Simulation of multibody systems with the use of coupling techniques: a case study

Simulation coupling (or cosimulation) techniques provide a framework for the analysis of decomposed dynamical systems with the use of independent numerical procedures for decomposed subsystems. These methods are often seen as very promising because they enable the utilization of the existing software for subsystem analysis and usually are easy to parallelize, and run in a distributed environment. For example, in the domain of multibody systems dynamics, a general setup for “Gluing Algorithms” was proposed by Wang et al. It was intended to provide a basis for multilevel distributed simulation environments. The authors presented an example where Newton’s method was used to synchronize the responses of subsystem simulators.In this paper, we discuss some properties of a simplified iterative coupling scheme, where subsystems’ responses are synchronized at discrete time points. We use a simple multibody model to investigate the influence of synchronization parameters on computations. We also try to provide explanation to the oscillatory behavior of the solutions obtained from this method.

[1]  A.L. Sangiovanni-Vincentelli,et al.  A survey of third-generation simulation techniques , 1981, Proceedings of the IEEE.

[2]  Benedict Leimkuhler RELAXATION TECHNIQUES IN MULTIBODY DYNAMICS , 1993 .

[3]  Roy Featherstone,et al.  A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n)) Calculation of Rigid-Body Dynamics. Part 1: Basic Algorithm , 1999, Int. J. Robotics Res..

[4]  H. Harry Asada,et al.  Co-simulation of algebraically coupled dynamic subsystems using discrete-time sliding mode , 2001 .

[5]  J. F. Andrus,et al.  Numerical Solution of Systems of Ordinary Differential Equations Separated into Subsystems , 1979 .

[6]  Zheng-Dong Ma,et al.  Gluing for Dynamic Simulation of Distributed Mechanical Systems , 2005 .

[7]  Martin Arnold,et al.  Multi-Rate Time Integration for Large Scale Multibody System Models , 2007 .

[8]  Bei Gu,et al.  Co-simulation of coupled dynamic subsystems: a differential-algebraic approach using singularly perturbed sliding manifolds , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[9]  Roy Featherstone,et al.  A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n)) Calculation of Rigid-Body Dynamics. Part 2: Trees, Loops, and Accuracy , 1999, Int. J. Robotics Res..

[10]  Alberto L. Sangiovanni-Vincentelli,et al.  The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits , 1982, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[11]  Bei Gu,et al.  Co-Simulation of Algebraically Coupled Dynamic Subsystems Without Disclosure of Proprietary Subsystem Models , 2004 .

[12]  Edward J. Haug,et al.  A Recursive Formulation for Constrained Mechanical System Dynamics: Part III. Parallel Processor Implementation , 1988 .

[13]  Basant R. Chawla,et al.  Motis - an mos timing simulator , 1975 .

[14]  Martin Arnold,et al.  EFFICIENT SIMULATION OF BUSH AND ROLLER CHAIN DRIVES , 2005 .

[15]  Martin P. Bendsøe,et al.  Sensitivity analysis and optimal design of elastic plates with unilateral point supports , 1987 .

[16]  Bei Gu,et al.  Co-simulation of algebraically coupled dynamic subsystems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[17]  Werner Schiehlen,et al.  Modular Simulation in Multibody System Dynamics , 2000 .

[18]  Kurt S. Anderson,et al.  Highly Parallelizable Low-Order Dynamics Simulation Algorithm for Multi-Rigid-Body Systems , 2000 .

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

[20]  C. W. Gear,et al.  Automatic integration of Euler-Lagrange equations with constraints , 1985 .

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

[22]  Zheng-Dong Ma,et al.  A Gluing Algorithm for Distributed Simulation of Multibody Systems , 2003 .

[23]  Benedict J. Leimkuhler Estimating Waveform Relaxation Convergence , 1993, SIAM J. Sci. Comput..

[24]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .

[25]  G. Hulbert,et al.  Efficient numerical solution of constrained multibody dynamics systems , 2003 .

[26]  Zheng-Dong Ma,et al.  A Distributed Mechanical System Simulation Platform Based on a "Gluing Algorithm" , 2005, J. Comput. Inf. Sci. Eng..

[27]  Fan-Chung Tseng Multibody dynamics simulation in network -distributed environments. , 2000 .

[28]  C. W. Gear,et al.  Multirate linear multistep methods , 1984 .

[29]  Werner Schiehlen,et al.  Force Coupling Versus Differential Algebraic Description of Constrained Multibody Systems , 2000 .