Co-Simulation Interface Model Reduction for Large-Scale Coupled Simulations

The paper presents a novel approach for reducing the co-simulation interface representation between multiple large-scale models. The methodology leverages model order reduction through component mode synthesis in some specific small deformation flexible multibody formulations that yield a constant transformation matrix between Cartesian coordinates and general multibody coordinates, such as the flexible natural coordinates formulation or the generalized component mode synthesis. The constant transformation matrix stemming from these techniques is further modified using modified Gram-Schmidt orthonormalization and the effective independence methodology to create a constant interface model reduction matrix. This matrix effectively connects a minimal set of interface nodes to the entire nodal domain, while simultaneously projecting the forces acting on the entire nodal domain onto the interface nodes. Notably, the proposed methodology scales the size of the required co-simulation interface representation with the considered set of mode shapes rather than the size of the numerical finite element mesh. This co-simulation interface model reduction strategy not only renders large distributed load models compatible with the Functional Mock-Up Interface but also extends its applicability to any structural model beyond the flexible multibody scope, provided that deformations remain relatively small. Numerical validation with a simply supported beam, connected to springs at each node, demonstrates that the interface model reduction error is significantly smaller than the co-simulation error. This suggests that substantial interface model reduction can be achieved without compromising accuracy. Moreover, additional numerical validation performed with a rotor-drum model showcases the versatility and scalability of the proposed approach, particularly in addressing dynamic structural systems.