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Multibody System Dynamics

, 16:237 | Cite as

Sliding joints in 3D beams: Conserving algorithms using the master–slave approach

  • José J. MuñozEmail author
  • Gordan Jelenić
Article

Abstract

This paper proposes two time-integration algorithms for motion of geometrically exact 3D beams under sliding contact conditions. The algorithms are derived using the so-called master–slave approach, in which constraint equations and the related time-integration of a system of differential and algebraic equations are eliminated by design. Specifically, we study conservation of energy and momenta when the sliding conditions on beams are imposed and discuss their algorithmic viability. Situations where the contact jumps to adjacent finite elements are analysed in detail and the results are tested on two representative numerical examples. It is concluded that an algorithmic preservation of kinematic constraint conditions is of utmost importance.

Keywords

Master–slave method Conserving time-integration Sliding contact Large rotations 3D beams 

References

  1. Argyris, J.H.: An excursion into large rotations. Comp. Meth. Appl. Mech. Engng. 32, 81–155 (1982)Google Scholar
  2. Armero, F., PetH ocz, E.: Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems. Comp. Meth. Appl. Mech. Engng. 158, 269–300 (1998)zbMATHMathSciNetCrossRefGoogle Scholar
  3. Bauchau, O.: On the modeling of prismatic joints in flexible multi-body systems. Comp. Meth. Appl. Mech. Engng. 181, 87–105 (2000)zbMATHCrossRefGoogle Scholar
  4. Bauchau, O., Bottasso, C.L.: Contact lowercaseConditions for Cylindrical, Prismatic, and Screw Joints in Flexible Multibody Systems. Multibody System Dyn. 5, 251–278 (2001)zbMATHCrossRefGoogle Scholar
  5. Betsch, P.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part I: Holonomic constraints. Comp. Meth. Appl. Mech. Engng. 194, 5159–5190 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  6. Bottasso, C.L.: Personal communication (2002).Google Scholar
  7. Cardona, A., Géradin, M.A.: A beam finite element non-linear theory with finite rotations. Int. J. Num. Meth. Engng. 26, 2403–2438 (1988)zbMATHCrossRefGoogle Scholar
  8. Crisfield, M.A., Jelenić, G.: Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation. Proc. Royal Soc. London 455, 1125–1147break (1999)zbMATHCrossRefGoogle Scholar
  9. Géradin, M.A., Cardona, A.: Flexible multibody dynamics. A Finite Element Approach. John Wiley & Sons (2001)Google Scholar
  10. Ibrahimbegović, A., Mamouri, S.: On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3D geometrically exact beam model. Comp. Meth. Appl. Mech. Engng. 188, 805–831 (2000)CrossRefzbMATHGoogle Scholar
  11. Jelenić, G., Crisfield, M.A.: Non-linear master-slave relationships for joints in 3D beams with large rotations. Comp. Meth. Appl. Mech. Engng. 135, 211–228 (1996)CrossRefzbMATHGoogle Scholar
  12. Jelenić, G., Crisfield, M.A.: Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics. Comp. Meth. Appl. Mech. Engng. 171, 141–171 (1999)CrossRefzbMATHGoogle Scholar
  13. Jelenić, G., Crisfield, M.A.: Stability and convergence characteristics of conserving algorithms for dynamics of 3D rods. Technical report, Department of Aeronautics, Imperial College, London (1999)Google Scholar
  14. Jelenić, G., Crisfield, M.A.: Dynamic analysis of 3D beams with joints in presence of large rotations. Comp. Meth. Appl. Mech. Engng. 190, 4195–4230 (2001)CrossRefzbMATHGoogle Scholar
  15. Jelenić, G., Crisfield, M.A.: Problems associated with the use of Cayley transform and tangent scaling for conserving energy and momenta in the Reissner-Simo beam theory. Comm. Num. Meth. Engng. 18, 711–720 (2002)CrossRefzbMATHGoogle Scholar
  16. Laursen, T.A., Chawla, V.: Design of energy conserving algorithms for frictionless dynamic contact problems. Int. J. Num. Meth. Engng. 40, 863–886 (1997)zbMATHMathSciNetCrossRefGoogle Scholar
  17. Leyendecker, S., Betsch, P., Steinmann, P.: Objective energy-momentum conserving integration for the constrained dynamics of geometrically act beams. Comp. Meth. Appl. Mech. Engng. 195, 2131–2333 (2006)MathSciNetCrossRefGoogle Scholar
  18. Marjamäki, H., Mäkinen, J.: Modelling telescopic boom – The plane case: Part I. Comput. Struct. 81, 1597–1609 (2003)CrossRefGoogle Scholar
  19. Mitsugi, J.: Direct strain measure for large displacement analyses on hinge connected beam structures. Comput. Struct. 64, 509–517 (1997)zbMATHCrossRefGoogle Scholar
  20. Munoz, J.: Finite-element analysis of flexible mechanisms using the master-slave approach with emphasis on the modelling of joints. PhD thesis, Imperial College London (2004)Google Scholar
  21. Munoz, J., Jelenić, G.: Sliding contact conditions using the master–slave approach with application on the geometrically non-linear beams. Int. J. Solids Struct. 41, 6963–6992 (2004)zbMATHCrossRefGoogle Scholar
  22. Munoz, J., Jelenić, G., Crisfield, M.: Master-slave approach for the modelling of joints with dependent degrees of freedom in flexible mechanisms. Comm. Num. Meth. Engng. 19, 689–702 (2003)zbMATHCrossRefGoogle Scholar
  23. Romero, I., Armero, F.: An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy–momentum conserving scheme in dynamics. Int. J. Num. Meth. Engng. 54, 1683–1716 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  24. Simo, J.C.: A finite strain beam formulation. The three dimensional dynamic problem. Part I. Comp. Meth. Appl. Mech. Engng. 49, 55–70 (1985)zbMATHCrossRefGoogle Scholar
  25. Simo, J.C., Tarnow, N., Doblare, M.: Non-linear dynamics of three-dimensional rods: exact energy and momentum conserving algorithms. Int. J. Num. Meth. Engng. 38, 1431–1473 (1995)zbMATHMathSciNetCrossRefGoogle Scholar
  26. Wriggers, P.: Computational Contact Mechanics, Wiley (2002)Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Applied Mathematics IIIUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Department of Civil EngineeringUniversity of RijekaRijekaRepublic of Croatia

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