Dynamic simulation of frictional contacts of thin beams during large overall motions via absolute nodal coordinate formulation

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• 作者：Qingtao Wang (1)
  Qiang Tian (2)
  Haiyan Hu (1) (2)
  
• 关键词：Frictional contact ; Absolute nodal coordinate formulation (ANCF) ; Minimal distance criterion ; Master ; slave approach ; Penalty method
• 刊名：Nonlinear Dynamics
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：77
• 期：4
• 页码：1411-1425
• 全文大小：1,625 KB
• 参考文献：1. Weyler, R., Oliver, J., Sain, T., Cante, J.C.: On the contact domain method: a comparison of penalty and Lagrange multiplier implementations. Comput. Methods Appl. Mech. Eng. 205鈥?08, 68鈥?2 (2012) CrossRef
  2. Oliver, J., Hartmann, S., Cante, J.C., Weyler, R., Hern谩ndez, J.A.: A contact domain method for large deformation frictional problems. Part 1: theoretical basis. Comput. Methods Appl. Mech. Eng. 198, 2591鈥?606 (2009) CrossRef
  3. Popp, A., Seitz, A., Gee, M.W., Wall, W.A.: Improved robustness and consistency of 3D contact algorithms based on a dual mortar approach. Comput. Methods Appl. Mech. Eng. 264, 67鈥?0 (2013) CrossRef
  4. Flores, P., Ambr贸sio, J.: On the contact detection for contact-impact analysis in multibody systems. Multibody Syst. Dyn. 24(1), 103鈥?22 (2010) CrossRef
  5. Machado, M., Moreira, P., Flores, P., Lankarani, H.M.: Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mech. Mach. Theory. 53, 99鈥?21 (2012) CrossRef
  6. Wriggers, P., Zavarise, G.: On contact between three-dimensional beams undergoing large deflections. Commun. Numer. Methods Eng. 13, 429鈥?38 (1997) CrossRef
  7. Zavarise, G., Wriggers, P.: Contact with friction between beams in 3-D space. Int. J. Numer. Methods Eng. 49, 977鈥?006 (2000) CrossRef
  8. Litewka, P., Wriggers, P.: Contact between 3D beams with rectangular cross-sections. Int. J. Numer. Methods Eng. 53, 2019鈥?041 (2002) CrossRef
  9. Litewka, P., Wriggers, P.: Frictional contact between 3D beams. Comput. Mech. 28, 26鈥?9 (2002) CrossRef
  10. Boso, D.P., Litewka, P., Schrefler, B.A., Wriggers, P.: A 3D beam-to-beam contact finite element for coupled electric-mechanical fields. Int. J. Numer. Methods Eng. 64, 1800鈥?815 (2005)
  11. Litewka, P.: Hermite polynomial smoothing in beam-to-bema frictional contact. Comput. Mech. 40, 815鈥?26 (2007) CrossRef
  12. Litewka, P.: Smooth frictional contact between beams in 3D. In: Nackenhorst, U., Wriggers, P. (eds.) IUTAM Symposium on Computational Contact Mechanics. IUTAM Bookseries, pp. 157鈥?76. Springer, Dordrecht (2007) CrossRef
  13. Konyukhov, A., Schweizerhof, K.: Geometrically exact covariant approach for contact between curves. Comput. Methods Appl. Mech. Eng. 199, 2510鈥?531 (2010) CrossRef
  14. Konyukhov, A., Schweizerhof, K.: On a geometrically exact theory for contact interactions. In: Zavarise, G., Wriggers, P. (eds.) Trends in Computational Contact Mechanics. Lecture Notes in Applied and Computational Mechanics, pp. 41鈥?6. Springer, Berlin (2011) CrossRef
  15. Durville, D.: Contact-friction modeling within elastic beam assemblies: an application to knot tightening. Comput. Mech. 49(6), 687鈥?07 (2012) CrossRef
  16. Litewka, P.: Multiple-point beam-to-beam contact finite element. In: 19th International Conference on Computer Methods in Mechanics, Warsaw, Poland, 9鈥?2 May 2011
  17. Litewka, P.: Enhanced multiple-point beam-to-beam frictionless contact finite element. Comput. Mech. 52(6), 1365鈥?380 (2013) CrossRef
  18. Durville, D.: Modelling of contact-friction interactions in entangled fibrous materials. In: Proceedings of the 6th World Congress on Computational Mechanics (WCCM VI) (2004)
  19. Durville, D.: Numerical simulation of entangled materials mechanical properties. J. Mater. Sci. 40(22), 5941鈥?948 (2005) CrossRef
  20. Khude, N., Melanz, D., Stanciulescu, L., Negrut, D.: A parallel GPU implementation of the absolute nodal coordinate formulation with a frictional/contact model for the Simulation of large flexible body systems. In: ASME Conference on Multibody Systems and Nonlinear Dynamics (2011)
  21. Repupilli, M.: A robust method for beam-to-beam contact problems based on a novel tunneling constraint. Ph.D. Dissertation, University of California (2012)
  22. Chamekh, M., Mani-Aouadi, S., Moaker, M.: Modeling and numerical treatment of elastic rods with frictionless self-contact. Comput. Methods Appl. Mech. Eng. 198, 3751鈥?764 (2009) CrossRef
  23. Shabana, A.A.: An absolute nodal coordinate formulation for the large rotation and deformation analysis of flexible bodies. Technical Report. No. MBS96-1-UIC, University of Illinois at Chicago (1996)
  24. Shabana, A.A., Yakoub, R.Y.: Three dimensional absolute nodal coordinate formulation for beam elements: theory. ASME J. Mech. Des. 123, 606鈥?13 (2001) CrossRef
  25. Yakoub, R.Y., Shabana, A.A.: Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. ASME J. Mech. Des. 123, 614鈥?21 (2001) CrossRef
  26. Garc铆a-Vallejo, D., Mayo, J., Escalona, J.L., Dom铆nguez, J.: Efficient evaluation of the elastic forces and the Jacobian in the absolute nodal coordinate formulation. Nonlinear Dyn. 35, 313鈥?29 (2004) CrossRef
  27. Gerstmayr, J., Shabana, A.A.: Efficient integration of the elastic forces and thin three-dimensional beam elements in the absolute nodal coordinate formulation. In: ECCOMAS Thematic Conference, Madrid, Spain, 21鈥?4 June 2005
  28. Tian, Q., Zhang, Y.Q., Chen, L.P., Yang, J.Z.: An efficient hybrid method for multibody dynamics simulation based on absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn. 4(2), 021009-1鈥?21009-1-14 (2009) CrossRef
  29. Sugiyama, H., Escalona, J., Shabana, A.A.: Formulation of three-dimensional joint constraints using the absolute nodal coordinates. Nonlinear Dyn. 31, 167鈥?95 (2003) CrossRef
  30. Tian, Q., Zhang, Y.Q., Chen, L.P., Flores, P.: Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Comput. Struct. 87, 913鈥?29 (2009)
  31. Tian, Q., Zhang, Y.Q., Chen, L.P., Yang, J.Z.: Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dyn. 60, 489鈥?11 (2010) CrossRef
  32. Tian, Q., Liu, C., Machado, M., Flores, P.: A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems. Nonlinear Dyn. 64, 25鈥?7 (2011)
  33. Liu, C., Tian, Q., Hu, H.Y.: Dynamics and control of a spatial rigid-flexible multibody system with multiple cylindrical clearance joints. Mech. Mach. Theory. 52, 106鈥?29 (2012) CrossRef
  34. Liu, C., Tian, Q., Hu, H.Y., Garc铆a-Vallejo, D.: Simiple formulations of imposing moments and evaluating joint reaction forces for rigid-flexible multibody systems. Nonlinear Dyn. 69, 127鈥?47 (2012) CrossRef
  35. Tian, Q., Sun, Y.L., Liu, C., Hu, H.Y., Flores, P.: ElastoHydroDynamic lubricated cylindrical joints for rigid-flexible multibody dynamics. Comput. Struct. 114鈥?15, 106鈥?20 (2013) CrossRef
  36. Koshy, C.S., Flores, P., Lankarani, H.M.: Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches. Nonlinear Dyn. 73(1鈥?), 325鈥?38 (2013) CrossRef
  37. Liu, C., Tian, Q., Hu, H.Y.: Dynamics of large scale rigid-flexible multibody system composed of composite laminated plates. Multibody Syst. Dyn. 26, 283鈥?05 (2011) CrossRef
  38. Zhao, J., Tian, Q., Hu, H.Y.: Deployment dynamics of a simplified spinning IKAROS solar sail via absolute coordinate based method. Acta. Mech. Sin. 29(1), 132鈥?42 (2013) CrossRef
  39. Liu, C., Tian, Q., Yan, D., Hu, H.Y.: Dynamic analysis of membrane systems undergoing overall motions, large deformations and wrinkles via thin shell elements of ANCF. Comput. Methods Appl. Mech. Eng. 258, 81鈥?5 (2013) CrossRef
  40. Garc铆a-Vallejo, D., Sugiyama, H., Shabana, A.A.: Finite element analysis of the geometric stiffening effect. Part 1: a correction in the floating frame of reference formulation. Proc. Inst. Mech. Eng. J. Multibody Dyn. 219, 187鈥?02 (2005)
  41. Garc铆a-Vallejo, D., Sugiyama, H., Shabana, A.A.: Finite element analysis of the geometric stiffening effect. Part 2: Non-linear elasticity. Proc. Inst. Mech. Eng. J. Multibody Dyn. 219, 203鈥?11 (2005)
  42. Zhao, J., Tian, Q., Hu, H.Y.: Modal analysis of a rotating thin plate via absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 6(4), 041013 (2011) CrossRef
  43. Omar, M.A., Shabana, A.A.: A two-dimensional shear deformable beam for large rotations and deformation problems. J. Sound Vib. 243(3), 565鈥?76 (2001) CrossRef
  44. Gerstmayr, J., Shabana, A.A.: Analysis of thin beams and cables using the absolute nodal co-ordinate formulation. Nonlinear Dyn. 5, 109鈥?30 (2006) CrossRef
  45. Liu, C., Tian, Q., Hu, H.Y.: New spatial curved beam and cylindrical shell elements of gradient-deficient absolute nodal coordinate formulation. Nonlinear Dyn. 70(3), 1903鈥?918 (2012)
  46. Berzeri, M., Shabana, A.A.: Development of simple models for the elastic forces in the absolute nodal coordinate formulation. J. Sound Vib. 235(4), 539鈥?65 (2000)
  47. Litewka, P.: Finite Element Analysis of Beam-to-Beam Contact. Lecture Notes in Applied and Computational Mechanics. Springer, Berlin (2010)
  48. Hussein, B., Negrut, D., Shabana, A.A.: Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations. Nonlinear Dyn. 54, 283鈥?96 (2008)
  49. Shabana, A.A., Hussein, B.: A two-loop sparse matrix numerical integration procedure for the solution of differential/algebraic equations: application to multibody systems. J. Sound Vib. 327, 557鈥?63 (2009) CrossRef
  50. Hussein, B., Shabana, A.A.: Sparse matrix implicit numerical integration of the stiff differential/algebraic equation: implementation. Nonlinear Dyn. 65, 369鈥?82 (2011) CrossRef
  51. Chung, J., Hulbert, G.: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized- alpha method. J. Appl. Mech. 60, 371鈥?75 (1993) CrossRef
  52. Arnold, M., Br眉ls, O.: Convergence of the generalized-alpha scheme for constrained mechanical systems. Multibody Syst. Dyn. 18, 185鈥?02 (2007) CrossRef
  
• 作者单位：Qingtao Wang (1)
  Qiang Tian (2)
  Haiyan Hu (1) (2)
  
  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street, Nanjing, 210016, China
  2. MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China
  
• ISSN：1573-269X

文摘

The aim of this study is to develop an approach of simulating the frictional contact dynamics of thin beams with large deformations and continuous contact zones of large size during their large overall motions. For this purpose, the thin beams are meshed via initially straight and gradient deficient thin beam elements of the absolute nodal coordinate formulation (ANCF) degenerated from a curved beam element of ANCF. A detection strategy for contact zone is proposed based on the combination of the minimal distance criterion and master-slave approach. By making use of the minimal distance criterion, the closest points of two thin beams can be found efficiently. The master-slave approach is employed to determine the continuous contact zone. The generalized frictional contact forces and their Jacobians are derived based on the principle of virtual work. Gauss integration is used to integrate the contact forces over the continuous contact zone. The generalized-alpha method is used to solve the dynamic equations of contacting beams. Numerical simulations of four static and dynamic contact problems, including those with continuous contact zones of large size, are completed to validate the high performance of the approach.