A logarithmic complexity divide-and-conquer algorithm for multi-flexible articulated body dynamics

This paper presents an efficient algorithm for the dynamics simulation and analysis of multi-flexible-body systems. This algorithm formulates and solves the nonlinear equations of motion for mechanical systems with interconnected flexible bodies subject to the limitations of modal superposition, and body substructuring, with arbitrarily large rotations and translations. The large rotations or translations are modelled as rigid body degrees of freedom associated with the interconnecting kinematic joint degrees of freedom. The elastic deformation of the component bodies is modelled through the use of modal coordinates and associated admissible shape functions. Apart from the approximation associated with the elastic deformations, this algorithm is exact, non-iterative, and applicable to generalized multi-flexible chain and tree topologies. In its basic form, the algorithm is both time and processor optimal in its treatment of the n b joint variables, providing O(log(n b )) turnaround time per temporal integration step, achieved with O(n b ) processors. The actual cost associated with the parallel treatment of the n f flexible degrees of freedom depends on the specific parallel method chosen for dealing with the individual coefficient matrices which are associated locally with each flexible body.

[1]  William W. Hooker,et al.  The Dynamical Attitude Equations for n-Body Satellite , 1965 .

[2]  David E. Orin,et al.  Efficient Dynamic Computer Simulation of Robotic Mechanisms , 1982 .

[3]  R. Featherstone.  The Calculation of Robot Dynamics Using Articulated-Body Inertias , 1983 .

[4]  Thomas R. Kane,et al.  THEORY AND APPLICATIONS , 1984 .

[5]  Martin Otter,et al.  A very efficient algorithm for the simulation of robots and similar multibody systems without invers , 1986 .

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

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

[8]  Edward J. Haug,et al.  A Recursive Formation for Constrained Mechanical Systems Dynamics: Part I, Open Loop Systems , 1987 .

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

[10]  E. Haug,et al.  A recursive formulation constrained mechanical system dynamics. I: Open loop systems , 1987 .

[11]  E. Haug,et al.  A recursive formulation for flexible multibody dynamics, Part I: open-loop systems , 1988 .

[12]  Ronald L. Huston,et al.  Dynamics of Multibody Systems , 1988 .

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

[14]  Thomas R. Kane,et al.  Recursive derivation of explicit equations of motion for efficient dynamic/control simulation of large multibody systems , 1990 .

[15]  P. Nikravesh.  Systematic reduction of multibody equations of motion to a minimal set , 1990 .

[16]  Abhinandan Jain.  Unified formulation of dynamics for serial rigid multibody systems , 1991 .

[17]  Abhinandan Jain,et al.  RECURSIVE FLEXIBLE MULTIBODY SYSTEM DYNAMICS USING SPATIAL OPERATORS , 1992 .

[18]  K. Anderson.  An order n formulation for the motion simulation of general multi-rigid-body constrained systems , 1992 .

[19]  A. Banerjee.  Block-diagonal equations for multibody elastodynamics with geometric stiffness and constraints , 1993 .

[20]  Andrew J. Kurdila,et al.  Nonrecursive Order N formulation of multibody dynamics , 1993 .

[21]  M. J. Quinn,et al.  Parallel Computing: Theory and Practice , 1994 .

[22]  Amir Fijany,et al.  Parallel O(log N) algorithms for computation of manipulator forward dynamics , 1994, IEEE Trans. Robotics Autom..

[23]  Kurt S. Anderson,et al.  Efficient Modeling of General Multibody Dynamic Systems with Flexible Components , 1995 .

[24]  R. Scott,et al.  Dynamics of flexible beams undergoing overall motions , 1995 .

[25]  Ahmed A. Shabana.  RESONANCE CONDITIONS AND DEFORMABLE BODY CO-ORDINATE SYSTEMS , 1996 .

[26]  Ahmed A. Shabana,et al.  Flexible Multibody Dynamics: Review of Past and Recent Developments , 1997 .

[27]  Peter Hagedorn,et al.  Dynamic simulation of multibody systems including planar elastic beams using Autolev , 1997 .

[28]  Hong Hee Yoo,et al.  VIBRATION ANALYSIS OF ROTATING CANTILEVER BEAMS , 1998 .

[29]  Ahmed A. Shabana,et al.  Flexible Multibody Simulation and Choice of Shape Functions , 1999 .

[30]  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..

[31]  Oskar Wallrapp,et al.  Modal Representation of Stress in Flexible Multibody Simulation , 1999 .

[32]  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..

[33]  H. Claus.  A Deformation Approach to Stress Distribution in Flexible Multibody Systems , 2001 .

[34]  Jorge Ambrósio,et al.  Complex Flexible Multibody Systems with Application to Vehicle Dynamics , 2001 .

[35]  Mirko Krpan,et al.  Dynamics - Theory and application , 2001 .

[36]  H. Yoo,et al.  Dynamic Analysis of Flexible Beams Undergoing Overall Motion Employing Linear Strain Measures , 2002 .

[37]  Olivier A. Bauchau,et al.  Formulation of Modal-Based Elements in Nonlinear, Flexible Multibody Dynamics , 2003 .

[38]  K. Anderson,et al.  Orthogonal Complement Based Divide-and-Conquer Algorithm for constrained multibody systems , 2007 .