Mechanical Behavior Analysis of Flexible Parts in a Real-Time Virtual Environment for Aided Design

  • Frédéric Druesne
  • Jean-Luc Dulong
  • Pierre Villon


The interaction between a designer and a virtual prototype is a promising way to optimise the design of parts. Indeed mechanical industries of automotive and aeronautics already use real-time interactive simulators to evaluate virtual prototypes composed of rigid parts. Thus, there exists an industrial need to solve the problem of real-time deformation of flexible parts.

Our method is composed of two phases: a campaign is calculated during the first phase of training, and then these results are used during the second phase of real-time immersion. In this paper, we focus on the phase of training. We present an a posteriori method and an a priori method. The a posteriori method need to complete calculation campaign to apply the Karhunen—Loève expansion and keep only representative data. The a priori method is an adaptive strategy. As a linear combination of shape functions defines the displacement, these functions are enriched during the campaign. The size of the shape functions basis increases with time, so we use a model reduction approach. These two methods allow to calculate a surface response of possible displacements using a model reduction technique.

These methods are applied on an automotive hose, and should allow to simulate complex mechanical behaviour of flexible parts representative of many industrial applications.


virtual prototype real-time deformation nonlinear mechanical model Karhunen—Loève expansion enriched method 


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  1. 1.
    Ploye F. Trois ans au service de la Réalité Virtuelle, Harvest 85, 2004, 31–35.Google Scholar
  2. 2.
  3. 3.
    Amundarain A., Borro D., Garcia A., Gil J., Matey L., Savall J. Virtual reality for aircraft engines maintainability, Mecanique and Industries 5(2), 2004, 121–127.CrossRefGoogle Scholar
  4. 4.
    Son W., Kim K., Amato N.M., Trinckle J.C. A generalized framework for interactive dynamic simulation for multirigid bodies, IEEE Transactions on Systems Man and Cybernetics; Part B Cybernetics 34(2), 2004, 912–924.CrossRefGoogle Scholar
  5. 5.
    Hasegawa S., Sato M. Real-time rigid body simulation for haptic interactions based on contact volume of polygonal objects, Computer Graphics Forum 23(3), 2004, 529–538.CrossRefGoogle Scholar
  6. 6.
    Constantinescu D., Salcudean S.E., Croft E.A., Haptic rendering of rigid contacts using impulsive and penalty forces, IEEE Transactions on Robotics 21(3), 2005, 309–323.CrossRefGoogle Scholar
  7. 7.
    Krause F., Neumann J. Haptic interaction with non-rigid materials for assembly and dis-sassembly in product development, CIRP Annals Manufacturing Technology 50(1), 2001, 81–84.CrossRefGoogle Scholar
  8. 8.
    Terzopoulos D., Platt J., Barr A., Fleischer K. Elastically deformable models, Proceedings of SIGGRAPH’87, Computer Graphics 21(4), 1987, 205–214.CrossRefGoogle Scholar
  9. 9.
    Kry P.G., James D.L., Pai D.K. EigenSkin: Real time large deformation character skinning in hardware, in ACM SIGGRAPH Symposium on Computer Animation, 2002, pp. 153– 160.Google Scholar
  10. 10.
    Kühnapfel U., Cakmak H.K., Maass H. Endoscopic surgery training using virtual reality and deformable tissue simulation, Computers and Graphics 24, 2000, 671–682.CrossRefGoogle Scholar
  11. 11.
    Picinbono G., Delingette H., Ayache N. Non-linear anisotropic elasticity for real-time surgery simulation, Graphical Models 65(5), 2003, 305–321.MATHCrossRefGoogle Scholar
  12. 12.
    Mikchevitch A., Léon J.C., Gouskov A. Realistic force simulation in path planning for virtual assembly of flexible beam parts, in Proceedings of Virtual Concept, Biarritz, 2003.Google Scholar
  13. 13.
    Duriez C., Andriot C., Kheddar A. A multi-threaded approach for deformable/rigid contacts with haptic feedback, in HapticSymposium, 2004.Google Scholar
  14. 14.
    Dulong J.L., Druesne F., Villon P. La réduction de modèle pour déformer en temps réel une structure à comportement non linéaire, in Colloque National en Calcul des Structures, Giens, 2005.Google Scholar
  15. 15.
    Druesne F., Dulong J.L., Villon P. Real time simulation of non linear mechanical model, in Proceedings of Virtual Concept, Biarritz, 2005.Google Scholar
  16. 16.
    Karhunen K. Zur Spektraltheorie stochasticher Prozesse, Annales Academiae Scientiarum Fennicae, 37, 1946.Google Scholar
  17. 17.
    Lumley J.L. Stochastic Tools in Turbulence, Academic Press, New York, 1970.MATHGoogle Scholar
  18. 18.
    Ma X., Vakakis A.F., System identification by means of Karhunen–Loeve decomposition of the transient dynamics of a multi-bay truss, AIAA Journal 3(2), 1999, 939–946.Google Scholar
  19. 19.
    Ryckelynck D. A priori hyperreduction method: An adaptive approach, Journal of Computational Physics 202 2005, 346–366.MATHCrossRefGoogle Scholar
  20. 20.
    Krysl P., Lall S., Marsden J.E., Dimensional model reduction in non-linear finite element dynamics of solids and structures, International Journal for Numerical Methods in Engineering 51, 2001, 479–504.MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Rey C., Calcul intensif et multirésolution en mécanique non linéaire, in XVII e Congrès Français de Mécanique, 2005.Google Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Frédéric Druesne
    • 1
  • Jean-Luc Dulong
    • 1
  • Pierre Villon
    • 1
  1. 1.Roberval Laboratory, Université de Technologie CompiègneCompiegne CedexFrance

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