Object-Oriented Modelling of Flexible Beams

In this paper the problem of modelling flexible thin beams in multibody systems is tackled. The proposed model, implemented with the object-oriented modelling language Modelica, is completely modular, allowing the realization of complex systems by simple aggregation of basic components. The finite element method is employed as the basic scheme to spatially discretize the model equations. Exploiting the modular features of the language, the beam substructuring discretisation scheme (mixed finite element-finite volume) is derived as well. Selected simulation results are presented in order to validate the model with respect to both theoretical predictions and literature reference results.

[1]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[2]  L. Meirovitch.  Analytical Methods in Vibrations , 1967 .

[3]  P. E. Wellstead,et al.  Introduction to physical system modelling , 1979 .

[4]  P. V. Remoortere.  Physical systems theory in terms of bond graphs : P.C. Breedveld: Vakgroep Besturingsystemen en Computertechniek, THT, Afdeling Electrotechniek, Postbus 217, 7500 AE Enschede, The Netherlands. 1984, 200 pages, ISBN 90-9000599-4 , 1984 .

[5]  C. Pantelides.  The consistent intialization of differential-algebraic systems , 1988 .

[6]  E. Haug,et al.  Geometric non‐linear substructuring for dynamics of flexible mechanical systems , 1988 .

[7]  Peter Piela.  Ascend: an object-oriented computer environment for modeling and analysis , 1989 .

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

[9]  Sven Erik Mattsson,et al.  Omola—An Object-Oriented Modelling Language , 1989 .

[10]  O. C. Zienkiewicz,et al.  The finite element method, fourth edition; volume 2: solid and fluid mechanics, dynamics and non-linearity , 1991 .

[11]  H. Elmqvist,et al.  Automated formula manipulation supports object-oriented continuous-system modeling , 1993, IEEE Control Systems.

[12]  Sven Erik Mattsson,et al.  Index Reduction in Differential-Algebraic Equations Using Dummy Derivatives , 1993, SIAM J. Sci. Comput..

[13]  Ashitava Ghosal,et al.  Comparison of the Assumed Modes and Finite Element Models for Flexible Multilink Manipulators , 1995, Int. J. Robotics Res..

[14]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[15]  C. C. Pantelides,et al.  A modelling and simulation language for combined lumped and distributed parameter systems , 1996 .

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

[17]  A. A. Shabana,et al.  Geometric stiffness and stability of rigid body modes , 1997 .

[18]  Ahmed A. Shabana,et al.  APPLICATION OF THE ABSOLUTE NODAL CO-ORDINATE FORMULATION TO MULTIBODY SYSTEM DYNAMICS , 1997 .

[19]  Hilding Elmqvist,et al.  Modelica — A unified object-oriented language for physical systems modeling , 1997 .

[20]  C. Maffezzoni,et al.  Moses: modular modelling of physical systems in an object-oriented database , 1998 .

[21]  Hilding Elmqvist,et al.  Physical system modeling with Modelica , 1998 .

[22]  E. Hairer,et al.  Stiff differential equations solved by Radau methods , 1999 .

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

[24]  J. McPhee,et al.  Dynamics of Flexible Multibody Systems Using Virtual Work and Linear Graph Theory , 2000 .

[25]  M. Otter,et al.  Modelica - A Unified Object-Oriented Language for Physical Systems Modeling - Language Specification , 2000 .

[26]  Michael Tiller,et al.  Introduction to Physical Modeling with Modelica , 2001 .

[27]  Madeleine Pascal,et al.  Some Open Problems in Dynamic Analysis of Flexible Multibody Systems , 2001 .

[28]  A. Shabana,et al.  Study of the Centrifugal Stiffening Effect Using the Finite Element Absolute Nodal Coordinate Formulation , 2002 .

[29]  Hilding Elmqvist,et al.  The New Modelica MultiBody Library , 2003 .

[30]  John McPhee,et al.  A Comparison of Different Methods for Modelling Electromechanical Multibody Systems , 2004 .

[31]  Daniel García-Vallejo,et al.  Study of the Geometric Stiffening Effect: Comparison of Different Formulations , 2004 .

[32]  Gianni Ferretti,et al.  Object-oriented modelling and simulation of flexible multibody thin beams in Modelica with the finite element method , 2005 .