DOI QR코드

DOI QR Code

Non-linear rheology of tension structural element under single and variable loading history Part I: Theoretical derivations

  • Kmet, S. (Faculty of Civil Engineering, Technical University of Kosice)
  • 투고 : 2003.07.16
  • 심사 : 2004.06.24
  • 발행 : 2004.11.25

초록

The present paper concerns the macroscopic overall description of rheologic properties for steel wire and synthetic fibre cables under variable loading actions according to non-linear creep and/or relaxation theory. The general constitutive equations of non-linear creep and/or relaxation of tension elements - cables under one-step and the variable stress or strain inputs using the product and two types of additive approximations of the kernel functions are presented in the paper. The derived non-linear constitutive equations describe a non-linear rheologic behaviour of the cables for a variable stress or strain history using the kernel functions determined only by one-step - constant creep or relaxation tests. The developed constitutive equations enable to simulate and to predict in a general way non-linear rheologic behaviour of the cables under an arbitrary loading or straining history. The derived constitutive equations can be used for the various tension structural elements with the non-linear rheologic properties under uniaxial variable stressing or straining.

키워드

참고문헌

  1. Anderssen, R.S. and Loy, R.J. (2002), "Rheological implications of completely monotone fading memory", Journal of Rheology, 46(6), 1459-1472. https://doi.org/10.1122/1.1514203
  2. Banfield, S.J. and Flory, J.F. (1995), "Computer modelling of large high-performance fiber rope properties", Proc. of Oceans '95, San Diego.
  3. Banfield, S.J., Hearle, J.W.S., Leech, C.M., Tebay, R. and Lawrence, C.A. (2003), "Fibre Rope Modeller (FRM): A CAD program for the performance prediction of advanced cords and ropes under complex loading environments", http://www.tensiontech.com/papers/papers/FRM_2/rope_CAD.pdf, Tension Technology International.
  4. Beijer, J.G.J. and Spoormaker, J.L. (2002), "Solution strategies for FEM analysis with nonlinear viscoelastic polymers", Comput. Struct., 80(14-15), 1213-1229. https://doi.org/10.1016/S0045-7949(02)00089-5
  5. Bonet, J. (2001), "Large strain viscoelastic constitutive models", Int. J. Solids Struct., 38(17), 2953-2968. https://doi.org/10.1016/S0020-7683(00)00215-8
  6. Cheung, J.B. (1970), "Nonlinear viscoelastic stress analysis of blood vessels", Ph.D. Thesis, University of Minnesota.
  7. Conway, T.A. and Costello, G.A. (1993), "Viscoelastic response of a simple strand", Int. J. Solids Struct., 30(4), 553-567. https://doi.org/10.1016/0020-7683(93)90187-C
  8. Costello, G.A. (1997), Theory of Wire Rope, 2nd ed. New York: Springer-Verlag.
  9. Drozdov, A.D. (1998), "A model for the nonlinear viscoelastic response in polymers at finite strains", Int. J. Solids Struct., 35(18), 2315-2347. https://doi.org/10.1016/S0020-7683(97)00184-4
  10. Evans, J.J., Ridge, I.M. and Chaplin, C.R. (2001), "Wire strain variations in normal and overloaded ropes in tension-tension fatigue and their effect on endurance", The Journal of Strain Analysis for Engineering Design, 36(2), 219-230. https://doi.org/10.1243/0309324011512766
  11. Fafard, M., Boudjelal, M.T., Bissonnette, B. and Cloutier, A. (2001), "Three-dimensional viscoelastic model with nonconstant coefficients", J. Eng. Mech., 127(8), 808-815. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:8(808)
  12. Findley, W.N. and Onaran, K. (1968), "Product form of kernel functions for non-linear viscoelasticity of PVC under constant rate stressing", Trans. Society of Rheology, 12(2), 217-231. https://doi.org/10.1122/1.549107
  13. Findley, W.N., Lai, J.S. and Onaran, K. (1976), Creep and Relaxation of Nonlinear Viscoelastic Materials, Applied Mathematics and Mechanics, North − Holland Publishing Company, New York.
  14. Frank, G.J. and Brockman, R.A. (2001), "A viscoelastic − viscoplastic constitutive model for glassy polymers", Int. J. Solids Struct., 38(30-31), 5149-5164. https://doi.org/10.1016/S0020-7683(00)00339-5
  15. Gottenberg, W.G., Bird, J.O. and Agrawall, G.L. (1969), "An experimental study of a non-linear viscoelastic solid in uniaxial tension", Trans. ASME, J. Appl. Mech., 36(3), 558-572. https://doi.org/10.1115/1.3564717
  16. Green, A.E., Rivlin, R.S. and Spencer, A.J.M. (1959), "The mechanics of nonlinear materials with memory, Part II", Archive for Rational Mechanics and Analysis, 3(1), 82-96. https://doi.org/10.1007/BF00284166
  17. Green, A.E. and Rivlin, R.S. (1960), "The mechanics of nonlinear materials with memory, Part III", Archive for Rational Mechanics and Analysis, 4(2), 387-398.
  18. Guimaraes, G.B. and Burgoyne, C.J. (1992), "Creep behaviour of a parallel-lay aramid rope", J. Mater. Sci., 27(8), 2473-2489. https://doi.org/10.1007/BF01105061
  19. Haitian, Y. and Yan, L. (2003), "A combined approach of EFGM and precise algorithm in time domain solving viscoelasticity problems", Int. J. Solids Struct., 40(3), 701-714. https://doi.org/10.1016/S0020-7683(02)00614-5
  20. Hartmann, S. (2002), "Computation in finite-strain viscoelasticity: Finite elements based on the interpretation as differential − Algebraic equations", Comput. Meth. Appl. Mech. Eng., 191(13-14), 1439-1470. https://doi.org/10.1016/S0045-7825(01)00332-2
  21. Huang, X.L. and Vinogradov, O.G. (1996), "Extension of a cable in the presence of dry friction", Struct. Eng. Mech., An Int. J., 4(3), 313-329. https://doi.org/10.12989/sem.1996.4.3.313
  22. Husiar, B. and Switka, R. (1986), "Creep and relaxation in net structures", Proc. of the IASS Symposium on Membrane Structures and Space Frames, Osaka.
  23. Jiang, W.G., Henshall, J.L. and Walton, J.M. (2000), "A concise finite element model for three-layered straight wire rope strand", Int. J. Mech. Sci., 42(1), 63-86. https://doi.org/10.1016/S0020-7403(98)00111-8
  24. Jung, G.D. and Youn, S.K. (1999), "A nonlinear viscoelastic constitutive model of solid propellant", Int. J. Solids Struct., 36(25), 3755-3777. https://doi.org/10.1016/S0020-7683(98)00175-9
  25. Kaliske, M., Nasdala, L. and Rothert, H. (2001), "On damage modelling for elastic and viscoelastic materials at large strain", Comput. Struct., 79(22-25), 2133-2141. https://doi.org/10.1016/S0045-7949(01)00061-X
  26. Kmet, S. (1989), "Cable strain as a time and stress function under nonlinear creep", J. Civil Eng., 37(10), 534-540.
  27. Kmet, S. (1994), "Rheology of prestressed cable structures", Proc. of the Int. Conf. on Civil and Structural Engineering Computing, Civil-Comp 1994, Advanced in Finite Element Techniques, Edinburgh.
  28. Kmet, S. and Holickova, L. (2000), "Creep of high-strength initially stretched steel ropes", Acta Mechanica Slovaca, 4(3), 47-56.
  29. Kwon, Y. and Soo Cho, K. (2001), "Time-strain nonseparability in viscoelastic constitutive equations", Journal of Rheology, 45(6), 1441-1452. https://doi.org/10.1122/1.1413505
  30. Labrosse, M., Nawrocki, A. and Conway, T. (2000), "Frictional dissipation in axially loaded simple straight strands", J. Eng. Mech., 126(6), 641-646. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:6(641)
  31. Leech, C.M. (1987), "Theoretical and numerical methods for the modelling of synthetic ropes", Communications in Applied Numerical Methods, 3(2), 214-223.
  32. Leech, C.M., Hearle, J.W.S., Overington, M.S. and Banfield, S.J. (1993), "Modelling tension and torque properties of fibre ropes and splices", Proc. of the Third (1993) Int. Offshore and Polar Engineering Conf., Singapore.
  33. Leech, C.M. (2002), "The modelling of friction in polymer fibre ropes", Int. J. Mech. Sci., 44(3), 621-643. https://doi.org/10.1016/S0020-7403(01)00095-9
  34. Lefik, M. and Schrefler, B.A. (2002), "Artificial neural network for parameter identifications for an elasto-plastic model of superconducting cable under cyclic loading", Comput. Struct., 80(22), 1699-1713. https://doi.org/10.1016/S0045-7949(02)00162-1
  35. Meo, S., Boukamel, A. and Debordes, O. (2002), "Analysis of a thermoviscoelastic model in large strain", Comput. Struct., 80(27-30), 2085-2098. https://doi.org/10.1016/S0045-7949(02)00246-8
  36. Meskuita, A.D. and Coda, H.B. (2003), "New methodology for treatment of two dimensional viscoelastic coupling problems", Comput. Meth. Appl. Mech. Eng., 192(16-18), 1911-1927. https://doi.org/10.1016/S0045-7825(02)00598-4
  37. Nakada, O. (1960), "Theory of non-linear responses", Journal of the Physical Society of Japan, 15, 2280-2296. https://doi.org/10.1143/JPSJ.15.2280
  38. Nakai, M., Sato, S., Aida, T. and Tomioka, H. (1975), "On the creep and the relaxation of spiral ropes", Bulletin of the JSME, 18(125), 1308-1314. https://doi.org/10.1299/jsme1958.18.1308
  39. Nawrocki, A. and Labrosse, M. (2000), "A finite element model for simple straight wire rope strands", Comput. Struct., 77(4), 345-359. https://doi.org/10.1016/S0045-7949(00)00026-2
  40. Onaran, K. and Findley, W.N. (1965), "Combined stress creep experiments on a nonlinear viscoelastic material to determine the kernel functions for a multiple integral representation of creep", Transactions of the Society of Rheology, 9(4), 299-317. https://doi.org/10.1122/1.549002
  41. Park, S.W. and Schapery, R.A. (1999), "Methods of interconversion between linear viscoelastic material functions. Part I − A numerical method based on Prony series", Int. J. Solids Struct., 36(11), 1653-1675. https://doi.org/10.1016/S0020-7683(98)00055-9
  42. Patlashenko, I., Givoli, D. and Barbone, P. (2001), "Time-stepping schemes for systems of Volterra integrodifferential equations", Comput. Meth. Appl. Mech. Eng., 190(43-44), 5691-5718. https://doi.org/10.1016/S0045-7825(01)00192-X
  43. Pipkin, A.C. (1964), "Small finite deformations of viscoelastic solids", Review of Modern Physics, 36(6), 1034- 1046. https://doi.org/10.1103/RevModPhys.36.1034
  44. Ponter, R.S. and Boulbibane, M. (2002), "Minimum theorems and the linear matching method for bodies in a cyclic state of creep", European Journal of Mechanics - A/Solids, 21(6), 915-925. https://doi.org/10.1016/S0997-7538(02)01245-7
  45. Poon, H. and Fouad Ahmad, M. (1999), "A finite element constitutive update scheme for anisotropic viscoelastic solids exhibiting non-linearity of the Schapery type", Int. J. Numer. Meth. Eng., 46(12), 2027-2041. https://doi.org/10.1002/(SICI)1097-0207(19991230)46:12<2027::AID-NME575>3.0.CO;2-5
  46. Quintanilla, R. (2004), "Comparison arguments and decay estimates in non-linear viscoelasticity", Int. J. Non- Linear Mechanics, 39(1), 55-61. https://doi.org/10.1016/S0020-7462(02)00127-0
  47. Raoof, M. and Kraincanic, I. (1998), "Prediction of coupled axial/torsional stiffness coefficients of locked-coil ropes", Comput. Struct., 69(3), 305-319. https://doi.org/10.1016/S0045-7949(98)00128-X
  48. Reese, S. and Govindjee, S. (1998), "A theory of finite viscoelasticity and numerical aspects", Int. J. Solids Struct., 35(26-27), 3455-3482. https://doi.org/10.1016/S0020-7683(97)00217-5
  49. Roshan Fekr, M., McGlure, G. and Farzaneh, M. (1999), "Application of ADINA to stress analysis of an optical ground wire", Comput. Struct., 72(1-3), 301-316. https://doi.org/10.1016/S0045-7949(99)00037-1
  50. Schapery, R.A. (2000), "Nonlinear viscoelastic solids", Int. J. Solids Struct., 37(1-2), 359-366. https://doi.org/10.1016/S0020-7683(99)00099-2
  51. Schapery, R.A. and Park, S.W. (1999), "Methods of interconversion between linear viscoelastic material functions. Part II − An approximate analytical method", Int. J. Solids Struct., 36(11), 1677-1699. https://doi.org/10.1016/S0020-7683(98)00060-2
  52. Schreyer, H.L. (2002), "On time integration of viscoplastic constitutive models suitable for creep", Int. J. Numer. Meth. Eng., 53(3), 637-652. https://doi.org/10.1002/nme.293
  53. Sobotka, Z. (1984), Rheology of Materials and Engineering Structures, Academia, Prague.
  54. Wineman, A., Van Dyke, T. and Shixiang, S. (1998), "A nonlinear viscoelastic model for one dimensional response of elastomeric bushings", Int. J. Mech. Sci., 40(12), 1295-1305. https://doi.org/10.1016/S0020-7403(98)00023-X
  55. Zheng, S.F. and Weng, G.J. (2002), "A new constitutive equation for the long-term creep of polymers based on physical aging", European Journal of Mechanics - A/Solids, 21(3), 411-421. https://doi.org/10.1016/S0997-7538(02)01215-9

피인용 문헌

  1. Time-Dependent Analysis of Prestressed Cable Nets vol.142, pp.7, 2016, https://doi.org/10.1061/(ASCE)ST.1943-541X.0001465
  2. Finite element simulation of creep of spiral strands vol.117, 2016, https://doi.org/10.1016/j.engstruct.2016.02.053
  3. Time-dependent analysis of cable nets using a modified nonlinear force-density method and creep theory vol.148, 2015, https://doi.org/10.1016/j.compstruc.2014.11.004
  4. Vibrations of an aramid anchor cable subjected to turbulent wind vol.72, 2014, https://doi.org/10.1016/j.advengsoft.2013.08.004
  5. Time-dependent analysis of cable domes using a modified dynamic relaxation method and creep theory vol.125, 2013, https://doi.org/10.1016/j.compstruc.2013.04.019
  6. Artificial Neural Network for Creep Behaviour Predictions of a Parallel-lay Aramid Rope Under Varying Stresses vol.47, 2011, https://doi.org/10.1111/j.1475-1305.2010.00747.x
  7. Time-dependent analysis of cable trusses -Part I. Closed-form computational model vol.38, pp.2, 2004, https://doi.org/10.12989/sem.2011.38.2.157