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Institute of Engineering and Computational Mechanics

Contact Problems in Multibody Dynamics


Contact Problems in Machine Dynamics

Project Description

The simulation of a mechanical system with impacts and contacts requires a suitable mechanical modeling. The interaction of colliding machine elements is usually modeled with unilateral constraints. For the transition from the free motion of a multibody system to the motion with unilateral constraints different models may be used resulting in different time scales, accuracies and efficiencies. During contact local deformations of the colliding bodies and the contact forces are computed. After collisions the initial state of the continuing motion are determined. For this purpose, the boundary element method is coupled with the multibody system method.

The project is a collaborative work between the mathematicians at the Institute of Mathematics and the engineers at the Institute of Engineering and Computational Mechanics on contact problems in machine dynamics. The main goal of the research is the development of a simulation method for multibody systems with impacts and contacts where the global motion of the system is described using the multibody system method and where the local contact forces during impacts and contacts are computed using the boundary element method. Important topics include the simulation of multibody systems with impacts and contacts, the collision detection for contact problems, the boundary element method for impacts and contacts and experiemental vilidation.


  • Hu, Bin; Eberhard, Peter; Schiehlen, Werner: Symbolical Wave Propagation Analysis of a Falling Conical Rod Impacting a Rigid Ground. Journal of Sound and Vibration, Vol. 240, No. 1, 2001, pp.41-57.
  • Eberhard, Peter; Hu, Bin; Bestler, Dieter: Longitudinal Wave Propagation in Multiple Impacted Rods. ZAMM, Vol. 81 No. 12, pp. 795-801.
  • Hu, Bin; Eberhard, Peter; Symbolic Computation of Longitudinal Impact Waves. Computer Methods in Applied Mechanics and Engineering, Vol. 190, Nos. 37-38, pp. 4805-4815.
  • Eberhard, Peter; Hu, Bin; Schiehlen, Werner: Experiments on Longitudinal Impact Waves in an Elastic Rod. Honorary Volume Prof. Kounadis, 2000.
  • Eberhard, Peter: Kontaktuntersuchungen durch hybride Mehrk├Ârpersystem/ Finite Elemente Simulationen. Aachen: Shaker Verlag, 2000.
  • Eberhard, Peter; Hu, Bin; Schiehlen, Werner: Longitudinal Wave Propagation in Conical Rods Subject to Impacts. In: `Multifield Problems - State of the Art' by S├Ąndig A.-M., Schiehlen, W. and Wendland, W. (Eds.), Berlin: Springer, 2000, pp. 246-253.
  • Eberhard, Peter; Hu, Bin; Li, Zhou: Wavelet Analysis of Longitudinal Impact Responses. Proceedings 7. Int. Congress on Sound and Vibration, 4.-7. July 2000, Garmisch-Partenkirchen, by Guidati, G., Hunt, H., Heller, H., Heiss, A. (Eds.), München: Kramer Techn. Publ., 2000, pp. 3511-3518.
  • Eberhard, Peter: ├ťberg├Ąnge in der hybriden Mehrk├Ârpersystem/FE Kontaktsimulation. Proceedings GAMM2000, 3.-7. April 2000, G├Âttingen
  • Eberhard, Peter; Jiang, Shuoshan: Collision Detection Using Interpolation Schemes. Mathematical and Computer Modelling of Dynamical Systems, Vol. 6, No. 3, 2000, pp. 309-322.
  • Escalona, J.L.; Mayo, J.M.; Hu, Bin; Eberhard, Peter: Dynamics of Axial Impacts on Rods. Proceedings 10th World Congress on the Theory of Machines and Mechanisms IFToMM, 20.-24. 6. 99, Oulu, Finland, Vol. 1 by Leinonen, T. (Ed.). Oulu: Oulu University Press, 1999, pp. 116-121.
  • Hu, Bin; Eberhard, Peter; Schiehlen, Werner: Solving Wave Propagation Problems Symbolically Using Computer Algebra. In: Dynamics of Vibro-Impact Systems:  Proceedings EUROMECH 386 by Babitsky, V.I. (Ed.) Berlin: Springer, 1999, pp. 231-240.
  • Eberhard, P.; Itigin, A.: Tangential Contact Stiffness Matrices for Quadratically Interpolating Elements in a Hybrid FEM/Multibody Simulation. In: Proc. of the European Conference on Computational Mechanics ECCM┬ĺ99 (M├╝nchen, 31. August ┬ľ 3. September 1999). W. Wunderlich (ed.). M├╝nchen: Lehrstuhl f├╝r Statik, TU M├╝nchen 1999. CD-ROM.
  • K├╝bler, Ralf; Schiehlen, Werner: Modular Modelling and Simulation of Multibody Sy- stems. In: Proc. 1999 ASME Design Eng.Technical Conferences, Las Vegas, NV, USA, 12 - 15 September 1999). New York: ASME 1999, DETC 99 VIB- 8227, pp. 1-9. CD-ROM.
  • Eberhard, Peter : Collision Detection and Contact Approaches for a Hybrid Multibody System / Finite Element Simulation. In: `IUTAM Symposium on Unilateral Multibody Contacts' by Pfeiffer, F. and Glocker, C. (Eds.). Series: Solid Mechanics and its Applications, Vol. 72. Dordrecht: Kluwer Acad. Publishers, 1999, pp. 193-203.
  • Eberhard, Peter; Jiang, Shuoshan: Collision Detection for Contact Problems in Mechanics with a Boundary Search Algorithm. Mathematical Modelling of Systems. Mathematical Modelling of Systems, 3,4, 1997, pp. 265-281.

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