A model reduction approach for real-time part deformation with nonlinear mechanical behavior

Interaction, in real time, between a designer and a virtual prototype is a promising way to optimize the parts design in mechanical industries. These interactions can induce deformation of some flexible parts of the prototype. The analysis in real time of nonlinear mechanical model by finite element method (FEM) is impossible. Our approach is based on two phases: 1-some load cases, characteristic of possible handlings, are precalculated; 2-results of this campaign are interpolated during the real-time immersion. This paper compares 4 approaches to calculate a reduced result of the campaign as fast as possible: an a posteriori reduction, an a priori enrichment method, an a priori enrichment-reduction and the hyperreduction.

[1]  O. Morgenthaler,et al.  Proceedings of the Conference , 1930 .

[2]  John C. Platt,et al.  Elastically deformable models , 1987, SIGGRAPH.

[3]  Uwe G. Kühnapfel,et al.  Endoscopic surgery training using virtual reality and deformable tissue simulation , 2000, Computers & graphics.

[4]  D. Ryckelynck,et al.  A priori hyperreduction method: an adaptive approach , 2005 .

[5]  François Conti,et al.  CHAI: An Open-Source Library for the Rapid Development of Haptic Scenes , 2005 .

[6]  L. Sirovich.  Turbulence and the dynamics of coherent structures. II. Symmetries and transformations , 1987 .

[7]  Alexander F. Vakakis,et al.  Karhunen-Loève decomposition of the transient dynamics of a multibay truss , 1999 .

[8]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[9]  Hervé Delingette,et al.  Non-linear anisotropic elasticity for real-time surgery simulation , 2003, Graph. Model..

[10]  Diego Borro,et al.  Virtual reality for aircraft engines maintainability , 2004 .

[11]  Elías Cueto,et al.  On thea priori model reduction: Overview and recent developments , 2006 .

[12]  Nancy M. Amato,et al.  A generalized framework for interactive dynamic simulation for multirigid bodies , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Dinesh K. Pai,et al.  EigenSkin: real time large deformation character skinning in hardware , 2002, SCA '02.

[14]  E. B. Manoukian.  Symmetries and Transformations , 2006 .

[15]  F.-L. Krause,et al.  Haptic Interaction with Non-rigid Materials for Assembly and Dissassembly in Product Development , 2001 .

[16]  Christian Duriez,et al.  A multi-threaded approach for deformable/rigid contacts with haptic feedback , 2004, 12th International Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems, 2004. HAPTICS '04. Proceedings..

[17]  J. Marsden,et al.  Dimensional model reduction in non‐linear finite element dynamics of solids and structures , 2001 .

[18]  J. Lumley.  Stochastic tools in turbulence , 1970 .

[19]  Makoto Sato,et al.  Real‐time Rigid Body Simulation for Haptic Interactions Based on Contact Volume of Polygonal Objects , 2004, Comput. Graph. Forum.

[20]  Doug L. James,et al.  Real-Time subspace integration for St. Venant-Kirchhoff deformable models , 2005, SIGGRAPH 2005.

[21]  Elizabeth A. Croft,et al.  Haptic rendering of rigid contacts using impulsive and penalty forces , 2005, IEEE Transactions on Robotics.