On the generalized Bezier-based integration approach for co-simulation applications

This paper investigates the efficiency of a recently developed numerical approach for the integration of the dynamics of co-simulation subsystems. In this regard, a robust Bezier-based multi-step integration approach is implemented in the subsystem solvers instead of conventional approaches, like the Euler method. Although such simplistic integration formulas proved to be accurate and easy to incorporate, they often suffer from instability when using large step sizes, particularly in solving stiff differential equations. On the other side, multistep methods can show better accuracy and convergence properties, which make them proper candidates for the solution of co-simulated dynamics. This paper puts forward the use of the Bezier integration formulas in the integration of Multibody system (MBS) dynamics, with a particular focus on co-simulation algorithms. To evaluate the proposed method efficiency, some straightforward benchmark problems are considered as case studies, such as a linear oscillator and two nonlinear hydraulic cranes. This study reveals the ability of the Bezier formula to keep the mechanical energy balance of the overall system. As a consequence, the stability of co-simulation results is improved. Furthermore, implementing the Bezier formulas minimizes the residual energy, which consequently reduces the energy errors in the co-simulation environment.