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Nonlinear flexibility-based beam element on Winkler-Pasternak foundation

  • Sae-Long, Worathep (Department of Civil Engineering, School of Engineering, University of Phayao) ;
  • Limkatanyu, Suchart (Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University) ;
  • Hansapinyo, Chayanon (Excellence Center in Infrastructure and Transportation Engingeering (ExCITE), Department of Civil Engineering, Chiang Mai University) ;
  • Prachasaree, Woraphot (Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University) ;
  • Rungamornrat, Jaroon (Applied Mechanics and Structures Research Unit, Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University) ;
  • Kwon, Minho (Department of Civil Engineering, ERI, Gyeongsang National University)
  • 투고 : 2020.05.10
  • 심사 : 2021.01.31
  • 발행 : 2021.02.25

초록

A novel flexibility-based beam-foundation model for inelastic analyses of beams resting on foundation is presented in this paper. To model the deformability of supporting foundation media, the Winkler-Pasternak foundation model is adopted. Following the derivation of basic equations of the problem (strong form), the flexibility-based finite beam-foundation element (weak form) is formulated within the framework of the matrix virtual force principle. Through equilibrated force shape functions, the internal force fields are related to the element force degrees of freedom. Tonti's diagrams are adopted to present both strong and weak forms of the problem. Three numerical simulations are employed to assess validity and to show effectiveness of the proposed flexibility-based beam-foundation model. The first two simulations focus on elastic beam-foundation systems while the last simulation emphasizes on an inelastic beam-foundation system. The influences of the adopted foundation model to represent the underlying foundation medium are also discussed.

키워드

참고문헌

  1. Aslami, M. and Akimov, P.A. (2016), "Analytical solution for beams with multipoint boundary conditions on two-parameter elastic foundations", Arch. Civ. Mech. Eng., 16(4), 668-677. https://doi.org/10.1016/j.acme.2016.04.005.
  2. Bohlooly, M. and Fard, K.M. (2019), "Buckling and postbuckling of concentrically stiffened piezo-composite plates on elastic foundations", J. Appl. Comput. Mech., 5(1), 128-140. https://doi.org/10.22055/jacm.2018.25539.1277.
  3. Civalek, O. and Ozturk, B. (2010), "Free vibration analysis of tapered beam-column with pinned ends embedded in WinklerPasternak elastic foundation", Geomech. Eng., 2(1), 45-56. https://doi.org/10.12989/gae.2010.2.1.045.
  4. Demir, C., Mercan, K., Numanoglu, H.M. and Civalek, O. (2018), "Bending response of nanobeams resting on elastic foundation", J. Appl. Comput. Mech., 4(2), 105-114. https://doi.org/10.22055/jacm.2017.22594.1137.
  5. Dutta, S.C. and Roy, R.A. (2002), "Critical review on idealization and modeling for interaction among soil-foundation-structure system", Comput. Struct., 80(20-21), 1579-1594. https://doi.org/10.1016/S0045-7949(02)00115-3.
  6. Ebrahimi, F. and Barati, M.R. (2017), "Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects", Nanomater. Nanotechnol., 7(2), 1-11. https://doi.org/10.1177/1847980417713106.
  7. Eisenberger, M. and Yankelevsky, D.Z. (1985), "Exact stiffness matrix for beams on elastic foundation", Comput. Struct., 21(6), 1355-1359. https://doi.org/10.1016/0045-7949(85)90189-0.
  8. Feng, D.C., Wu, G. and Ning, C.L. (2019), "A regularized forcebased Timoshenko fiber element including flexure-shear interaction for cyclic analysis of RC structures", Int. J. Mech. Sci., 160, 59-74. https://doi.org/10.1016/j.ijmecsci.2019.06.011.
  9. Gangadean, D., Mcilroy, D.N., Faulkner, B.E. and Aston D.E. (2010), "Winkler boundary conditions for three-point bending tests on 1D nanomaterials", Nanotechnol., 21(22), 1-19. https://doi.org/10.1088/0957-4484/21/22/225704.
  10. Ghosh, P., Rajesh, S. and Chand, J.S. (2017), "Linear and nonlinear elastic analysis of closely spaced strip foundations using Pasternak model", Front. Struct. Civ. Eng., 11(2), 228-243. https://doi.org/10.1007/s11709-016-0370-x.
  11. Gülkan, P. and Alemdar, B.N. (1999), "Exact finite element for a beam on a two-parameter elastic foundation: A revisit", Struct. Eng. Mech., 7(3), 259-276. https://doi.org/10.12989/sem.1999.7.3.259.
  12. He, X.G. and Kwan, A.K.H. (2001), "Modeling dowel action of reinforcement bars for finite element analysis of concrete structures", Comput. Struct., 79(6), 595-604. https://doi.org/10.1016/S0045-7949(00)00158-9.
  13. Hetenyi, M. (1946), Beams on Elastic Foundations, University of Michigan Press, Ann Arbor, Michigan, U.S.A.
  14. Horvath, J.S. and Colasanti, R.J. (2011), "Practical subgrade model for improved soil-structure interaction analysis: Model development", Int. J. Geomech., 11(1), 59-64. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000070.
  15. ICC (2012), International building code, International Code Council, Country Club Hills, Illinois, U.S.A.
  16. Jafari, V., Abyaneh, M.A., Vahdani, S.H. and Rahimian M. (2009), "Improved displacement-field approximation for geometrical nonlinear flexibility-based planar curved element in state space", Mech. Based Des. Struct. Mach., 37(4), 475-502. https://doi.org/10.1080/15397730903164094.
  17. Jamil, I. and Ahmad, I. (2019), "Bending moments in raft of a piled raft system using Winkler analysis", Geomech. Eng., 18(1), 41-48. https://doi.org/10.12989/gae.2019.18.1.041.
  18. Kerr, A.D. (1964), "Elastic and viscoelastic foundation models", J. Appl. Mech., 31(4), 491-498. https://doi.org/10.1115/1.3629667.
  19. Khemis, A., Chaouche, A.H., Athmani, A. and Tee, K.F. (2016), "Uncertainty effects of soil and structural properties on the buckling of flexible pipes shallowly buried in Winkler foundation", Struct. Eng. Mech., 59(4), 739-759. https://doi.org/10.12989/sem.2016.59.4.739.
  20. Kim, S., Ceylan, H. and Gopalakrishnan, K. (2014), "Finite element modeling of environmental effects on rigid pavement deformation", Front. Struct. Civ. Eng., 8(2), 101-114. https://doi.org/10.1007/s11709-014-0254-x.
  21. Kim, J.S., Kim, M.K. and Jung, S.D. (2015), "Two-dimensional numerical tunnel model using a Winkler-based beam element and its application into tunnel monitoring systems", Cluster Comput., 18(2), 707-719. https://doi.org/10.1007/s10586-014-0418-4.
  22. Limkatanyu, S. and Spacone, E. (2002a), "Reinforced concrete frame element with bond interfaces. I: Displacement-based, force-based, and mixed formulations", J. Struct. Eng., 128(3), 346-355. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:3(346).
  23. Limkatanyu, S. and Spacone, E. (2002b), "Reinforced concrete frame element with bond interfaces. II: State determination and numerical validations", J. Struct. Eng., 128(3), 356-364. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:3(356).
  24. Limkatanyu, S. and Spacone, E. (2006), "Frame element with lateral deformable supports: Formulations and numerical validation", Comput. Struct., 84(13-14), 942-954. https://doi.org/10.1016/j.compstruc.2005.12.002.
  25. Limkatanyu, S., Kwon, M., Prachasaree, W. and Chaiviriyawong, P. (2012a), "Contact interface fiber section element: Shallow foundation modeling", Geomech. Eng., 4(3), 173-190. https://doi.org/10.12989/gae.2012.4.3.173.
  26. Limkatanyu, S., Kuntiyawichai, K., Spacone, E. and Kwon, M. (2012b), "Natural stiffness matrix for beams on Winkler foundation: Exact force-based derivation", Struct. Eng. Mech., 42(1), 39-53. https://doi.org/10.12989/sem.2012.42.1.039.
  27. Limkatanyu, S., Kuntiyawichai, K., Spacone, E. and Kwon, M. (2013), "Nonlinear Winkler-based beam element with improved displacement shape functions", KSCE J. Civ. Eng., 17(1), 192-201. https://doi.org/10.1007/s12205-013-1606-0.
  28. Limkatanyu, S., Sae-Long, W., Prachasaree, W. and Kwon, M. (2015b), "Improved nonlinear displacement-based beam element on a two-parameter foundation", Eur. J. Environ. Civ. Eng., 19(6), 649-671. https://doi.org/10.1080/19648189.2014.965847.
  29. Mindlin, R.D. (1936), "Force at a point in the interior of a semi-infinite solid", Phys., 7(5), 195-202. https://doi.org/10.1063/1.1745385.
  30. Mullapudi, R. and Ayoub, A. (2010), "Nonlinear finite element modeling of beams on two-parameter foundations", Comput. Geotech., 37(3), 334-342. https://doi.org/10.1016/j.compgeo.2009.11.006.
  31. Neuenhofer, A. and Filippou, F.C. (1997), "Evaluation of nonlinear frame finite-element models", J. Struct. Eng., 123(7), 958-966. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:7(958).
  32. Pasternak, P.L. (1954), On a New Method of Analysis of an Elastic Foundation by means of Two Constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu I Arkhitekture, Moscow, Russia.
  33. Patil, V.A., Sawant, V.A. and Deb, K. (2012), "Finite element analysis of rigid pavement on a nonlinear two parameter foundation model", Int. J. Geotech. Eng., 6(3), 275-286. https://doi.org/10.3328/IJGE.2012.06.03.274-286.
  34. Raychowdhury, P. and Jindal, S. (2014), "Shallow foundation response variability due to soil and model parameter uncertainty", Front. Struct. Civ. Eng., 8(3), 237-251. https://doi.org/10.1007/s11709-014-0242-1.
  35. Salari, M.R., Spacone, E., Shing, P.B. and Frangopol, D.M. (1998), "Nonlinear analysis of composite beams with deformable shear connections", J. Struct. Eng., 124(10), 1148-1158. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:10(1148).
  36. Sapountzakis, E.J. and Kampitsis, A.E. (2013), "Inelastic analysis of beams on two-parameter tensionless elastoplastic foundation", Eng. Struct., 48, 389-401. https://doi.org/10.1016/j.engstruct.2012.09.012.
  37. Selvadurai, A.P.S. (1979), Elastic Analysis of Soil-Foundation Interaction, Elsevier Publishing Company, Inc., New York, U.S.A.
  38. Shirima, L.M. and Giger, M.W. (1992), "Timoshenko beam element resting on two-parameter elastic foundation", J. Eng. Mech., 118(2), 280-295. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:2(280).
  39. Shokrieh, M.M. and Heidari-Rarani, M. (2011), "A comparative study for beams on elastic foundation models to analysis of mode I delamination in DCB specimen", Struct. Eng. Mech., 37(2), 149-162. https://doi.org/10.12989/sem.2011.37.2.149.
  40. Spacone, E., Filippou, F.C. and Taucer, F.F. (1996a), "Fiber beamcolumn model for nonlinear analysis of r/c frames. Part I: Formulation", Earthq. Eng. Struct. Dyn., 25(7), 711-725. https://doi.org/10.1002/(SICI)1096-9845(199607)25:7<711::AID-EQE576>3.0.CO;2-9.
  41. Spacone, E., Filippou, F.C. and Taucer, F.F. (1996b), "Fiber beamcolumn model for nonlinear analysis of r/c frames. Part II: Applications", Earthq. Eng. Struct. Dyn., 25(7), 727-742. https://doi.org/10.1002/(SICI)1096-9845(199607)25:7<727::AID-EQE577>3.0.CO;2-O.
  42. Taylor, R.L. (2000), FEAP: A Finite Element Analysis Program, User manual: version 7.3, University of California, Berkeley, California, U.S.A.
  43. Teodoru, I.B. and Musat, V. (2010), "The modified Vlasov foundation model: An attractive approach for beams resting on elastic supports", Electron. J. Geotech. Eng., 15(C), 1-13.
  44. Tonti, E. (1976), "The reason for analogies between physical theories", Appl. Math. Modell., 1(1), 37-50. https://doi.org/10.1016/0307-904X(76)90023-8.
  45. Vlasov, V.Z. and Leontiev, U.N. (1966), Beams, plates, and shells on elastic foundations, Israel Program for Scientific Translations Ltd, Jerusalem, Israel.
  46. Winkler, E. (1867), Theory of Elasticity and Srength, Dominicus, Prague, Czechoslovakia.
  47. Wolfram, S. (1992), Mathematica Reference Guide, Addison-Wesley Publishing Company, Redwood City, California, U.S.A.
  48. Zarepour, M., Hosseini, S.A. and Kokaba, M.R. (2017), "Electro-thermo-mechanical nonlinear free vibration of nanobeam resting on the Winkler-Pasternak foundations based on nonlocal elasticity using differential transform method", Microsyst. Technol., 23(7), 2641-2648. https://doi.org/10.1007/s00542-016-2935-y.
  49. Zendaoui, A., Kadid, A. and Yahiaoui, D. (2016), "Comparison of different numerical models of RC elements for predicting the seismic performance of structures", Int. J. Concr. Struct. Mater., 10(4), 461-478. https://doi.org/10.1007/s40069-016-0170-7.
  50. Zhang, L., Zhao, M., Zou, X. and Zhao, H. (2009), "Deformation analysis of geocell reinforcement using Winkler model", Comput. Geotech., 36(6), 977-983. https://doi.org/10.1016/j.compgeo.2009.03.005.
  51. Zhaohua, F. and Cook, R.D. (1983), "Beam elements on two-parameter elastic foundations", J. Eng. Mech., 109(3), 1390-1401. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:6(1390).