Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  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. 205–208, 68–82 (2012)

    Article  MathSciNet  Google Scholar 

  2. Oliver, J., Hartmann, S., Cante, J.C., Weyler, R., Hernández, J.A.: A contact domain method for large deformation frictional problems. Part 1: theoretical basis. Comput. Methods Appl. Mech. Eng. 198, 2591–2606 (2009)

    Article  MATH  Google Scholar 

  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, 67–80 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  4. Flores, P., Ambrósio, J.: On the contact detection for contact-impact analysis in multibody systems. Multibody Syst. Dyn. 24(1), 103–122 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  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, 99–121 (2012)

    Article  Google Scholar 

  6. Wriggers, P., Zavarise, G.: On contact between three-dimensional beams undergoing large deflections. Commun. Numer. Methods Eng. 13, 429–438 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Zavarise, G., Wriggers, P.: Contact with friction between beams in 3-D space. Int. J. Numer. Methods Eng. 49, 977–1006 (2000)

    Article  MATH  Google Scholar 

  8. Litewka, P., Wriggers, P.: Contact between 3D beams with rectangular cross-sections. Int. J. Numer. Methods Eng. 53, 2019–2041 (2002)

    Article  MATH  Google Scholar 

  9. Litewka, P., Wriggers, P.: Frictional contact between 3D beams. Comput. Mech. 28, 26–39 (2002)

    Article  MATH  Google Scholar 

  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, 1800–1815 (2005)

    Google Scholar 

  11. Litewka, P.: Hermite polynomial smoothing in beam-to-bema frictional contact. Comput. Mech. 40, 815–826 (2007)

    Article  MATH  Google Scholar 

  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. 157–176. Springer, Dordrecht (2007)

    Chapter  Google Scholar 

  13. Konyukhov, A., Schweizerhof, K.: Geometrically exact covariant approach for contact between curves. Comput. Methods Appl. Mech. Eng. 199, 2510–2531 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  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. 41–56. Springer, Berlin (2011)

    Chapter  Google Scholar 

  15. Durville, D.: Contact-friction modeling within elastic beam assemblies: an application to knot tightening. Comput. Mech. 49(6), 687–707 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  16. Litewka, P.: Multiple-point beam-to-beam contact finite element. In: 19th International Conference on Computer Methods in Mechanics, Warsaw, Poland, 9–12 May 2011

  17. Litewka, P.: Enhanced multiple-point beam-to-beam frictionless contact finite element. Comput. Mech. 52(6), 1365–1380 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  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), 5941–5948 (2005)

    Article  Google Scholar 

  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, 3751–3764 (2009)

    Article  MATH  Google Scholar 

  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, 606–613 (2001)

    Article  Google Scholar 

  25. Yakoub, R.Y., Shabana, A.A.: Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. ASME J. Mech. Des. 123, 614–621 (2001)

    Article  Google Scholar 

  26. García-Vallejo, D., Mayo, J., Escalona, J.L., Domínguez, J.: Efficient evaluation of the elastic forces and the Jacobian in the absolute nodal coordinate formulation. Nonlinear Dyn. 35, 313–329 (2004)

    Article  MATH  Google Scholar 

  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, 21–24 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), 021009-1–021009-1-14 (2009)

    Article  Google Scholar 

  29. Sugiyama, H., Escalona, J., Shabana, A.A.: Formulation of three-dimensional joint constraints using the absolute nodal coordinates. Nonlinear Dyn. 31, 167–195 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  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, 913–929 (2009)

    Google Scholar 

  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, 489–511 (2010)

    Article  MATH  Google Scholar 

  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, 25–47 (2011)

    Google Scholar 

  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, 106–129 (2012)

    Article  Google Scholar 

  34. Liu, C., Tian, Q., Hu, H.Y., García-Vallejo, D.: Simiple formulations of imposing moments and evaluating joint reaction forces for rigid-flexible multibody systems. Nonlinear Dyn. 69, 127–147 (2012)

    Article  MATH  Google Scholar 

  35. Tian, Q., Sun, Y.L., Liu, C., Hu, H.Y., Flores, P.: ElastoHydroDynamic lubricated cylindrical joints for rigid-flexible multibody dynamics. Comput. Struct. 114–115, 106–120 (2013)

    Article  Google Scholar 

  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(1–2), 325–338 (2013)

    Article  Google Scholar 

  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, 283–305 (2011)

    Article  MATH  Google Scholar 

  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), 132–142 (2013)

    Article  MATH  Google Scholar 

  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, 81–95 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  40. García-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, 187–202 (2005)

    Google Scholar 

  41. García-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, 203–211 (2005)

    Google Scholar 

  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)

    Article  Google Scholar 

  43. Omar, M.A., Shabana, A.A.: A two-dimensional shear deformable beam for large rotations and deformation problems. J. Sound Vib. 243(3), 565–576 (2001)

    Article  Google Scholar 

  44. Gerstmayr, J., Shabana, A.A.: Analysis of thin beams and cables using the absolute nodal co-ordinate formulation. Nonlinear Dyn. 5, 109–130 (2006)

    Article  Google Scholar 

  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), 1903–1918 (2012)

    Google Scholar 

  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), 539–565 (2000)

    Google Scholar 

  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, 283–296 (2008)

    Google Scholar 

  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, 557–563 (2009)

    Article  Google Scholar 

  50. Hussein, B., Shabana, A.A.: Sparse matrix implicit numerical integration of the stiff differential/algebraic equation: implementation. Nonlinear Dyn. 65, 369–382 (2011)

    Article  MathSciNet  Google Scholar 

  51. Chung, J., Hulbert, G.: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized- alpha method. J. Appl. Mech. 60, 371–375 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  52. Arnold, M., Brüls, O.: Convergence of the generalized-alpha scheme for constrained mechanical systems. Multibody Syst. Dyn. 18, 185–202 (2007)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 11290151 and 11221202. It was also supported in part by the Beijing Higher Education Young Elite Teacher Project under Grant YETP1201.

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street, Nanjing, 210016, China

    Qingtao Wang & Haiyan Hu

  2. MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Qiang Tian & Haiyan Hu

Authors
  1. Qingtao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiang Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haiyan Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haiyan Hu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, Q., Tian, Q. & Hu, H. Dynamic simulation of frictional contacts of thin beams during large overall motions via absolute nodal coordinate formulation. Nonlinear Dyn 77, 1411–1425 (2014). https://doi.org/10.1007/s11071-014-1387-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1387-0

Keywords

Search

Navigation