Multibody System Dynamics

, Volume 44, Issue 4, pp 335–366 | Cite as

Dynamic contact model of shell for multibody system applications

  • Jiabei Shi
  • Zhuyong LiuEmail author
  • Jiazhen Hong


In a multibody system consisting of shell structures, the contact may appear in any area of shells. It is difficult to simulate the contact of shells with large deformation because of the geometric nonlinearity of deformation and the boundary nonlinearity of contact. This study presents a rotation-free shell formulation and an extended contact discretization in multibody systems using a corotational frame. This model is different from previous formulations in the definition of the local frame and the processing of local large curvature. In order to deal with the shell contact, a unified contact discretization scheme including edge-to-edge contact for facet triangle shell elements is proposed to solve the large penetration problem. A series of numerical examples of multibody dynamics have validated the approach of the nonlinear shell model and contact treatments. Moreover, a practical application of deployment of solar cells shows the capability of the proposed formulation in solving large-scale problems of flexible multibody system with large deformation and contact.


Shell contact Corotational formulation Rotation-free element Geometric nonlinearity Flexible multibody dynamics 



This research was supported by the National Natural Science Foundation of China (No. 11772188, No. 11132007), for which the authors are grateful.


  1. 1.
    ABAQUS: ABAQUS Theory Guide. Dassault Systèmes, Providence, RI, USA (2017) Google Scholar
  2. 2.
    ABAQUS: ABAQUS Users’s Guide Volume V: Prescribed Conditions, Constraint & Interactions. Dassault Systèmes, Providence, RI, USA (2017) Google Scholar
  3. 3.
    Areias, P., Garção, J., Pires, E.B., Barbosa, J.I.: Exact corotational shell for finite strains and fracture. Comput. Mech. 48, 385–406 (2011) MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Arnold, M., Brüls, O.: Convergence of the generalized-\(\alpha \) scheme for constrained mechanical systems. Multibody Syst. Dyn. 18(2), 185–202 (2007) MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bauchau, O., Choi, J.Y., Bottasso, C.L.: On the modeling of shells in multibody dynamics. Multibody Syst. Dyn. 8, 459–489 (2002) CrossRefzbMATHGoogle Scholar
  6. 6.
    Crisfield, M.A.: A unified co-rotational framework solids, shells and beams. Int. J. Solids Struct. 33(1986), 2969–2992 (1996) CrossRefzbMATHGoogle Scholar
  7. 7.
    Das, M., Barut, A., Madenci, E.: Analysis of multibody systems experiencing large elastic deformations. Multibody Syst. Dyn. 23(1), 1–31 (2009) MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Eberhard, P., Hu, B.: Advanced Contact Dynamics. Southeast University Press, Nanjing (2003) Google Scholar
  9. 9.
    Felippa, C.A., Haugen, B.: A unified formulation of small-strain corotational finite elements: I. Theory. In: Computer Methods in Applied Mechanics and Engineering (2005) Google Scholar
  10. 10.
    Flores, F.G., Oñate, E.: Improvements in the membrane behaviour of the three node rotation-free BST shell triangle using an assumed strain approach. Comput. Methods Appl. Mech. Eng. 194(6–8), 907–932 (2005) CrossRefzbMATHGoogle Scholar
  11. 11.
    Flores, F.G., Oñate, E.: Wrinkling and folding analysis of elastic membranes using an enhanced rotation-free thin shell triangular element. Finite Elem. Anal. Des. 47(9), 982–990 (2011) MathSciNetCrossRefGoogle Scholar
  12. 12.
    Gärdsback, M., Tibert, G.: A comparison of rotation-free triangular shell elements for unstructured meshes. Comput. Methods Appl. Mech. Eng. 196(49–52), 5001–5015 (2007) CrossRefzbMATHGoogle Scholar
  13. 13.
    Guo, Y.Q., Gati, W., Naceur, H., Batoz, J.L.: An efficient DKT rotation free shell element for springback simulation in sheet metal forming. Comput. Struct. 80, 2299–2312 (2002) CrossRefGoogle Scholar
  14. 14.
    Hallquist, J.O.: LS-DYNA Theory manual. March (2006) Google Scholar
  15. 15.
    Hallquist, J.O., Goudreau, G.L., Benson, D.J.: Sliding interfaces with contact-impact in large-scale Lagrangian computations. Comput. Methods Appl. Mech. Eng. 51(1–3), 107–137 (1985) MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Klaus-Jurgen, B., Chaudhary, A.: A solution method for planar and axisymmetric contact problems. Int. J. Numer. Methods Eng. 21, 65–88 (1985) CrossRefzbMATHGoogle Scholar
  17. 17.
    Konyukhov, A., Izi, R.: Introduction to Computational Contact Mechanics. Wiley, Chichester (2015) zbMATHGoogle Scholar
  18. 18.
    Linhard, J., Wüchner, R., Bletzinger, K.U.: “Upgrading” membranes to shells—the CEG rotation free shell element and its application in structural analysis. Finite Elem. Anal. Des. 44(1–2), 63–74 (2007) MathSciNetCrossRefGoogle Scholar
  19. 19.
    Liu, Z., Hong, J., Liu, J.: Finite element formulation for dynamics of planar flexible multi-beam system. Multibody Syst. Dyn. 22(1), 1–26 (2009) MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Liu, Z., Liu, J.: Experimental validation of rigid-flexible coupling dynamic formulation for hub–beam system. Multibody Syst. Dyn. 40(3), 303–326 (2017) MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    LS-DYNA: LS-DYNA keyword user’s manual volume I. Livermore Software Technology Corporation, Livermore, California (2017) Google Scholar
  22. 22.
    Lu, J., Zheng, C.: Dynamic cloth simulation by isogeometric analysis. Comput. Methods Appl. Mech. Eng. 268, 475–493 (2014) MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Mcdevitt, T.W., Laursen, T.A.: A mortar-finite element formulation for frictional contact problems. Int. J. Numer. Methods Eng. 48(10), 1525–1547 (2000) MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Mikkola, A.K.I.M., Shabana, A.A.: A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications. Multibody Syst. Dyn. 9, 283–309 (2003) MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Moller, T.: Fast triangle-triangle intersection test. Doktorsavh. Chalmers Tek. Högsk. 1425, 123–129 (1998) Google Scholar
  26. 26.
    Nour-Omid, B., Rankin, C.: Finite rotation analysis and consistent linearization using projectors. Comput. Methods Appl. Mech. Eng. 93(3), 353–384 (1991) CrossRefzbMATHGoogle Scholar
  27. 27.
    Oñate, E., Cendoya, P., Miquel, J.: Non-linear explicit dynamic analysis of shells using the BST rotation-free triangle. Eng. Comput. 19(6), 662–706 (2002) CrossRefzbMATHGoogle Scholar
  28. 28.
    Oñate, E., Cervera, M.: Derivation of thin plate bending elements with one degree of freedom per node: a simple three node triangle. Eng. Comput. 10(6), 543–561 (1993) CrossRefGoogle Scholar
  29. 29.
    Oñate, E., Flores, F.G.: Advances in the formulation of the rotation-free basic shell triangle. Comput. Methods Appl. Mech. Eng. 194(21–24), 2406–2443 (2005) CrossRefzbMATHGoogle Scholar
  30. 30.
    Phaal, R., Calladine, C.R.: A simple class of finite elements for plate and shell problems. I: Elements for beams and thin flat plates. Int. J. Numer. Methods Eng. 35(5), 955–977 (1992) CrossRefzbMATHGoogle Scholar
  31. 31.
    Phaal, R., Calladine, C.R.: Simple class of finite elements for plate and shell problems. II: An element for thin shells, with only translational degrees of freedom. Int. J. Numer. Methods Eng. 35(5), 979–996 (1992) CrossRefzbMATHGoogle Scholar
  32. 32.
    Puso, M.A., Laursen, T.A.: A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. Eng. 193(6–8), 601–629 (2004) CrossRefzbMATHGoogle Scholar
  33. 33.
    Sabourin, F., Brunet, M.: Analysis of plates and shells with a simplified three node triangular element. Thin-Walled Struct. 21(3), 209–223 (1995) CrossRefGoogle Scholar
  34. 34.
    Sabourin, F., Brunet, M.: Detailed formulation of the rotation-free triangular element “S3” for general purpose shell analysis. Eng. Comput. 23(5), 469–502 (2006) CrossRefzbMATHGoogle Scholar
  35. 35.
    Schiehlen, W., Guse, N., Seifried, R.: Multibody dynamics in computational mechanics and engineering applications. Comput. Methods Appl. Mech. Eng. 195(41–43), 5509–5522 (2006) MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Schiehlen, W., Seifried, R.: Three approaches for elastodynamic contact in multibody systems. Multibody Syst. Dyn. 12(1), 1–16 (2004) CrossRefzbMATHGoogle Scholar
  37. 37.
    Shabana, A., Christensen, A.: Three dimensional absolute nodal coordinate formulation: plate problem. Int. J. Numer. Methods Eng. 40, 2775–2790 (1997). CrossRefzbMATHGoogle Scholar
  38. 38.
    Simo, J.: On a stress resultant geometrically exact shell model. Part VII: Shell intersections with 5/6-DOF finite element formulations. Comput. Methods Appl. Mech. Eng. 108(3–4), 319–339 (1993) CrossRefzbMATHGoogle Scholar
  39. 39.
    Sze, K.Y., Zhou, Y.X.: An efficient rotation-free triangle for drape/cloth simulations—part I: model improvement, dynamic simulation and adaptive remeshing. Int. J. Comput. Methods 13(3), 1650021 (2016) MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Temizer, I., Wriggers, P., Hughes, T.: Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS. Comput. Methods Appl. Mech. Eng. 209–212, 115–128 (2012) MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Wriggers, P.: Computational Contact Mechanics. Springer, Berlin (2006) CrossRefzbMATHGoogle Scholar
  42. 42.
    Wriggws, P., Stbin, E.: Finite element formulation deformation impact-contact with friction of large problems. Comput. Struct. 37(3), 319–331 (1990) CrossRefGoogle Scholar
  43. 43.
    Zhou, Y., Sze, K.: A geometric nonlinear rotation-free triangle and its application to drape simulation. Int. J. Numer. Methods Eng. 89, 509–536 (2011) CrossRefzbMATHGoogle Scholar
  44. 44.
    Zhou, Y.X., Sze, K.: An Efficient Rotation-Free Triangle and its Application in Cloth Simulations. Ph.D. thesis, The University of Hong Kong (2013) Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Naval Architecture, Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.MOE Key Laboratory of HydrodynamicsShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations