vector as additional variables. Compared with the primal assembly, this force-based coupling is better suited to non-matching interfaces and yields the interconnecting forces explicitly. However, this augmentation entails additional degrees of freedom (DOFs), leading to a null space in the system matrix. Furthermore, such a null space has the potential to induce numerical instability. To eliminate these augmented DOFs, this study adopts the variable condensation originally developed for the displacement-partitioned equation of motion and applies it within flexibility-based component mode synthesis, condensing the Lagrange multipliers and frame nodes, thereby removing the null space they introduce and constructing a numerically stable model. Unlike conventional interface reduction methods, which improve compactness at the expense of accuracy, the proposed condensation markedly reduces the model size while retaining accuracy comparable to, or marginally better than, that of the original model. Consequently, the method substantially enhances numerical robustness and compactness without compromising accuracy. An iterative extension is also introduced to account for higher-order dynamic effects, yielding additional accuracy improvements while preserving model compactness. The proposed models are verified through a series of plate examples in terms of the eigenfrequency accuracy, the mode shape consistency, and the computational cost.