Penalty, Semi-Recursive and Hybrid Methods for MBS Real-Time Dynamics in the Context of Structural Integrators

In a previous work, the authors presented a new real-time formulation for the dynamics of multibody systems, which encompasses high ranks of efficiency, accuracy, robustness and easiness of implementation. The new method, called hybrid, was obtained as a combination of a topological semi-recursive formulation based on velocities transformation, and a global penalty formulation for closed-loops consideration. It was proven to be more robust and efficient that its predecessors for large problems. For the three methods compared, the implicit, single-step trapezoidal rule was used as numerical integrator. In this paper, the influence of the integration scheme on the performance of the three mentioned methods is studied. Since the hybrid formulation becomes competitive for large multibody systems, a rather demanding simulation of the full model of a car vehicle is selected as benchmark problem. Computer codes implementing the three dynamic formulations in combination with different structural integrators, like Newmark, HHT and Generalized-α algorithms, are used to run the simulation, so that the performance of each couple dynamic-formulation/numerical-integrator can be appraised. The example is also analyzed through a commercial tool, so as to provide the readers with a well-known reference for comparison.

[1]  Roy Featherstone,et al.  Robot Dynamics Algorithms , 1987 .

[2]  Javier Cuadrado,et al.  Modeling and Solution Methods for Efficient Real-Time Simulation of Multibody Dynamics , 1997 .

[3]  M. Géradin,et al.  Flexible Multibody Dynamics: A Finite Element Approach , 2001 .

[4]  R. Schwertassek,et al.  Reduction of multibody simulation time by appropriate formulation of dynamical system equations , 1994 .

[5]  Javier García de Jalón,et al.  Kinematic and Dynamic Simulation of Multibody Systems , 1994 .

[6]  R. Schwertassek,et al.  The benefits of parallel multibody simulation , 1994 .

[7]  Sung-Soo Kim,et al.  A Subsystem Synthesis Method for Efficient Vehicle Multibody Dynamics , 2002 .

[8]  H. Yoo,et al.  A generalized recursive formulation for constrained mechanical system dynamics , 1999 .

[9]  C. Führer,et al.  Simulation of Multibody Systems by a Parallel Extrapolation Method , 1994 .

[10]  S. S. Kim,et al.  A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations , 1986 .

[11]  Javier Cuadrado,et al.  A comparison in terms of accuracy and efficiency between a MBS dynamic formulation with stress analysis and a non‐linear FEA code , 2001 .

[12]  D. Negrut.  Linear Algebra Considerations for the Multi-Threaded Simulation of Mechanical Systems , 2003 .

[13]  Edward J. Haug,et al.  High Speed Multibody Dynamic Simulation and Its Impact on Man-Machine Systems , 1993 .

[14]  Edward J. Haug,et al.  Real-Time Multibody System Dynamic Simulation: Part II. A Parallel Algorithm and Numerical Results , 1991 .

[15]  Edward J. Haug,et al.  Real-time multibody system dynamic simulation. I : A modified recursive formulation and topological analysis , 1991 .

[16]  Daniel Dopico,et al.  A Combined Penalty and Recursive Real-Time Formulation for Multibody Dynamics , 2004 .

[17]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[18]  E. Haug,et al.  A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems , 1987 .

[19]  Javier Cuadrado,et al.  Intelligent Simulation of Multibody Dynamics: Space-State and Descriptor Methods in Sequential and Parallel Computing Environments , 2000 .

[20]  José Ignacio Rodríguez Garrido.  Análisis eficiente de mecanismos 3D con métodos topológicos y tecnología de componentes en Internet , 2000 .

[21]  Parviz E. Nikravesh,et al.  Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops , 1989 .