Skip to main content
SpringerLink
Log in

An overview of the ANCF approach, justifications for its use, implementation issues, and future research directions

  • Research
  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

This paper presents an overview of the finite-element (FE) absolute nodal coordinate formulation (ANCF), provides justifications for its use, and discusses issues relevant to its proper computer implementation and interpretation of its numerical results. The paper discusses future research directions for using ANCF finite elements in new areas such as soft tissues and materials relevant to broader areas of computational engineering and science. Selection of coordinates, definitions of forces and moments, geometric interpretation of the position gradients, and noncommutativity of finite rotations are among the topics discussed. To address concerns associated with finite-rotation noncommutativity and definition of moments in flexible-body dynamics, the paper demonstrates that the interpolation order is not preserved when the finite-rotation sequence is changed. Position gradients, on the other hand, are unique and preserve the highest interpolation order. It is shown that, while the spin tensor used to define the ANCF generalized forces due to moment application is associated with a rigid frame defined by the polar decomposition theorem, explicit polar decomposition of the matrix of position-gradient vectors is not required. ANCF elements have features that distinguish them from conventional finite elements and make them suited for large-displacement analysis of multibody systems (MBS). Their displacement fields, which allow increasing interpolation order without increasing number of nodes or using noncommutative finite rotations, are the basis for developing lower-dimension consistent rotation-based formulations (CRBF) without lowering the interpolation order. Nonetheless, the continuum-kinematic description of fully parameterized ANCF elements cannot be ignored when interpreting the ANCF numerical results. This issue is particularly important when comparing ANCF results with solutions obtained using semi-continuum conventional beam and plate models and simplified analytical approaches.

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

Similar content being viewed by others

Data Availability

All the data used in this investigation are presented in the paper.

References

  1. Abbas, L.K., Rui, X., Hammoudi, Z.S.: Plate/shell element of variable thickness based on the absolute nodal coordinate formulation. IMechE J. Multibody Dyn. 224, 127–141 (2010)

    Google Scholar 

  2. Bayoumy, A.H., Nada, A.A., Megahed, S.M.: A continuum based three-dimensional modeling of wind turbine blades. ASME J. Comput. Nonlinear Dyn. 8, 031004 (2012). https://doi.org/10.1115/1.4007798

    Article  Google Scholar 

  3. Bayoumy, A.H., Nada, A.A., Megahed, S.M.: Methods of modeling slope discontinuities in large size wind turbine blades using absolute nodal coordinate formulation. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 228(3), 314–329 (2014)

    Google Scholar 

  4. Bozorgmehri, B., Hurskainen, V.V., Matikainen, M.K., Mikkola, A.: Dynamic analysis of rotating shafts using the absolute nodal coordinate formulation. J. Sound Vib. 453, 214–236 (2019). https://doi.org/10.1016/j.jsv.2019.03.022. ISSN 0022-460X

    Article  Google Scholar 

  5. Bozorgmehri, B., Matikainen, M.K., Mikkola, A.: Development of line-to-line contact formulation for continuum beams. In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Vol. 85376, p. V002T02A004. American Society of Mechanical Engineers, New York (2021)

    Google Scholar 

  6. Bozorgmehri, B., Obrezkov, L.P., Harish, A.B., Mikkola, A., Matikainen, M.K.: A contact description for continuum beams with deformable arbitrary cross-section. Finite Elem. Anal. Des. 214, 103863 (2023). https://doi.org/10.1016/j.finel.2022.103863. ISSN 0168-874X

    Article  MathSciNet  Google Scholar 

  7. Bozorgmehri, B., Yu, X., Matikainen, M.K., Harish, A.B., Mikkola, A.: A study of contact methods in the application of large deformation dynamics in self-contact beam. Nonlinear Dyn. 103, 581–616 (2021)

    Article  MATH  Google Scholar 

  8. Bulín, R., Dyk, Š., Hajžman, M.: Nonlinear dynamics of flexible slender structures moving in a limited space with application in nuclear reactors. Nonlinear Dyn. 104, 3561–3579 (2021)

    Article  Google Scholar 

  9. Bulín, R., Hajžman, M.: Efficient computational approaches for analysis of thin and flexible multibody structures. Nonlinear Dyn. 103, 2475–2492 (2021). https://doi.org/10.1007/s11071-021-06225-5

    Article  Google Scholar 

  10. Bulín, R., Hajžman, M., Polach, P.: Nonlinear dynamics of a cable–pulley system using the absolute nodal coordinate formulation. Mech. Res. Commun. 82, 21–28 (2017)

    Article  Google Scholar 

  11. Cepon, G., Boltezar, M.: Dynamics of a belt-drive system using a linear complementarity problem for belt-pulley contact description. J. Sound Vib. 319, 1019–1035 (2008)

    Article  Google Scholar 

  12. Cepon, G., Manin, L., Boltezar, M.: Introduction of damping into the flexible multibody belt-drive model: a numerical and experimental investigation. J. Sound Vib. 324, 283–296 (2009)

    Article  Google Scholar 

  13. Cepon, G., Manin, L., Boltezar, M.: Validation of a flexible multibody belt-drive model. J. Mechan. Eng., Univ. Vestn. Ljublj. Fak. Stroj. 2011(57), 539–546 (2011). https://doi.org/10.5545/sv-jme.2010.257.hal-00756331

    Article  Google Scholar 

  14. Cepon, G., Starc, B., Zupancic, B., Boltezar, M.: Coupled thermo-structural analysis of a bimetallic strip using the absolute nodal coordinate formulation. Multibody Syst. Dyn. 41, 391–402 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  15. Chen, Y., Zhang, D.G., Li, L.: Dynamic analysis of rotating curved beams by using absolute nodal coordinate formulation based on radial point interpolation method. J. Sound Vib. 441, 63–83 (2019)

    Article  Google Scholar 

  16. Chang, H., Liu, C., Tian, Q., Hu, H., Mikkola, A.: Three new triangular shell elements of ANCF represented by Bézier triangles. Multibody Syst. Dyn. 35, 321–351 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. Cheng, L., Tian, Q.T., Dong, Y., Hu, H.: 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  MathSciNet  MATH  Google Scholar 

  18. Cui, Y., Lan, P., Zhou, H., Yu, Z.: The rigid-flexible-thermal coupled analysis for spacecraft carrying large-aperture paraboloid antenna. ASME J. Comput. Nonlinear Dyn. 15, 031003 (2020). https://doi.org/10.1115/1.4045890

    Article  Google Scholar 

  19. Dibold, M., Gerstmayr, J., Irschik, H.: A detailed comparison of the absolute nodal coordinate and the floating frame of reference formulation in deformable multibody systems. ASME J. Comput. Nonlinear Dyn. 4, 10 (2009)

    Google Scholar 

  20. Ding, Z., Ouyang, B.A.: Variable-length rational finite element based on the absolute nodal coordinate formulation. Machines 10, 174 (2022). https://doi.org/10.3390/machines10030174

    Article  Google Scholar 

  21. Dmitrochenko, O., Mikkola, A.M.: Two simple triangular plate elements based on the absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 3, 041012 (2008)

    Article  Google Scholar 

  22. Dmitrochenko, O., Mikkola, A.M.: A formal procedure and invariants of a transition from conventional finite elements to the absolute nodal coordinate formulation. Multibody Syst. Dyn. 22, 323–339 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Dmitrochenko, O.N., Pogorelov, D.Y.: Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody Syst. Dyn. 10, 17–43 (2003)

    Article  MATH  Google Scholar 

  24. Dmitrochenko, O., Yoo, W.S., Pogorelov, D.: Helicoseir as shape of a rotating string (II): 3D theory and simulation using ANCF. Multibody Syst. Dyn. 15, 181–200 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  25. Dufva, K., Sopanen, J.T., Mikkola, A.M.: A two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. J. Sound Vib. 280, 719–738 (2005)

    Article  Google Scholar 

  26. Dufva, K.E., Sopanen, J.T., Mikkola, A.M.: Three-dimensional beam element based on a cross-sectional coordinate system approach. Nonlinear Dyn. 43, 311–327 (2006)

    Article  MATH  Google Scholar 

  27. Ebel, H., Matikainen, M.K., Hurskainen, V.V., Mikkola, A.: Higher-order plate elements for large deformation analysis in multibody applications. In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 50183, p. V006T09A024. American Society of Mechanical Engineers, New York (2016)

    Google Scholar 

  28. Ebel, H., Matikainen, M.K., Hurskainen, V.V., Mikkola, A.: Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity. Nonlinear Dyn. 88, 1075–1091 (2017). https://doi.org/10.1007/s11071-016-3296-x

    Article  Google Scholar 

  29. Ebel, H., Matikainen, M.K., Hurskainen, V.V., Mikkola, A.: Analysis of high-order quadrilateral plate elements based on the absolute nodal coordinate formulation for three-dimensional elasticity. Adv. Mech. Eng. 9, 1687814017705069 (2017)

    Article  Google Scholar 

  30. Fan, W., Ren, H., Zhu, W., Zhu, H.: Dynamic analysis of power transmission lines with ice-shedding using an efficient absolute nodal coordinate beam formulation. ASME J. Comput. Nonlinear Dyn. 16, 011005 (2021)

    Article  Google Scholar 

  31. Fan, B., Wang, Z., Wang, Q.: Nonlinear forced transient response of rotating ring on the elastic foundation by using adaptive ANCF curved beam element. Appl. Math. Model. 108, 748–769 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  32. Fotland, G., Haskins, C., Rølvåg, T.: Trade study to select best alternative for cable and pulley simulation for cranes on offshore vessels. Syst. Eng. 23, 177–188 (2019). https://doi.org/10.1002/sys.21503

    Article  Google Scholar 

  33. Fotland, G., Haugen, B.: Numerical integration algorithms and constraint formulations for an ALE-ANCF cable element. Mech. Mach. Theory 170, 104659 (2022). https://doi.org/10.1016/j.mechmachtheory.2021.104659

    Article  Google Scholar 

  34. Garcıa-Vallejo, D., Escalona, J.L., Mayo, J., Dominguez, J.: Describing rigid-flexible multibody systems using absolute coordinates. Nonlinear Dyn. 34, 75–94 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  35. Garcia-Vallejo, D., Mayo, J., Escalona, J.L., Dominguez, 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 

  36. Garcıa-Vallejo, D., Mayo, J., Escalona, J.L., Dominguez, J.: Three-dimensional formulation of rigid-flexible multibody systems with flexible beam elements. Multibody Syst. Dyn. 20, 1–28 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  37. Garcıa-Vallejo, D., Mikkola, A.M., Escalona, J.L.: A new locking-free shear deformable finite element based on absolute nodal coordinates. Nonlinear Dyn. 50, 249–264 (2007)

    Article  MATH  Google Scholar 

  38. Garcia Vallejo, D., Valverde Garcia, J.S.: Stability and bifurcation analysis of a rotating beam substructured model. In: Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C, San Diego, California, USA, August 30–September 2, pp. 1371–1380. ASME, New York (2009). https://doi.org/10.1115/DETC2009-86210.

    Chapter  Google Scholar 

  39. Garcia-Vallejo, D., Valverde, J., Dominguez, J.: An internal damping model for the absolute nodal coordinate formulation. Nonlinear Dyn. 42, 347–369 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  40. Gerstmayr, J., Humer, A., Gruber, P., Nachbagauer, K.: The absolute nodal coordinate formulation. In: Structure-Preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics, pp. 159–200. Springer, Cham (2016)

    Chapter  Google Scholar 

  41. Gerstmayr, J., Irschik, H.: On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach. J. Sound Vib. 318, 461–487 (2008)

    Article  Google Scholar 

  42. Gerstmayr, J., Matikainen, M.K.: Analysis of stress and strain in the absolute nodal coordinate formulation. Mech. Based Des. Struct. Mach. 34, 409–430 (2006)

    Article  Google Scholar 

  43. Gerstmayr, J., Matikainen, M.K., Mikkola, A.M.: A geometrically exact beam element based on the absolute nodal coordinate formulation. Multibody Syst. Dyn. 20, 359–384 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  44. Gerstmayr, J., Sugiyama, H., Mikkola, A.: Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems. ASME J. Comput. Nonlinear Dyn. 8, 031016 (2013). https://doi.org/10.1115/1.4023487

    Article  Google Scholar 

  45. Ghorbani, H., Tarvirdizadeh, B., Alipour, K., Hadi, A.: Near-time-optimal motion control for flexible-link systems using absolute nodal coordinates formulation. Mech. Mach. Theory 140, 686–710 (2019). https://doi.org/10.1016/j.mechmachtheory.2019.06.032. ISSN 0094-114X

    Article  Google Scholar 

  46. Gregori, S., Tur, M., Nadal, E., Aguado, J.V., Fuenmayor, F.J., Chinesta, F.: Fast simulation of the pantograph–catenary dynamic interaction. Finite Elem. Anal. Des. 129, 1–13 (2017)

    Article  Google Scholar 

  47. Gregori, S., Tur, M., Nadal, E., Fuenmayor, F.J., Chinesta, F.: Parametric model for the simulation of the railway catenary system static equilibrium problem. Finite Elem. Anal. Des. 115, 21–32 (2016)

    Article  Google Scholar 

  48. Gruber, P.G., Nachbagauer, K., Vetyukov, Y., Gerstmayr, J.: A novel director-based Bernoulli–Euler beam finite element in absolute nodal coordinate formulation free of geometric singularities. Mech. Sci. 4, 279–289 (2013)

    Article  Google Scholar 

  49. Gufler, V., Wehrle, E., Zwölfer, A.A.: Review of flexible multibody dynamics for gradient-based design optimization. Multibody Syst. Dyn. (2021). https://doi.org/10.1007/s11044-021-09802-z

    Article  MathSciNet  MATH  Google Scholar 

  50. Gu, Y., Lan, P., Cui, Y., Li, K., Yu, Z.: Dynamic interaction between the transmission wire and cross-frame. Mech. Mach. Theory 155, 104068 (2021)

    Article  Google Scholar 

  51. Guo, X., Sun, J.Y., Li, L., Zhang, D.G., Chen, Y.Z.: Large deformations of piezoelectric laminated beams based on the absolute nodal coordinate formulation. Compos. Struct. 275, 114426 (2021)

    Article  Google Scholar 

  52. Haiquan, L., Jianxun, L., Shuang, W., Qian, L., Wenming, Z.: Dynamics modeling and experiment of a flexible capturing mechanism in a space manipulator. Chin. J. Theor. Appl. Mech. 52, 1465–1474 (2020)

    Google Scholar 

  53. Hara, K., Watanabe, M.: Development of an efficient calculation procedure for elastic forces in the ANCF beam element by using a constrained formulation. Multibody Syst. Dyn. 43, 369–386 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  54. He, G., Gao, K., Yu, Z., Jiang, J., Li, Q.: Adaptive subdomain integration method for representing complex localized geometry in ANCF. Acta Mech. Sin. 38, 521442 (2022). https://doi.org/10.1007/s10409-021-09032-x

    Article  MathSciNet  Google Scholar 

  55. He, J., Lilley, C.M.: The finite element absolute nodal coordinate formulation incorporated with surface stress effect to model elastic bending nanowires in large deformation. Comput. Mech. 44, 395–403 (2009)

    Article  MATH  Google Scholar 

  56. Heidaria, H.R., Korayem, M.H., Haghpanahi, M.: Maximum allowable load of very flexible manipulators by using absolute nodal coordinate. Aerosp. Sci. Technol. 45, 67–77 (2015)

    Article  Google Scholar 

  57. Hewlett, J.: Methods for real-time simulation of systems of rigid and flexible bodies with unilateral contact and friction. PhD Thesis, Department of Mechanical Engineering, McGill University (2019)

  58. Hewlett, J., Arbatani, S., Kovecses, J.: A fast and stable first-order method for simulation of flexible beams and cables. Nonlinear Dyn. 99, 1211–1226 (2020)

    Article  Google Scholar 

  59. Hong, D., Ren, G.: A modeling of sliding joint on one-dimensional flexible medium. Multibody Syst. Dyn. 26, 91–106 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  60. Hong, D., Tang, J., Ren, G.: Dynamic modeling of mass-flowing linear medium with large amplitude displacement and rotation. J. Fluids Struct. 27, 1137–1148 (2011). https://doi.org/10.1016/j.jfluidstructs.2011.06.006. ISSN 0889-9746

    Article  Google Scholar 

  61. Htun, T.Z., Suzuki, H., Garcia-Vallejo, D.: Dynamic modeling of a radially multilayered tether cable for a remotely-operated underwater vehicle (ROV) based on the absolute nodal coordinate formulation (ANCF). Mech. Mach. Theory 153, 103961 (2020). https://doi.org/10.1016/j.mechmachtheory.2020.103961

    Article  Google Scholar 

  62. Htun, T.Z., Suzuki, H., García-Vallejo, D.: On the theory and application of absolute coordinates-based multibody modelling of the rigid–flexible coupled dynamics of a deep-sea ROV-TMS (tether management system) integrated model. Ocean Eng. 258, 111748 (2022). https://doi.org/10.1016/j.oceaneng.2022.111748. ISSN 0029-8018

    Article  Google Scholar 

  63. Hu, W., Deng, Z.A.: Review of dynamic analysis on space solar power station. Astrodynamics (2022). https://doi.org/10.1007/s42064-022-0144-2

    Article  Google Scholar 

  64. Hu, H., Tian, Q., Liu, C.: Computational dynamics of soft machines. Acta Mech. Sin. 33, 516–528 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  65. Huang, X., Zou, J., Gu, G.: Kinematic modeling and control of variable curvature soft continuum robots. IEEE/ASME Trans. Mechatron. 26(6), 3175–3185 (2021). https://doi.org/10.1109/TMECH.2021.3055339. Dec. 2021

    Article  Google Scholar 

  66. Hung, L.Q., Kang, Z., Shaojie, L.: Numerical investigation of dynamics of the flexible riser by applying absolute nodal coordinate formulation. Mar. Technol. Soc. J. 55, 179–195 (2021)

    Article  Google Scholar 

  67. Hung, L.Q., Kang, Z., Zhang, C., Jie, L.S.: Numerical investigation on dynamics of the tendon system of a TLP by applying absolute nodal coordinate formulation. China Ocean Eng. 35, 384–397 (2021)

    Article  Google Scholar 

  68. Hurskainen, V.T., Matikainen, M.K., Wang, J.J., Mikkola, A.M.: A planar beam finite-element formulation with individually interpolated shear deformation. ASME J. Comput. Nonlinear Dyn. 12, 041007 (2017). https://doi.org/10.1115/1.4035413

    Article  Google Scholar 

  69. Hyldahl, P.: Rectangular Shell Elements Based on the Absolute Nodal Coordinate Formulation. Aarhus University, Aarhus (2015)

    Google Scholar 

  70. Hyldahl, P., Mikkola, A.M., Balling, O., Sopanen, J.T.: Behavior of thin rectangular ANCF shell elements in various mesh configurations. Nonlinear Dyn. 78, 1277–1291 (2014)

    Article  Google Scholar 

  71. Ishikura, M., Takeuchi, E., Konyo, M., Tadokoro, S.: Shape estimation of flexible cable. In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2539–2546. IEEE Press, New York (2012)

    Chapter  Google Scholar 

  72. Iwai, R., Kobayashi, N.: A new flexible multibody beam element based on the absolute nodal coordinate formulation using the global shape function and the analytical mode shape function. Nonlinear Dyn. 34, 207–232 (2003)

    Article  MATH  Google Scholar 

  73. Jung, S.P., Park, T.W., Chung, W.S.: Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the non-linear constitutive law. Nonlinear Dyn. 63, 149–157 (2011)

    Article  Google Scholar 

  74. Kato, I., Terumichi, Y., Adachi, M., Sogabe, K.: Dynamics of track/wheel systems on high-speed vehicles. J. Mech. Sci. Technol. 1, 328–335 (2005)

    Article  Google Scholar 

  75. Kawaguti, K., Terumichi, Y., Takehara, S., Kaczmarczyk, S., Sogabe, K.: The study of the tether motion with time-varying length using the absolute nodal coordinate formulation with multiple nonlinear time scales. J. Syst. Des. Dyn. 1, 491–500 (2007)

    Google Scholar 

  76. Kerkkanen, K.S., Garcıa-Vallejo, D., Mikkola, A.M.: Modeling of belt-drives using a large deformation finite element formulation. Nonlinear Dyn. 43, 239–256 (2006)

    Article  MATH  Google Scholar 

  77. Kerkkanen, K.S., Sopanen, J.T., Mikkola, A.M.: A linear beam finite element based on the absolute nodal coordinate formulation. ASME J. Mech. Des. 127, 621–630 (2005)

    Article  Google Scholar 

  78. Khan, I.M., Anderson, K.S.: Divide-and-conquer-based large deformation formulations for multi-flexible body systems. In: Proceedings of the ASME 9th International Conference on Multibody Systems. Nonlinear Dynamics, and Control, vol. 7B, Portland, Oregon, USA, pp. V07BT10A002-1–V07BT10A002-10 (2013)

    Google Scholar 

  79. Khude, K., Melanz, D., Stanciulescu, I., 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: Proceedings of the 8th International Conference on Multibody Systems, Nonlinear Dynamics and Control (2011)

    Google Scholar 

  80. Kim, E., Kim, H., Cho, M.: Model order reduction of multibody system dynamics based on stiffness evaluation in the absolute nodal coordinate formulation. Nonlinear Dyn. 87, 1901–1915 (2017). https://doi.org/10.1007/s11071-016-3161-y

    Article  Google Scholar 

  81. Kim, H., Lee, H., Lee, K., Cho, H., Cho, M.: Efficient flexible multibody dynamic analysis via improved C0 absolute nodal coordinate formulation-based element. Mech. Adv. Mat. Struct, 1–13 (2021). https://doi.org/10.1080/15376494.2021.1919804

    Article  Google Scholar 

  82. Kłodowski, A., Rantalainen, T., Mikkola, A., Heinonen, A., Sievänen, H.: Flexible multibody approach in forward dynamic simulation of locomotive strains in human skeleton with flexible lower body bones. Multibody Syst. Dyn. 25(4), 395–409 (2011)

    Article  MATH  Google Scholar 

  83. Laflin, J.J., Anderson, K.S., Khan, I.M., Poursina, M.: New and extended applications of the divide-and-conquer algorithm for multibody dynamics. ASME J. Comput. Nonlinear Dyn. 9(4), 041004 (2014)

    Article  Google Scholar 

  84. Lan, P., Li, K., Yu, Z.: Computer implementation of piecewise cable element based on the absolute nodal coordinate formulation and its application in wire modeling. Acta Mech. 230, 1145–1158 (2019)

    Article  MathSciNet  Google Scholar 

  85. Lan, P., Tian, Q., Yu, Z.: A new absolute nodal coordinate formulation beam element with multilayer circular cross-section. Acta Mech. Sin. 36, 82–96 (2020)

    Article  MathSciNet  Google Scholar 

  86. Lee, J.W., Kim, H.W., Ku, H.C., Yoo, W.S.: Comparison of external damping models in a large deformation problem. J. Sound Vib. 325, 722–741 (2009)

    Article  Google Scholar 

  87. Lee, J.W., Kim, H.W., Ku, H.C., Yoo, W.S.: Measurement and correlation of high frequency behaviors of a very flexible beam undergoing large deformation. J. Mech. Sci. Technol. 23, 2766–2775 (2009)

    Article  Google Scholar 

  88. Lee, J.H., Park, T.W.: Dynamic analysis model for the current collection performance of high-speed trains using the absolute nodal coordinate formulation. Trans. Korean Soc. Mech. Eng. A 36, 339–346 (2012)

    Article  Google Scholar 

  89. Lee, S.H., Park, T.W., Seo, J.H., Yoon, J.W., Jun, K.J.: The development of a sliding joint for very flexible multibody dynamics using absolute coordinate formulation. Multibody Syst. Dyn. 20, 223–237 (2008)

    Article  MATH  Google Scholar 

  90. Lei, B., Ma, Z., Liu, J., Liu, C.: Dynamic modelling and analysis for a flexible brush sampling mechanism. Multibody Syst. Dyn. 56, 335–365 (2022). https://doi.org/10.1007/s11044-022-09848-7

    Article  MATH  Google Scholar 

  91. Li, B., Duan, C., Peng, Q., et al.: Parametric study of planar flexible deployable structures consisting of scissor-like elements using a novel multibody dynamic analysis methodology. Arch. Appl. Mech. (2021). https://doi.org/10.1007/s00419-021-01997-z

    Article  Google Scholar 

  92. Li, J., Liu, C., Hu, H., Zhang, S.: Analysis of elasto-plastic thin-shell structures using layered plastic modeling and absolute nodal coordinate formulation. Nonlinear Dyn. 105, 2899–2920 (2021). https://doi.org/10.1007/s11071-021-06766-9

    Article  Google Scholar 

  93. Li, K., Liu, M., Yu, Z., Lan, P., Lu, N.: Multibody system dynamic analysis and payload swing control of tower crane. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. (2022). https://doi.org/10.1177/146441932211019.

    Article  Google Scholar 

  94. Li, L., Wang, Y., Guo, Y., Zhang, D.: Large deformations of hyperelastic curved beams based on the absolute nodal coordinate formulation. Nonlinear Dyn. (2022). https://doi.org/10.1007/s11071-022-08076-0

    Article  Google Scholar 

  95. Li, S., Wang, Y., Ma, X., Wang, S.: Modeling and simulation of a moving yarn segment: based on the absolute nodal coordinate formulation. Math. Probl. Eng. 2019, 6567802 (2019). https://doi.org/10.1155/2019/6567802

    Article  Google Scholar 

  96. Li, H., Zhong, H.: Weak form quadrature elements based on absolute nodal coordinate formulation for planar beamlike structures. Acta Mech. 232, 4289–4307 (2021). https://doi.org/10.1007/s00707-021-03052-y

    Article  MathSciNet  MATH  Google Scholar 

  97. Liu, J., Hong, J.: Nonlinear formulation for flexible multibody system with large deformation. Acta Mech. Sin. 23, 111–119 (2007)

    Article  MATH  Google Scholar 

  98. Liu, C., Tian, Q., Hu, H.: Dynamics of a large scale rigid-flexible multibody system composed of composite laminated plates. Multibody Syst. Dyn. 26, 283–305 (2011)

    Article  MATH  Google Scholar 

  99. Luo, K., Liu, C., Tian, Q., Hu, H.Y.: Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation. Nonlinear Dyn. 85, 949–971 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  100. Ma, L., Wei, C., Ma, C., Zhao, Y.: Modeling and verification of a RANCF fluid element based on cubic rational Bezier volume. ASME J. Comput. Nonlinear Dyn. 15, 041005 (2020)

    Article  Google Scholar 

  101. Ma, C., Wei, C., Sun, J., Liu, B.: Modeling method and application of rational finite element based on absolute nodal coordinate formulation. Acta Mech. Solida Sin. 31, 2 (2018). https://doi.org/10.1007/s10338-018-0020-z

    Article  Google Scholar 

  102. Matikainen, M.K., Dmitrochenko, O., Mikkola, A.M.: Beam elements with trapezoidal cross-section deformation modes based on the absolute nodal coordinate formulation. In: International Conference of Numerical Analysis and Applied Mathematics, pp. 19–25 (2010)

    Google Scholar 

  103. Matikainen, M.K., Mikkola, A., Schwab, A.L.: The quadrilateral fully-parametrized plate elements based on the absolute nodal coordinate formulation. J. Struct. Mech. 42, 138–148 (2009)

    Google Scholar 

  104. Matikainen, M.K., Schwab, A.L., Mikkola, A.M.: Comparison of two moderately thick plate elements based on the absolute nodal coordinate formulation. In: Multibody Dynamics ECCOMAS Thematic Conference, 29 June–2 July 2009, Warsaw, Poland (2009)

    Google Scholar 

  105. Matikainen, M.K., Valkeapää, A.I., Mikkola, A.M., Schwab, A.L.: A study of moderately thick quadrilateral plate elements based on the absolute nodal coordinate formulation. Multibody Syst. Dyn. 31, 309–338 (2014). https://doi.org/10.1007/s11044-013-9383-6

    Article  MathSciNet  Google Scholar 

  106. Matikainen, M.K., von Hertzen, R., Mikkola, A.M., Gerstmayr, J.: Elimination of high frequencies in absolute nodal coordinate formulation. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 224, 103–116 (2010)

    Google Scholar 

  107. Mikkola, A.M., Dmitrochenko, O., Matikainen, M.K.: A procedure for the inclusion of transverse shear deformation in a beam element based on the absolute nodal coordinate formulation. In: Proceedings of the 6th International Conference on Multibody Systems, Nonlinear Dynamics and Control (2007)

    Google Scholar 

  108. Mikkola, A.M., Matikainen, M.K.: Development of elastic forces for the large deformation plate element based on the absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 1, 103–108 (2006)

    Article  Google Scholar 

  109. Mohamed, A.N.A.: Three-dimensional fully parameterized triangular plate element based on the absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 8, 041016 (2013)

    Article  Google Scholar 

  110. Nachbagauer, K.: Development of shear and cross-section deformable beam finite elements applied to large deformation and dynamics problems. PhD Dissertation, Johannes Kepler University, Linz, Austria (2013)

  111. Nachbagauer, K.: Development of shear and cross-section deformable beam finite elements applied to large deformation and dynamics problems. In: 2nd ECCOMAS Young Investigators Conference (YIC 2013) (2013)

    Google Scholar 

  112. Nachbagauer, K.: State of the art of ANCF elements regarding geometric description, interpolation strategies, definition of elastic forces, validation and locking phenomenon in comparison with proposed beam finite elements. Arch. Comput. Methods Eng. 21(3), 293–319 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  113. Nachbagauer, K., Gerstmayr, J.: Structural and continuum mechanics approaches for a 3D shear deformable ANCF beam finite element: application to buckling and nonlinear dynamic examples. J. Comput. Nonlinear Dyn. 9, 011013 (2014). https://doi.org/10.1115/1.4025282

    Article  Google Scholar 

  114. Nachbagauer, K., Gruber, P., Gerstmayr, J.: Structural and continuum mechanics approaches for a 3D shear deformable ANCF beam finite element: application to static and linearized dynamic examples. ASME J. Comput. Nonlinear Dyn. 8, 021004 (2013)

    Article  Google Scholar 

  115. Nachbagauer, K., Gruber, P., Gerstmayr, J.: A 3D shear deformable finite element based on the absolute nodal coordinate formulation. In: Multibody Dynamics, pp. 77–96. Springer, Dordrecht (2013)

    Chapter  Google Scholar 

  116. Nachbagauer, K., Gruber, P., Vetyukov, Y., Gerstmayr, J.: A spatial thin beam element based on the absolute nodal coordinate formulation without singularities. In: Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 1–9 (2011)

    Google Scholar 

  117. Nachbagauer, K., Pechstein, A.S., Irschik, H., Gerstmayr, J.: A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation. Multibody Syst. Dyn. 26(3), 245–263 (2011)

    Article  MATH  Google Scholar 

  118. Nada, A.A.: Use of B-spline surface to model large-deformation continuum plates: procedure and applications. Nonlinear Dyn. 72, 243–263 (2013). https://doi.org/10.1007/s11071-012-0709-3

    Article  MathSciNet  MATH  Google Scholar 

  119. Nada, A.A.: Efficient modeling of continuum blades using ANCF curved shell element. In: 5th European Conference on Computational Mechanics (ECCM V), Barcelona, Spain, pp. 3092–3103 (2014) July

    Google Scholar 

  120. Nada, A.A., El-Assal, A.M.: Absolute nodal coordinate formulation of large-deformation piezoelectric laminated plates. Nonlinear Dyn. 67, 2441–2454 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  121. Nemov, A.S., Matikainen, M.K., Wang, T., Mikkola, A.: Analysis of electromechanical systems based on the absolute nodal coordinate formulation. Acta Mech. 233, 1019–1030 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  122. Obrezkov, L., Bozorgmehri, B., Finni, T., Matikainen, M.K.: Approximation of pre-twisted Achilles sub-tendons with continuum-based beam elements. Appl. Math. Model. 112, 669–689 (2022). https://doi.org/10.1016/j.apm.2022.08.014. ISSN 0307-904X

    Article  MathSciNet  MATH  Google Scholar 

  123. Obrezkov, L., Eliasson, P., Harish, A.B., Matikainen, M.K.: Usability of finite elements based on the absolute nodal coordinate formulation for deformation analysis of the Achilles tendon. Int. J. Non-Linear Mech. 129, 103662 (2021). https://doi.org/10.1016/j.ijnonlinmec.2020.103662

    Article  Google Scholar 

  124. Obrezkov, L.P., Matikainen, M.K., Harish, A.B.: A finite element for soft tissue deformation based on the absolute nodal coordinate formulation. Acta Mech. 231, 1519–1538 (2020). https://doi.org/10.1007/s00707-019-02607-4

    Article  MathSciNet  MATH  Google Scholar 

  125. Obrezkov, L., Matikainen, M.K., Kouhia, R.: Micropolar beam-like structures under large deformation. Int. J. Solids Struct. 254–255, 111899 (2022). https://doi.org/10.1016/j.ijsolstr.2022.111899. ISSN 0020-7683

    Article  Google Scholar 

  126. Obrezkov, L.P., Mikkola, A., Matikainen, M.K.: Performance review of locking alleviation methods for continuum ANCF beam elements. Nonlinear Dyn. 109, 531–546 (2022). https://doi.org/10.1007/s11071-022-07518-z

    Article  Google Scholar 

  127. Olshevskiy, A., Dmitrochenko, O., Dai, M.D., Kim, C.W.: The simplest 3-, 6- and 8-noded fully-parameterized ANCF plate elements using only transverse slopes. Multibody Syst. Dyn. 34, 23–51 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  128. Olshevskiy, A., Dmitrochenko, O., Kim, C.: Three- and four-noded planar elements using absolute nodal coordinate formulation. Multibody Syst. Dyn. 29, 255–269 (2013). https://doi.org/10.1007/s11044-012-9314-y37

    Article  MathSciNet  Google Scholar 

  129. Olshevskiy, A., Dmitrochenko, O., Kim, C.W.: Three-dimensional solid brick element using slopes in the absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 9(2), 021001 (2014)

    Article  Google Scholar 

  130. Orzechowski, G.: Analysis of beam elements of circular cross-section using the absolute nodal coordinate formulation. Arch. Mech. Eng. 59(3), 283–296 (2012)

    Article  MathSciNet  Google Scholar 

  131. Orzechowski, G., Fraczek, J.: Beam element of circular cross-section based on the ANCF continuum mechanics approach. In: Multibody Dynamics 2011, ECCOMAS Thematic Conference on Multibody Dynamics, Brussels (2011)

    Google Scholar 

  132. Orzechowski, G., Frączek, J.: Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements. J. Theor. Appl. Mech. 55, 977–990 (2017)

    Article  Google Scholar 

  133. Orzechowski, G., Frączek, J.: Integration of the equations of motion of multibody systems using absolute nodal coordinate formulation. Acta Mech. Autom. 6(2), 75–83 (2012)

    Google Scholar 

  134. Orzechowski, G., Fraczek, J.: Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF. Nonlinear Dyn. 82(1), 451–464 (2023)

    MathSciNet  Google Scholar 

  135. Otsuka, K., Makihara, K.: Absolute nodal coordinate beam element for modeling flexible and deployable aerospace structures. AIAA J. 57, 1343–1346 (2019)

    Article  Google Scholar 

  136. Otsuka, K., Makihara, K., Sugiyama, H.: Recent advances in the absolute nodal coordinate formulation: literature review from 2012 to 2020. ASME J. Comput. Nonlinear Dyn. 17, 080803 (2022)

    Article  Google Scholar 

  137. Otsuka, K., Wang, Y., Palacios, R., Makihara, K.: Strain-based geometrically nonlinear beam formulation for rigid–flexible multibody dynamic analysis. AIAA J. (2022). https://doi.org/10.2514/1.J061516

    Article  Google Scholar 

  138. Otsuka, K., Wang, Y., Fujita, K., Nagai, H., Makihara, K.: Consistent strain-based multifidelity modeling for geometrically nonlinear beam structures. ASME J. Comput. Nonlinear Dyn. 17(11), 111003 (2022). https://doi.org/10.1115/1.4055310

    Article  Google Scholar 

  139. Pan, K., Cao, D.: Absolute nodal coordinate finite element approach to the two-dimensional liquid sloshing problems. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 234(2), 1–25 (2020). https://doi.org/10.1177/1464419320907785

    Article  Google Scholar 

  140. Peng, H., Song, N., Kan, Z.: Data-driven model order reduction with proper symplectic decomposition for flexible multibody system. Nonlinear Dyn. 107, 173–203 (2022)

    Article  Google Scholar 

  141. Peng, C., Yang, C., Xue, J., Gong, Y., Zhang, W.: An adaptive variable-length cable element method for form-finding analysis of railway catenaries in an absolute nodal coordinate formulation. Eur. J. Mech. A, Solids (2022). https://doi.org/10.1016/j.euromechsol.2022.104545.

    Article  MathSciNet  MATH  Google Scholar 

  142. Polach, P., Hajžman, M., Bulín, R.: Approaches to fibre modelling in the model of an experimental laboratory mechanical system. In: European Congress on Computational Methods in Applied Sciences and Engineering, pp. 231–238. Springer, Cham (2019) August

    MATH  Google Scholar 

  143. Recuero, A., Serban, R., Peterson, B., Sugiyama, H., Jayakumar, P., Negrut, D.: A high-fidelity approach for vehicle mobility simulation: nonlinear finite element tyres operating on granular material. J. Terramech. 72, 39–54 (2017)

    Article  Google Scholar 

  144. Ren, H., Fan, W.: An adaptive triangular element of absolute nodal coordinate formulation for thin plates and membranes. Thin-Walled Struct. 182B 110257 (2023). https://doi.org/10.1016/j.tws.2022.110257 ISSN 0263-8231

    Article  Google Scholar 

  145. Sanborn, G.G., Choi, J., Choi, J.H.: Curved-induced distortion of polynomial space curves, flat-mapped extension modeling, and their impact on ANCF thin-plate finite elements. Multibody Syst. Dyn. 36, 191–211 (2011)

    Article  MATH  Google Scholar 

  146. Schwab, A.L., Gerstmayr, J., Meijaard, J.P.: Comparison of three-dimensional flexible thin plate elements for multibody dynamic analysis: finite element formulation and absolute nodal coordinate formulation. In: Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Las Vegas, Nevada (2007). Paper No. DETC2007-34754

    Google Scholar 

  147. Schwab, A.L., Meijaard, J.P.: Comparison of three-dimensional beam elements for dynamic analysis: finite element method and absolute nodal coordinate formulation. In: Proceedings of the ASME 2005 International Design Engineering Technical Conferences & Computer and Information in Engineering Conference (DETC2005–85104), September 24–28, Long Beach, CA (2005)

    Google Scholar 

  148. Schwab, A.L., Meijaard, J.P.: Comparison of three-dimensional flexible beam elements for dynamic analysis: finite element method and absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 5, 1–10 (2010)

    Google Scholar 

  149. Seo, J.H., Kim, S.W., Jung, I.H., Park, T.W., Mok, J.Y., Kim, Y.G., Chai, J.B.: Dynamic analysis of a pantograph-catenary system using absolute nodal coordinates. Veh. Syst. Dyn. 44, 615–630 (2006)

    Article  Google Scholar 

  150. Sereshk, M.V., Salimi, M.: Comparison of finite element method based on nodal displacement and absolute nodal coordinate formulation (ANCF) in thin shell analysis. Int. J. Numer. Methods Biomed. Eng. 27, 1185–1198 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  151. Shen, Z., Li, P., Liu, C., Hu, G.: A finite element beam model including cross-section distortion in the absolute nodal coordinate formulation. Nonlinear Dyn. 77, 1019–1033 (2014). https://doi.org/10.1007/s11071-014-1360-y

    Article  Google Scholar 

  152. Shen, Z., Liu, C., Li, H.: Viscoelastic analysis of bistable composite shells via absolute nodal coordinate formulation. Compos. Struct. (2020). https://doi.org/10.1016/j.compstruct.2020.112537

    Article  Google Scholar 

  153. Shen, Z., Tian, Q., Liu, X., Hu, G.: Thermally induced vibrations of flexible beams using absolute nodal coordinate formulation. Aerosp. Sci. Technol. 29(1), 386–393 (2013)

    Article  Google Scholar 

  154. Shen, Z., Xing, X., Li, B.: A new thin beam element with cross-section distortion of the absolute nodal coordinate formulation. IMechE J. Mech. Eng. Sci. C (2021). https://doi.org/10.1177/09544062211020046.

    Article  Google Scholar 

  155. Sheng, F., Zhong, Z., Wang, K.: Theory and model implementation for analyzing line structures subject to dynamic motions of large deformation and elongation using the absolute nodal coordinate formulation (ANCF) approach. Nonlinear Dyn. (2020). https://doi.org/10.1007/s11071-020-05783-4

    Article  Google Scholar 

  156. Skrinjar, L., Slavic, J., Boltežar, M.: Absolute nodal coordinate formulation in a pre-stressed large-displacements dynamical system. J. Mech. Eng. 63, 417–425 (2017). https://doi.org/10.5545/sv-jme.2017.4561

    Article  Google Scholar 

  157. Song, Z., Chen, J., Chen, C.: Application of discrete shape function in absolute nodal coordinate formulation. Math. Biosci. Eng. 18(4), 4603–4627 (2021). https://doi.org/10.3934/mbe.2021234

    Article  MathSciNet  Google Scholar 

  158. Sopanen, J.T., Mikkola, A.M.: Description of elastic forces in absolute nodal coordinate formulation. Nonlinear Dyn. 34, 53–74 (2003)

    Article  MATH  Google Scholar 

  159. Stangl, M., Gerstmayr, J., Irschik, H.: A large deformation planar finite element for pipes conveying fluid based on the absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 4, 031009 (2009)

    Article  Google Scholar 

  160. Takahashi, Y., Shimizu, N.: Study on elastic forces of the absolute nodal coordinate formulation for deformable beams. In: Proceedings of the ASME International Design Engineering Technical Conferences and Computer and Information in Engineering Conference, Las Vegas, NV (1999)

    Google Scholar 

  161. Takahashi, Y., Shimizu, N.: Seismic response analysis system by means of multibody dynamics approach: modeling and analysis of geometric time varying structure systems. In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 47438, pp. 1769–1778 (2005)

    Google Scholar 

  162. Takahashi, Y., Shimizu, N.: Study on characteristics of the numerical integration of dynamics analyses for the beam element formulated by ANC (flexible multibody dynamics). In: The Proceedings of the Asian Conference on Multibody Dynamics 2010, p. 58855. The Japan Society of Mechanical Engineers, Tokyo (2010)

    Google Scholar 

  163. Takahashi, Y., Shimizu, N., Suzuki, K.: Study on the frame structure modeling of the beam element formulated by absolute coordinate approach. J. Mech. Sci. Technol. 19, 283–291 (2005)

    Article  Google Scholar 

  164. Takahashi, Y., Shimizu, N., Suzuki, K.: Introduction of damping matrix into absolute nodal coordinate formulation. In: Proceedings of the Asian Conference on Multibody Dynamics, pp. 33–40 (2002)

    Google Scholar 

  165. Tang, L., Liu, J.: Frictional contact analysis of sliding joints with clearances between flexible beams and rigid holes in flexible multibody systems. Multibody Syst. Dyn. 49, 155–179 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  166. Tang, Y., Tian, Q., Hu, H.: Efficient modeling and order reduction of new 3D beam elements with warping via absolute nodal coordinate formulation. Nonlinear Dyn. (2022). https://doi.org/10.1007/s11071-022-07547-8

    Article  Google Scholar 

  167. Tian, Q., Chen, L.P., Zhang, Y.Q., Yang, J.Z.: An efficient hybrid method for multibody dynamics simulation based on absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 4(2), 021009 (2009)

    Article  Google Scholar 

  168. Tian, Q., Zhang, Y., Chen, L., Yang, J.: Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dyn. 60, 489–511 (2010)

    Article  MATH  Google Scholar 

  169. Tur, M., Baeza, L., Fuenmayor, F.J., García, E.: PACDIN statement of methods. Veh. Syst. Dyn. 53, 402–411 (2015)

    Article  Google Scholar 

  170. Tur, M., García, E., Baeza, L., Fuenmayor, F.J.: A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary. Eng. Struct. 71, 234–243 (2014)

    Article  Google Scholar 

  171. Valkeapää, A.I., Matikainen, M.K., Mikkola, A.M.: Meshing strategies in the absolute nodal coordinate formulation-based Euler–Bernoulli beam elements. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 230, 606–614 (2016)

    Google Scholar 

  172. Valverde Garcia, J.S., Garcıa-Vallejo, D.: Stability analysis of a substructuring model of the rotating beam. Nonlinear Dyn. 55, 355–372 (2009)

    Article  MATH  Google Scholar 

  173. Vohar, B., Kegl, M., Ren, Z.: Implementation of an ANCF beam finite element for dynamic response optimization of elastic manipulators. Eng. Optim. 40, 1137–1150 (2008)

    Article  MathSciNet  Google Scholar 

  174. Wang, T.F.: Two new triangular thin plate/shell elements based on the absolute nodal coordinate formulation. Nonlinear Dyn. 99, 2707–2725 (2020)

    Article  MATH  Google Scholar 

  175. Wang, J., Hurskainen, V.V., Matikainen, M.K., Sopanen, J., Mikkola, A.: On the dynamic analysis of rotating shafts using nonlinear superelement and absolute nodal coordinate formulations. Adv. Mech. Eng. 9 (2017). https://doi.org/10.1177/1687814017732672

  176. Wang, Y., Li, S., Ma, X., Zhang, D., Feng, P., Wang, S.: An analytical approach of filament bundle swinging dynamics, part I: modeling filament bundle by ANCF. Tex. Res. J. 89, 4607–4619 (2019)

    Article  Google Scholar 

  177. Wang, T.F., Mikkola, A., Matikainen, M.K.: An overview of higher-order beam elements based on the absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 17, 091001 (2022)

    Article  Google Scholar 

  178. Wang, T., Nemov, A.S., Matikainen, M.K., Mikkola, A.: Numerical analysis of the magnetic shape memory effect based on the absolute nodal coordinate formulation. Acta Mech. 233, 1941–1965 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  179. Wang, J., Wang, T.: Buckling analysis of beam structure with absolute nodal coordinate formulation. IMechE J. Mech. Eng. Sci. (2020). https://doi.org/10.1177/0954406220947117

    Article  Google Scholar 

  180. Wang, T., Wu, Z., Wang, J., Lan, P., Xu, M.: Simulation of membrane deployment accounting for the nonlinear crease effect based on absolute nodal coordinate formulation. Nonlinear Dyn. (2022). https://doi.org/10.1007/s11071-022-07952-z

    Article  Google Scholar 

  181. Xu, Q.P., Liu, J.Y.: An improved dynamic model for a silicone material beam with large deformation. Acta Mech. Sin. 34, 744–753 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  182. Xu, Q., Liu, J.: An improved dynamic formulation for nonlinear response analysis of thin soft silicone plates with large deflection. Thin-Walled Struct. 176, 109333 (2022). https://doi.org/10.1016/j.tws.2022.109333. ISSN 0263-8231

    Article  Google Scholar 

  183. Xu, Q.P., Liu, J.Y., Qu, L.Z.: Dynamic modeling for silicone beams using higher-order ANCF beam elements and experiment investigation. Multibody Syst. Dyn. 46, 307–328 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  184. Yamano, A., Shintani, A., Ito, T., Nakagawa, C., Ijima, H.: Influence of boundary conditions on a Flutter-Mill. J. Sound Vib. 478, 115359 (2020)

    Article  Google Scholar 

  185. Yamashita, H., Sugiyama, H.: Numerical convergence of finite element solutions of nonrational B-spline element and absolute nodal coordinate formulation. Nonlinear Dyn. 67, 177–189 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  186. Yoo, W.S., Dmitrochenko, O., Park, S.J., Lim, O.K.: A new thin spatial beam element using the absolute nodal coordinates: application to a rotating strip. Mech. Based Des. Struct. Mach. 33, 399–422 (2005)

    Article  Google Scholar 

  187. Yoo, W.S., Kim, M.S., Mun, S.H., Sohn, J.H.: Large displacement of beam with base motion: flexible multibody simulations and experiments. Comput. Methods Appl. Mech. Eng. 195, 7036–7051 (2006)

    Article  MATH  Google Scholar 

  188. Yoo, W.S., Lee, J.H., Park, S.J., Sohn, J.H., Dmitrochenko, O., Pogorelov, D.: Large oscillations of a thin cantilever beam: physical experiments and simulation using the absolute nodal coordinate formulation. Nonlinear Dyn. 34, 3–29 (2003)

    Article  MATH  Google Scholar 

  189. Yoo, W.S., Lee, J.H., Park, S.J., Sohn, J.H., Pogolev, D., Dmitrochenko, O.: Large deflection analysis of a thin plate: computer simulation and experiment. Multibody Syst. Dyn. 11, 185–208 (2004)

    Article  MATH  Google Scholar 

  190. Yu, Z., Cui, Y.: New ANCF solid-beam element: relationship with Bézier volume and application on leaf spring modeling. Acta Mech. Sin. 37, 1318–1330 (2021). https://doi.org/10.1007/s10409-021-01089-9

    Article  MathSciNet  Google Scholar 

  191. Yu, H., Zhao, C., Lai, X.: Compliant assembly variation analysis of scalloped segment plates with a new irregular quadrilateral plate element via ANCF. J. Manuf. Sci. Eng. 140(9), 091006 (2018)

    Article  Google Scholar 

  192. Yu, L., Zhao, Z., Ren, G.: Multibody dynamics model of web guiding system with moving web. ASME J. Dyn. Syst. Meas. Control 132, 051004 (2010)

    Article  Google Scholar 

  193. Yu, L., Zhao, Z., Tang, J., Ren, G.: Integration of absolute nodal elements into multibody system. Nonlinear Dyn. 62, 931–943 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  194. Yu, D., Zhao, Q., Wu, T., Jiang, D., Yang, Y., Hong, J.: An integrated framework of surface accuracy prediction for clearance-affected extendible support structures with dimensional deviations and elastic deformations. Eng. Struct. 274, 115177 (2023). https://doi.org/10.1016/j.engstruct.2022.115177. ISSN 0141-0296

    Article  Google Scholar 

  195. Yu, H.D., Zhao, Z.J., Yang, D., Gao, C.: A new composite plate/plate element for stiffened plate structures via absolute nodal coordinate formulation. Compos. Struct. 247, 112431 (2020)

    Article  Google Scholar 

  196. Yuan, T., Liu, Z., Zhou, Y., Liu, J.: Dynamic modeling for foldable origami space membrane structure with contact-impact during deployment. Multibody Syst. Dyn. 50, 1–24 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  197. Yuan, T., Tang, L., Liu, Z., Liu, J.: Nonlinear dynamic formulation for flexible origami-based deployable structures considering self-contact and friction. Nonlinear Dyn. (2021). https://doi.org/10.1007/s11071-021-06860-y

    Article  Google Scholar 

  198. Zemljarič, B., Azbe, V.: Analytically derived matrix end-form elastic-forces equations for a low-order cable element using the absolute nodal coordinate formulation. Sound Vib. 446, 263–272 (2019)

    Article  Google Scholar 

  199. Zhang, P., Duan, M., Gao, Q., Ma, J., Wang, J., Sævik, S.: Efficiency improvement on the ANCF cable element by using the dot product form of curvature. Appl. Math. Model. (2021). https://doi.org/10.1016/j.apm.2021.09.027

    Article  Google Scholar 

  200. Zhang, N., Cao, G., Yang, F.: Dynamic analysis of balance rope under multiple constraints with friction. Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci. 235, 7412–7429 (2021)

    Article  Google Scholar 

  201. Zhang, C., Kang, Z., Ma, G., et al.: Mechanical modeling of deepwater flexible structures with large deformation based on absolute nodal coordinate formulation. J. Mar. Sci. Technol. 24, 1241–1255 (2019). https://doi.org/10.1007/s00773-018-00621-0

    Article  Google Scholar 

  202. Zhang, D., Luo, J.: A comparative study of geometrical curvature expressions for the large displacement analysis of spatial absolute nodal coordinate formulation Euler–Bernoulli beam motion. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 233(3), 631–641 (2019)

    Google Scholar 

  203. Zhang, P., Ma, J.M., Duan, M.L., Yuan, Y., Wang, J.J.: A high-precision curvature constrained Bernoulli-Euler planar beam element for geometrically nonlinear analysis. Appl. Math. Comput. 397, 125986 (2021)

    MathSciNet  MATH  Google Scholar 

  204. Zhang, Z., Mao, H., Hou, J., Wang, L., Wang, G.: Development and implementation of model smoothing method in the framework of absolute nodal coordinate formulation. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 235, 312–325 (2021)

    Google Scholar 

  205. Zhang, Z., Ren, W., Zhou, W.: Research status and prospect of plate elements in absolute nodal coordinate formulation. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. (2022). https://doi.org/10.1177/14644193221098866 May

    Article  Google Scholar 

  206. Zhang, S., Shi, W., Wu, Z., Zhang, T., Liu, C., Li, W.: Continuum damage dynamics of a large-scale flexible multibody system comprised of composite beams. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. (2022). https://doi.org/10.1177/14644193211063179 May

    Article  Google Scholar 

  207. Zhang, Y., Tian, Q., Chen, L., Yang, J.: Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods. Multibody Syst. Dyn. 21, 281–303 (2009)

    Article  MATH  Google Scholar 

  208. Zhang, Y., Wei, C., Zhao, Y., Tan, C., Liu, Y.: Adaptive ANCF method and its application in planar flexible cables. Acta Mech. Sin. 34, 199–213 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  209. Zhang, P., Yan, Z., Luo, K., Tian, Q.: Optimal design of electrode topology of dielectric elastomer actuators based on the parameterized level set method. Soft Robot. (2022). https://doi.org/10.1089/soro.2021.0169

    Article  Google Scholar 

  210. Zhang, W., Zhu, W., Zhang, S.: Deployment dynamics for a flexible solar array composed of composite-laminated plates. ASCE J. Aerosp. Eng. 33, 04020071 (2020)

    Article  Google Scholar 

  211. Zhao, J., Tian, Q., Hu, H.: Modal analysis of a rotating thin plate via absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 6(4), 041013 (2011)

    Article  Google Scholar 

  212. Shabana, A.A.: An Absolute Nodal Coordinate Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies. Technical Report. No. MBS96–1-UIC, Department of Mechanical and Industrial Engineering, University of Illinois at Chicago (1996)

  213. von Dombrowski, S.: Modellierung von Balken bei grossen Verformungen fur ein kraftreflektierendes Eingabegerat. Diploma Thesis, University Stuttgart and DLR (1997)

  214. Shabana, A.A.: Computational Continuum Mechanics, 3rd edn. Cambridge University Press, Cambridge (2018)

    Book  MATH  Google Scholar 

  215. Cook, R.D.: Concepts and Applications of Finite Element Analysis. Wiley, New York (1981)

    MATH  Google Scholar 

  216. Logan, D.L.: A First Course in the Finite Element Method, 6th edn. Cengage Learning, Boston (2017). Chap. 15

    Google Scholar 

  217. Zienkiewicz, O.C.: The Finite Element Method, 3rd edn. McGraw-Hill, New York (1977)

    MATH  Google Scholar 

  218. Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method, vol. 2. Solid Mechanics, vol. 5. Butterworth-Heinemann, Oxford (2000)

    MATH  Google Scholar 

  219. Farin, G.: Curves and Surfaces for CAGD, Fifth edn. A Practical Guide. Morgan Kaufmann, San Francisco (1999)

    Google Scholar 

  220. Gallier, J.: Geometric Methods and Applications: For Computer Science and Engineering. Springer, New York (2011)

    Book  MATH  Google Scholar 

  221. Piegl, L., Tiller, W.: The NURBS Book, 2nd edn. Springer, Berlin (1997)

    Book  MATH  Google Scholar 

  222. Rogers, D.F.: An Introduction to NURBS with Historical Perspective. Academic Press, San Diego (2001)

    Google Scholar 

  223. Irschik, H., Nader, M., Stangl, M., von Garssen, H.G.: A floating frame-of-reference formulation for deformable rotors using the properties of free elastic vibration modes. In: Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, ASME, San Diego (2009)

    Google Scholar 

  224. Sherif, K., Witteveen, W.: Deformation mode selection and orthonormalization for an efficient simulation of the rolling contact problem. In: Dynamics of Coupled Structures, vol. 1, pp. 125–134. Springer, Cham (2014)

    Chapter  Google Scholar 

  225. Bonet, J., Wood, R.D.: Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  226. Bower, A.F.: Applied Mechanics of Solids, 1st edn. CRC Press, Boca Raton (2009)

    Book  Google Scholar 

  227. Ogden, R.W.: Non-Linear Elastic Deformations. Dover, Mineola (1984)

    MATH  Google Scholar 

  228. Spencer, A.J.M.: Continuum Mechanics. Longman, London (1980)

    MATH  Google Scholar 

  229. Shabana, A.A.: Integration of computer-aided design and analysis (I-CAD-A): application to multibody vehicle systems. Int. J. Veh. Perform. 5, 300–327 (2019)

    Article  Google Scholar 

  230. Yakoub, R.Y., Shabana, A.A.: Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. ASME J. Mech. Des. 123(4), 614–621 (2001)

    Article  Google Scholar 

  231. Shabana, A.A., Ling, H.: Noncommutativity of finite rotations and definitions of curvature and torsion. ASME J. Comput. Nonlinear Dyn. 14, 091005 (2019)

    Article  Google Scholar 

  232. Boresi, A.P., Chong, K.P.: Elasticity in Engineering Mechanics, 2nd edn. Wiley, New York (2000)

    MATH  Google Scholar 

  233. Dym, C.L., Shames, I.H.: Solid Mechanics: A Variational Approach. McGraw-Hill, New York (1973)

    MATH  Google Scholar 

  234. Fung, Y.C.: First Course in Continuum Mechanics, 2nd edn. Prentice Hall, Englewood Cliffs (1977)

    Google Scholar 

  235. Singer, F.L.: Strength of Materials, 2nd edn. Harper & Row, New York (1962)

    Google Scholar 

  236. Shabana, A.A.: Definition of ANCF finite elements. ASME J. Comput. Nonlinear Dyn. 10, 054506 (2015) https://doi.org/10.1115/1.4030369

    Article  Google Scholar 

  237. Eldeeb, A.E., Zhang, D., Shabana, A.A.: Cross-section deformation, geometric stiffening, and locking in the nonlinear vibration analysis of beams. Nonlinear Dyn. 108, 1425–1445 (2022)

    Article  Google Scholar 

  238. Pappalardo, C.M., Wallin, M., Shabana, A.A.: A new ANCF/CRBF fully parameterized plate finite element. ASME J. Comput. Nonlinear Dyn. 12, 031008 (2017)

    Article  Google Scholar 

  239. Zheng, Y., Shabana, A.A.: A two-dimensional shear deformable ANCF consistent rotation-based formulation beam element. Nonlinear Dyn. 87, 1031–1043 (2017)

    Article  Google Scholar 

  240. Kulkarni, S., Shabana, A.A.: Spatial ANCF/CRBF beam elements. Acta Mech. 230, 929–952 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  241. Shabana, A.A., Xu, L.: Rotation-based finite elements: reference-configuration geometry and motion description. Acta Mech. Sin. 37, 105–126 (2021)

    Article  MathSciNet  Google Scholar 

  242. Shabana, A.A., Elbakly, M., Zhang, D.: Constrained large-displacement thermal analysis. ASME J. Comput. Nonlinear Dyn. (2022). https://doi.org/10.1115/1.4056182

    Article  Google Scholar 

  243. Shabana, A.A.: ANCF tire assembly model for multibody system applications. ASME J. Comput. Nonlinear Dyn. 10, 024504 (2015)

    Article  Google Scholar 

  244. Shabana, A.A., Eldeeb, A.E.: Motion and shape control of soft robots and materials. Nonlinear Dyn. 104, 165–189 (2021)

    Article  Google Scholar 

  245. Shabana, A.A., Wang, G.: Durability analysis and implementation of the floating frame of reference formulation. IMechE J. Multibody Dyn. 232, 295–313 (2018)

    Google Scholar 

  246. Shabana, A.: Dynamics of Multibody Systems, Fifth edn. Cambridge University Press, New York (2020)

    Book  MATH  Google Scholar 

  247. Atkinson, K.E.: An Introduction to Numerical Analysis. Wiley, New York (1978)

    MATH  Google Scholar 

  248. Carnahan, B., Luther, H.A., Wilkes, J.O.: Applied Numerical Methods. Wiley, New York (1969)

    MATH  Google Scholar 

  249. Hamed, A.M., Shabana, A.A., Jayakumar, P., Letherwood, M.D.: Non-structural geometric discontinuities in finite element/multibody system analysis. Nonlinear Dyn. 66, 809–824 (2011)

    Article  Google Scholar 

  250. Recuero, M.A., Aceituno, J.F., Escalona, J.L., Shabana, A.A.: A nonlinear approach for modeling rail flexibility using the absolute nodal coordinate formulation. Nonlinear Dyn. 83, 463–481 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  251. Grossi, E., Shabana, A.A.: Analysis of high-frequency ANCF modes: Navier-Stokes physical damping and implicit numerical integration. Acta Mech. 230, 2581–2605 (2019)

    Article  MathSciNet  Google Scholar 

  252. Contreras, U., Li, G.B., Foster, C.D., Shabana, A.A., Jayakumar, P., Letherwood, M.: Soil models and vehicle system dynamics. Appl. Mech. Rev. 65(4), 040802 (2013). https://doi.org/10.1115/1.4024759

    Article  Google Scholar 

  253. Shabana, A.A., Patel, M.: Coupling between shear and bending in the analysis of beam problems: planar case. Sound Vib. 419, 510–525 (2018)

    Article  Google Scholar 

  254. Tang, L., Liu, J.: Modeling and analysis of sliding joints with clearances in flexible multibody systems. Nonlinear Dyn. 94, 2423–2440 (2018)

    Article  Google Scholar 

  255. Sun, D., Liu, C., Hu, H.: Dynamic computation of 2D segment-to-segment frictionless contact for a flexible multibody system subject to large deformation. Mech. Mach. Theory 140, 350–376 (2019)

    Article  Google Scholar 

  256. Sun, D., Liu, C., Hu, H.: Dynamic computation of 2D segment-to-segment frictional contact for a flexible multibody system subject to large deformations. Mech. Mach. Theory 158, 104197 (2021)

    Article  Google Scholar 

  257. Cui, Y., Yu, Z., Lan, P.: A novel method of thermo-mechanical coupled analysis based on the unified description. Mech. Mach. Theory 134, 376–392 (2019)

    Article  Google Scholar 

  258. Shen, Z., Hu, G.: Thermally induced vibrations of solar panel and their coupling with satellite. Int. J. Appl. Mech. 05, 1350031 (2013)

    Article  Google Scholar 

  259. Liu, C., Tian, Q., Yan, D., Hu, H.: 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  MathSciNet  MATH  Google Scholar 

  260. Liu, C., Tian, Q., Hu, H.: New spatial curved beam and cylindrical shell elements of gradient-deficient absolute nodal coordinate formulation. Nonlinear Dyn. 70, 1903–1918 (2012)

    Article  MathSciNet  Google Scholar 

  261. Ren, H.: Fast and robust full-quadrature triangular elements for thin plates/shells with large deformations and large rotations. ASME J. Comput. Nonlinear Dyn. 10, 051018 (2015)

    Article  Google Scholar 

  262. Ren, H.: A simple absolute nodal coordinate formulation for thin beams with large deformations and large rotations. ASME J. Comput. Nonlinear Dyn. 10(6), 061005 (2015).

    Article  Google Scholar 

  263. Li, Y., Wang, C., Huang, W.: Rigid-flexible-thermal analysis of planar composite solar array with clearance joint considering torsional spring, latch mechanism and attitude controller. Nonlinear Dyn. 96, 2031–2053 (2019)

    Article  Google Scholar 

  264. Shen, Z., Hu, G.: Thermally induced dynamics of a spinning spacecraft with an axial flexible boom. J. Spacecr. Rockets 52(5), 1503–1508 (2015)

    Article  Google Scholar 

  265. Li, H., Zhong, H.: Spatial weak form quadrature beam elements based on absolute nodal coordinate formulation. Mech. Mach. Theory 181, 105192 (2023). https://doi.org/10.1016/j.mechmachtheory.2022.105192. ISSN 0094-114X

    Article  Google Scholar 

  266. Zhao, C.H., Bao, K.W., Tao, Y.L.: Transversally higher-order interpolating polynomials for the two-dimensional shear deformable ANCF beam elements based on common coefficients. Multibody Syst. Dyn. 51, 475–495 (2021). https://doi.org/10.1007/s11044-020-09768-4

    Article  MathSciNet  MATH  Google Scholar 

  267. Taylor, M., Serban, R., Negrut, D.: Implementation implications on the performance of ANCF simulations. Int. J. Non-Linear Mech. 149, 104328 (2022). https://doi.org/10.1016/j.ijnonlinmec.2022.104328 ISSN 0020-7462

    Article  Google Scholar 

  268. Taylor, M., Serban, R., Negrut, D.: An efficiency comparison of different ANCF implementations. Int. J. Non-Linear Mech. 149, 104308 (2023)

    Article  Google Scholar 

  269. Obrezkov, L.P., Finni, T., Matikainen, M.K.: Modeling of the Achilles subtendons and their interactions in a framework of the absolute nodal coordinate formulation. Materials 15, 8906 (2022). https://doi.org/10.3390/ma15248906

    Article  Google Scholar 

  270. Dong, S., Otsuka, K., Makihara, K.: Hamiltonian formulation with reduced variables for flexible multibody systems under linear constraints: theory and experiment. J. Sound Vib. 547, 117535 (2023). https://doi.org/10.1016/j.jsv.2022.117535. ISSN 0022-460X

    Article  Google Scholar 

  271. Wu, M., Tan, S., Xu, H., Li, J.: Absolute nodal coordinate formulation-based shape sensing approach for large deformation: plane beam. AIAA J. (2023). https://doi.org/10.2514/1.J062266

    Article  Google Scholar 

  272. Zhou, K., Yi, H.R., Dai, H.L., Yan, H., Guo, Z.L., Xiong, F.R., Ni, Q., Hagedorn, P., Wang, L.: Nonlinear analysis of L-shaped pipe conveying fluid with the aid of absolute nodal coordinate formulation. Nonlinear Dyn. 107(1), 391–412 (2021)

    Article  Google Scholar 

  273. Yuan, J.R., Ding, H.: Dynamic model of curved pipe conveying fluid based on the absolute nodal coordinate formulation. Int. J. Mech. Sci. 232, 107625 (2022)

    Article  Google Scholar 

  274. Xu, Q., Liu, J.: Dynamic research on nonlinear locomotion of inchworm-inspired soft crawling robot. Soft Robot. (2023). https://doi.org/10.1089/soro.2022.0002

    Article  Google Scholar 

  275. Luo, S., Fan, Y., Cui, N.: Application of absolute nodal coordinate formulation in calculation of space elevator system. Appl. Sci. 11, 11576 (2021). https://doi.org/10.3390/app112311576

    Article  Google Scholar 

  276. Malik, S., Solaija, T.: Static and dynamic analysis of absolute nodal coordinate formulation planar elements. In: 2020 17th International Bhurban Conference on Applied Sciences and Technology (IBCAST), Islamabad, Pakistan, pp. 167–173 (2020). https://doi.org/10.1109/IBCAST47879.2020.9044494

    Chapter  Google Scholar 

  277. Kang, J.H., Yoo, W.S., Kim, H.R., Lee, J.W., Jang, J.S., Oh, J.Y., Kim, K.W.: Definition of non-dimensional strain energy for large deformable flexible beam in absolute nodal coordinate formulation. Trans. Korean Soc. Mech. Eng. A 42, 643–648 (2018). https://doi.org/10.3795/ksme-a.2018.42.7.643

    Article  Google Scholar 

  278. Xiao, H., Hedegaard, B.D.: Absolute nodal coordinate formulation for dynamic analysis of reinforced concrete structures. Structures 33, 201–213 (2021). https://doi.org/10.1016/j.istruc.2021.04.014

    Article  Google Scholar 

  279. Yang, M.S., Lee, J.W., Kang, J.H., Lee, S.Y., Kim, K.W.: Definition of non-dimensional strain energy for thin plate in the absolute nodal coordinate formulation. Trans. Korean Soc. Mech. Eng. A 45, 1085–1090 (2021). https://doi.org/10.3795/ksme-a.2021.45.12.1085

    Article  Google Scholar 

  280. Yu, H.D., Zhao, C.Z., Zheng, B., Wang, H.: A new higher-order locking-free beam element based on the absolute nodal coordinate formulation, Proceedings of the institution of mechanical engineers, part C. J. Mech. Eng. Sci. 232(19), 3410–3423 (2018)

    Article  Google Scholar 

  281. Li, L., Chen, Y.Z., Zhang, D.G., Liao, W.H.: Large deformation and vibration analysis of microbeams by absolute nodal coordinate formulation. Int. J. Struct. Stab. Dyn. 19(04), 1950049 (2019)

    Article  MathSciNet  Google Scholar 

  282. Gu, Y., Yu, Z., Lan, P., Lu, N.: Fractional derivative viscosity of ANCF cable element. Actuators 12, 64 (2023). https://doi.org/10.3390/act12020064

    Article  Google Scholar 

  283. Du, X., Du, J., Bao, H., Chen, X., Sun, G., Wu, X.: Dynamic analysis of the deployment for mesh reflector antennas driven with variable length cables. ASME J. Comput. Nonlinear Dyn. 14(11), 111006 (2019). https://doi.org/10.1115/1.4044315

    Article  Google Scholar 

  284. Li, P., Liu, C., Tian, Q., Hu, H., Song, Y.: Dynamics of a deployable mesh reflector of satellite antenna: parallel computation and deployment simulation. ASME J. Comput. Nonlinear Dyn. 11(6), 061005 (2016). https://doi.org/10.1115/1.4033657

    Article  Google Scholar 

  285. Li, P., Liu, C., Tian, Q., Hu, H., Song, Y.: Dynamics of a deployable mesh reflector of satellite antenna: form-finding and modal analysis. ASME J. Comput. Nonlinear Dyn. 11(4), 041017 (2016). https://doi.org/10.1115/1.4033440

    Article  Google Scholar 

  286. 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

    Article  MathSciNet  Google Scholar 

  287. Kim, H.W., Yoo, W.S., Sohn, J.H.: Experimental validation of two damping force models for the ANCF. In: Proceedings of the Asme International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Las Vegas, NV, USA, 4–7 September 2007, vol. 5, pp. 1025–1032 (2007)

    Google Scholar 

  288. Yu, H., Zhao, C., Zheng, H.: A higher-order variable cross-section viscoelastic beam element via ANCF for kinematic and dynamic analyses of two-link flexible manipulators. Int. J. Appl. Mech. 9, 1750116 (2017)

    Article  Google Scholar 

  289. Tian, Q., Zhang, P., Luo, K.: Dynamics of soft mechanical systems actuated by dielectric elastomers. Mech. Syst. Signal Process. 151, 107392 (2021)

    Article  Google Scholar 

  290. Lan, P., Cui, Y., Yu, Z.: A novel absolute nodal coordinate formulation thin plate tire model with fractional derivative viscosity and surface integral-based contact algorithm. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 233, 583–597 (2018)

    Google Scholar 

  291. Westin, C., Irani, R.A.: Modeling dynamic Cable–Sheave contact and detachment during towing operations. Mar. Struct. 77, 102960 (2021). https://doi.org/10.1016/j.marstruc.2021.102960.

    Article  Google Scholar 

  292. Westin, C., Irani, R.A.: Efficient semi-implicit numerical integration of ANCF and ALE-ANCF Cable models with holonomic constraints. Comput. Mech. (2023). https://doi.org/10.1007/s00466-022-02264-w

    Article  MathSciNet  MATH  Google Scholar 

  293. Westin, C., Irani, R.A.: Cable-Pulley interaction with dynamic wrap angle using the absolute nodal coordinate formulation. In: Proceedings of the 4th International Conference of Control, Dynamic Systems, and Robotics (2017). https://doi.org/10.11159/cdsr17.133

    Chapter  Google Scholar 

  294. Sun, J., Tian, Q., Hu, H., et al.: Topology optimization of a flexible multibody system with variable-length bodies described by ALE-ANCF. Nonlinear Dyn. 93(2), 413–441 (2018). https://doi.org/10.1007/s11071-018-4201-6

    Article  MATH  Google Scholar 

  295. Yu, X., You, B., Wei, C., Gu, H., Liu, Z.: Investigation on the improved absolute nodal coordinate formulation for variable cross-section beam with large aspect ratio. Mech. Adv. Mat. Struct. (2023). https://doi.org/10.1080/15376494.2023.2169795

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Science Foundation (Projects # 1852510).

Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL, 60607, USA

    Ahmed A. Shabana

Authors
  1. Ahmed A. Shabana
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.A. Shabana prepared and wrote this paper.

Corresponding author

Correspondence to Ahmed A. Shabana.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shabana, A.A. An overview of the ANCF approach, justifications for its use, implementation issues, and future research directions. Multibody Syst Dyn 58, 433–477 (2023). https://doi.org/10.1007/s11044-023-09890-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-023-09890-z

Keywords

Search

Navigation