Automated independent coordinates鈥?switching for the solution of stiff DAEs with the linearly implicit Euler method

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• 作者：Mariano Carpinelli ; Marco Gubitosa ; Domenico Mundo ; Wim Desmet
• 关键词：Multi ; body dynamics ; Real ; time simulations ; Independent coordinates鈥?formulation ; Vehicle dynamics
• 刊名：Multibody System Dynamics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：36
• 期：1
• 页码：67-85
• 全文大小：1,848 KB
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• 作者单位：Mariano Carpinelli (1)
  Marco Gubitosa (1)
  Domenico Mundo (2)
  Wim Desmet (3)
  
  1. Siemens Industry Software NV, Interleuvenlaan 68, 3001, Leuven, Belgium
  2. Department of Mechanical Engineering, University of Calabria, 87036, Rende, Italy
  3. Production Engineering, Machine Design and Automation (PMA) Section, KU Leuven, Celestijnenlaan 300, 3001, Leuven, Belgium
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Optimization
  Electronic and Computer Engineering
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-272X

文摘

The real-time (RT) integration of the equations of motion describing complex mechanical systems requires the employment of proper integration schemes which must be able to handle the time integration at each time step in less than an a priori fixed sampling time interval. The linearly implicit Euler method has been successfully employed for the RT integration of large stiff differential algebraic systems of equations (DAEs) which typically arise from the complex mechanical systems of interest in practical applications. The current industry demand is to further increase the degree of complexity of multibody models employed in RT applications, pushing researchers to improve the efficiency of the currently available integration methods. In this paper, we investigate the improvements in the efficiency of the linearly implicit Euler method coming from the conversion of the equations of motion at each time step from a dependent to an independent coordinates鈥?formulation. The automatic switching from dependent to independent coordinates is achieved exploiting the properties of the matrix R whose columns represent a basis of the null-space of the constraint Jacobian matrix. A non-iterative projection method is also applied in order to avoid the drift-off from the constraint conditions. Keywords Multi-body dynamics Real-time simulations Independent coordinates鈥?formulation Vehicle dynamics