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Dynamic modeling of a sliding ring on an elastic rod with incremental potential formulation (2208.01238v4)

Published 2 Aug 2022 in cs.GR

Abstract: Mechanical interactions between rigid rings and flexible cables find broad application in both daily life (hanging clothes) and engineering systems (closing a tether-net). A reduced-order method for the dynamic analysis of sliding rings on a deformable one-dimensional (1D) rod-like object is proposed. In contrast to the conventional approach of discretizing joint rings into multiple nodes and edges for contact detection and numerical simulation, a single point is used to reduce the order of the model. To ensure that the sliding ring and flexible rod do not deviate from their desired positions, a new barrier function is formulated using the incremental potential theory. Subsequently, the interaction between tangent frictional forces is obtained through a delayed dissipative approach. The proposed barrier functional and the associated frictional functional are C2 continuous, hence the nonlinear elastodynamic system can be solved variationally by an implicit time-stepping scheme. The numerical framework is initially applied to simple examples where the analytical solutions are available for validation. Then, multiple complex practical engineering examples are considered to showcase the effectiveness of the proposed method. The simplified ring-to-rod interaction model has the capacity to enhance the realism of visual effects in image animations, while simultaneously facilitating the optimization of designs for space debris removal systems.

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References (64)
  1. “On the nonlinear oscillation of an axially moving string”. Journal of Applied Mechanics, 33(2), pp. 463–464.
  2. “On the dynamics of an axially moving beam”. Journal of the Franklin Institute, 297(3), pp. 201–220.
  3. “Non-linear vibration of a traveling tensioned beam”. International Journal of Non-Linear Mechanics, 27(3), pp. 503–517.
  4. “Ale formulation for dynamic modeling and simulation of cable-driven mechanisms considering stick–slip frictions”. Mechanical Systems and Signal Processing, 168, p. 108633.
  5. “Modeling the flexural dynamic behavior of axially moving continua by using the finite element method”. Journal of Vibration and Acoustics, 136(1).
  6. “From multiscale modeling to design of synchronization mechanisms in mesh antennas”. Acta Astronautica, 159, pp. 156–165.
  7. “Flexible belt hanging on two pulleys: contact problem at non-material kinematic description”. International Journal of Solids and Structures, 168, pp. 183–193.
  8. “Dynamic analysis of a hyper-redundant space manipulator with a complex rope network”. Aerospace Science and Technology, 100, p. 105768.
  9. “Kinematics, dynamics, and control of a cable-driven hyper-redundant manipulator”. IEEE/ASME Transactions on Mechatronics, 23(4), pp. 1693–1704.
  10. “Dynamic analysis of a tethered satellite system for space debris capture”. Nonlinear Dynamics, 94(4), pp. 2391–2408.
  11. “Dynamical modelling and control of space tethers: a review of space tether research”. Nonlinear Dynamics, 77(4), pp. 1077–1099.
  12. “On the simulation of tether-nets for space debris capture with vortex dynamics”. Acta Astronautica, 123, pp. 91–102.
  13. “Simulation of tether-nets for capture of space debris and small asteroids”. Acta Astronautica, 155, pp. 448–461.
  14. “Contact dynamic models of space debris capturing using a net”. Acta Astronautica, 158, pp. 198–205.
  15. “Dynamic computation of a tether-net system capturing a space target via discrete elastic rods and an energy-conserving integrator”. Acta Astronautica, 186, pp. 118–134.
  16. “Experiments and simulation of a net closing mechanism for tether-net capture of space debris”. Acta Astronautica, 139, pp. 332–343.
  17. “Simulation and tension control of a tether-actuated closing mechanism for net-based capture of space debris”. Acta Astronautica, 174, pp. 347–358.
  18. “Nonlinear dynamic modeling of a tether-net system for space debris capture”. Nonlinear Dynamics.
  19. “Contact dynamic analysis of tether-net system for space debris capture using incremental potential formulation”. Advances in Space Research.
  20. “Numerical simulation and behavior prediction of a space net system throughout the capture process: Spread, contact, and close”. International Journal of Mechanical System Dynamics, 3(3), pp. 265–273.
  21. The finite element method: linear static and dynamic finite element analysis. Courier Corporation.
  22. “Geometrically exact beam finite element formulated on the special euclidean group se (3)”. Computer Methods in Applied Mechanics and Engineering, 268, pp. 451–474.
  23. “Experimentally validated geometrically exact model for extreme nonlinear motions of cantilevers”. Nonlinear Dynamics, 107(1), pp. 457–475.
  24. “An absolute nodal coordinate formulation for the large rotation and deformation analysis of flexible bodies”. Technical Report, Department of Mechanical Engineering, University of Illinois at Chicago.
  25. “Three dimensional absolute nodal coordinate formulation for beam elements: theory”. J. Mech. Des., 123(4), pp. 606–613.
  26. “Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications”. J. Mech. Des., 123(4), pp. 614–621.
  27. “Isogeometric collocation methods for the reissner–mindlin plate problem”. Computer Methods in Applied Mechanics and Engineering, 284, pp. 489–507.
  28. “On the numerical modeling of sliding beams: a comparison of different approaches”. Journal of Sound and Vibration, 408, pp. 270–290.
  29. “Configurational forces and geometrically exact formulation of sliding beams in non-material domains”. Computer Methods in Applied Mechanics and Engineering, 395, p. 115063.
  30. “The equations of lagrange written for a non-material volume”. Acta Mechanica, 153(3), pp. 231–248.
  31. “The application of lagrange equations to mechanical systems with mass explicitly dependent on position”. J. Appl. Mech., 70(5), pp. 751–756.
  32. “General sliding-beam formulation: A non-material description for analysis of sliding structures and axially moving beams”. Journal of Sound and Vibration, 480, p. 115341.
  33. “Extended hamilton’s principle applied to geometrically exact kirchhoff sliding rods”. Journal of Sound and Vibration, 516, p. 116511.
  34. “Numerical integration algorithms and constraint formulations for an ale-ancf cable element”. Mechanism and Machine Theory, 170, p. 104659.
  35. “Sliding contact conditions using the master–slave approach with application on geometrically non-linear beams”. International journal of solids and structures, 41(24-25), pp. 6963–6992.
  36. “The development of a sliding joint for very flexible multibody dynamics using absolute nodal coordinate formulation”. Multibody System Dynamics, 20(3), pp. 223–237.
  37. “A modeling of sliding joint on one-dimensional flexible medium”. Multibody System Dynamics, 26(1), pp. 91–106.
  38. “Energy–momentum integration and analysis for sliding contact coupling dynamics in large flexible multibody system”. Nonlinear Dynamics.
  39. “Dynamic simulation of articulated soft robots”. Nature communications, 11(1), pp. 1–9.
  40. “Propulsion and instability of a flexible helical rod rotating in a viscous fluid”. Physical review letters, 115(16), p. 168101.
  41. “Discrete differential geometry: an applied introduction”. ACM SIGGRAPH Course, 7, pp. 1–139.
  42. “Discrete elastic rods”. In ACM transactions on graphics (TOG), Vol. 27, ACM, p. 63.
  43. “Discrete viscous threads”. In ACM Transactions on Graphics (TOG), Vol. 29, ACM, p. 116.
  44. “Geometrically exact simulation of inextensible ribbon”. In Computer Graphics Forum, Vol. 34, Wiley Online Library, pp. 145–154.
  45. “Snap-through behaviors of a pre-deformed ribbon under midpoint loadings”. International Journal of Solids and Structures, p. 111184.
  46. “Large steps in cloth simulation”. In Proceedings of the 25th annual conference on Computer graphics and interactive techniques, ACM, pp. 43–54.
  47. “Shear induced supercritical pitchfork bifurcation of pre-buckled bands, from narrow strips to wide plates”. Journal of the Mechanics and Physics of Solids, 145, p. 104168.
  48. “X-shells: A new class of deployable beam structures”. ACM Transactions on Graphics (TOG), 38(4), p. 83.
  49. “Numerical method for direct solution to form-finding problem in convex gridshell”. Journal of Applied Mechanics, 88(2), p. 021012.
  50. “Coiling of elastic rods on rigid substrates”. Proceedings of the National Academy of Sciences, 111(41), pp. 14663–14668.
  51. “Physical validation of simulators in computer graphics: A new framework dedicated to slender elastic structures and frictional contact”. ACM Transactions on Graphics.
  52. “Form finding in elastic gridshells”. Proceedings of the National Academy of Sciences, 115(1), pp. 75–80.
  53. “Incremental potential contact: intersection-and inversion-free, large-deformation dynamics.”. ACM Trans. Graph., 39(4), p. 49.
  54. “Codimensional incremental potential contact”. arXiv preprint arXiv:2012.04457.
  55. “Implicit contact model for discrete elastic rods in knot tying”. Journal of Applied Mechanics, 88(5).
  56. “A fully implicit method for robust frictional contact handling in elastic rods”. arXiv preprint arXiv:2205.10309.
  57. “Modeling of magnetic cilia carpet robots using discrete differential geometry formulation”. Extreme Mechanics Letters, 59, p. 101967.
  58. “On unilateral constraints, friction and plasticity”. In New variational techniques in mathematical physics. Springer, pp. 171–322.
  59. “The shape of a long leaf”. Proceedings of the National Academy of Sciences, 106(52), pp. 22049–22054.
  60. “On the growth and form of the gut”. Nature, 476(7358), p. 57.
  61. “Newmark-beta method in discrete elastic rods algorithm to avoid energy dissipation”. Journal of Applied Mechanics, 86(8).
  62. “Static analysis of elastic cable structures under mechanical load using discrete catenary theory”. Fundamental Research, -(-), pp. –.
  63. “Research problems in clothing simulation”. Computer-aided design, 37(6), pp. 585–592.
  64. “Simulation of clothing with folds and wrinkles”. In ACM SIGGRAPH 2005 Courses, ACM, p. 3.

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