DOI QR코드

DOI QR Code

Limit point instability of shallow arches under localized sinusoidal loading

  • 투고 : 2021.12.06
  • 심사 : 2023.02.13
  • 발행 : 2023.03.10

초록

In the present study, the limit point buckling and postbuckling behaviors of sinusoidal, shallow arches with pinned supports subjected to localized sinusoidal loading, based on the Euler-Bernoulli beam theory, are numerically analyzed. There are some studies on the buckling of sinusoidal shallow arches under the effect of sinusoidal loading. However, in these studies, the sinusoidal loading acts along the horizontal projection of the entire shallow arch. No study has been found in the relevant literature pertaining to the stability of the shallow arches subjected to various lengths of sinusoidal loading. Therefore, the purpose of this paper is to contribute to the literature by examining the effect of the length of the localized sinusoidal loading and the initial rise of the shallow arch on the limit point buckling and postbuckling behaviors. Equilibrium paths corresponding to certain values of the length of the localized sinusoidal loading and various values of the initial rise parameter are presented. It has been observed that the length of the sinusoidal loading and the initial rise parameter affects the transition from no buckling to limit point instability remarkably. The deformed configurations of the sinusoidal shallow arch under localized loading regarding buckling and postbuckling states are illustrated, as well. The effects of the length of the localized sinusoidal loading on the internal forces of the shallow arch are investigated during various stages of the loading.

키워드

과제정보

The author is grateful to Prof. Dr. R. Faruk Yukseler for providing the field, his invaluable guidance and suggestions.

참고문헌

  1. Altekin, M. and Yukseler, R.F. (2008), "A parametric study on geometrically nonlinear analysis of initially imperfect shallow spherical shells", J. Elastom. Plast., 40(3), 253-270. https://doi.org/10.1177/0095244307084907.
  2. Altekin, M. and Yukseler, R.F. (2022), "Stress-driven nonlocal model on snapping of doubly hinged shallow arches", Mech. Adv. Mater. Struct., 1-11. https://doi.org/10.1080/15376494.2022.2029980.
  3. Arefi, A. and Nahvi, H. (2017), "Stability analysis of an embedded single-walled carbon nanotube with small initial curvature based on nonlocal theory", Mech. Adv. Mater. Struct., 24(11), 962-970. https://doi.org/10.1080/15376494.2016.1196800.
  4. Babaei, H., Kiani, Y. and Eslami, M.R. (2018), "Geometrically nonlinear analysis of functionally graded shallow curved tubes in thermal environment", Thin Wall. Struct., 132, 48-57. https://doi.org/10.1016/j.tws.2018.08.008.
  5. Bateni, M. and Eslami, M.R. (2014), "Non-linear in-plane stability analysis of FGM circular shallow arches under central concentrated force", Int. J. Nonlin. Mech., 60, 58-69. https://doi.org/10.1016/j.ijnonlinmec.2014.01.001.
  6. Cai, J.G., Zhou, Y. and Feng, J. (2013), "Post-buckling behavior of a fixed arch for variable geometry structures", Mech. Res. Commun., 52, 74-80. https://doi.org/10.1016/j.mechrescom.2013.07.002.
  7. Chandra, Y., Stanciulescu, I., Virgin, L.N., Eason, T.G. and Spottswood, S.M. (2013), "A numerical investigation of snap-through in a shallow arch-like model", J. Sound Vib., 332(10), 2532-2548. https://doi.org/10.1016/j.jsv.2012.12.019.
  8. Daikh, A.A., Houari, M.S.A., Karami, B., Eltaher, M.A., Dimitri, R. and Tornabene, F. (2021), "Buckling analysis of CNTRC curved sandwich nanobeams in thermal environment", Appl. Sci., 11(7), 3250. https://doi.org/10.3390/app11073250.
  9. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. https://doi.org/10.12989/sem.2021.80.1.063.
  10. Drosopoulos, G.A., Stavroulakis, G.E. and Massalas, C.V. (2008), "Influence of the geometry and the abutments movement on the collapse of stone arch bridges", Constr. Build. Mater., 22(3), 200-210. https://doi.org/10.1016/j.conbuildmat.2006.09.001.
  11. Eltaher, M.A., Mohamed, N. and Mohamed, S.A. (2020), "Nonlinear buckling and free vibration of curved CNTs by doublet mechanics", Smart Struct. Syst., 26(2), 213-226. https://doi.org/10.12989/sss.2020.26.2.213.
  12. Emam, S.A., Eltaher, M.A., Khater, M.E. and Abdalla, W.S. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci., 8(11), 2238. https://doi.org/10.3390/app8112238.
  13. Erdolen, A. and Yukseler, R.F. (2003), "An approach for finite strains and rotations of shells of revolution with application to a spherical shell under a uniformly distributed pressure", J. Elastom. Plast., 35(4), 357-365. https://doi.org/10.1177/009524403038015.
  14. Eslami, M.R. (2018), Buckling and Postbuckling of Beams, Plates, and Shells, Springer, Switzerland.
  15. Gao, Y., Xiao, W.S. and Zhu, H. (2020), "Snap-buckling of functionally graded multilayer graphene platelet-reinforced composite curved nanobeams with geometrical imperfections", Eur. J. Mech.-A/Solid., 82(5), 103993. https://doi.org/10.1016/j.euromechsol.2020.103993.
  16. Ha, J., Gutman, S., Shon, S. and Lee, S. (2014), "Stability of shallow arches under constant load", Int. J. Nonlin. Mech., 58, 120-127. https://doi.org/10.1016/j.ijnonlinmec.2013.08.004.
  17. Harvey, P.S. and Virgin, L.N. (2015), "Coexisting equilibria and stability of a shallow arch: Unilateral displacement-control experiments and theory", Int. J. Solid. Struct., 54, 1-11. https://doi.org/10.1016/j.ijsolstr.2014.11.016.
  18. Hu, C.F., Pi, Y.L., Gao, W. and Li, L. (2018), "In-Plane non-linear elastic stability of parabolic arches with different rise-to-span ratios", Thin Wall. Struct., 129, 74-84. https://doi.org/10.1016/j.tws.2018.03.019.
  19. Inan, M. (2019), Strength of Materials, ITu Vakfi, Istanbul, Turkey.
  20. Karamanli, A. and Vo, T.P. (2022), "Finite element model for free vibration analysis of curved zigzag nanobeams", Compos. Struct., 282, 115097. https://doi.org/10.1016/j.compstruct.2021.115097.
  21. Karnovsky, I.A. (2012), Theory of Arched Structures: Strength, Stability, Vibration, Springer-Verlag, New York.
  22. Kaviani, F. and Mirdamadi, H.R. (2013), "Snap-through and bifurcation of nano-arches on elastic foundation by the strain gradient and nonlocal theories", Int. J. Struct. Stab. Dyn., 13(05), 1350022. https://doi.org/10.1142/S0219455413500223.
  23. King, C. and Brown, D. (2001), Design of Curved Steel, Steel Construction Institute, Ascot, UK.
  24. Kiss, L.P. (2020), "Nonlinear stability analysis of FGM shallow arches under an arbitrary concentrated radial force", Int. J. Mech. Mater. Des., 16, 91-108. https://doi.org/10.1007/s10999-019-09460-2.
  25. Lu, H., Liu, A., Pi Y.L., Bradford, M.A., Fu J. and Huang, Y. (2018), "Localized loading and nonlinear instability and postinstability of fixed arches", Thin Wall. Struct., 131, 165-178. https://doi.org/10.1016/j.tws.2018.06.019.
  26. Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428.
  27. Maharana, P. and Ananthasuresh, G.K. (2022), "Switching dynamics of shallow arches", arXiv preprint arXiv:2210.05734.
  28. Maron, M.J. and Lopez, R.J. (1991), Numerical Analysis: A Practical Approach, Wadsworth Publishing Company, Belmont.
  29. Moghaddasie, B. and Stanciulescu, I. (2013), "Equilibria and stability boundaries of shallow arches under static loading in a thermal environment", Int. J. Nonlin. Mech., 51(1), 132-144. https://doi.org/10.1016/j.ijnonlinmec.2013.01.001
  30. Mohsen, S.N. and Moghaddasie, B. (2018), "Stability of a half-sine shallow arch under sinusoidal and step loads in thermal environment", Lat. Am. J. Solid. Struct., 15(8), 15. https://doi.org/10.1590/1679-78254607.
  31. Mortazavi, P., Mirdamadi, H.R. and Shahidi, A.R. (2018), "Postbuckling, limit point, and bifurcation analyses of hallow nano-arches by generalized displacement control and finite difference considering small-scale effects", Int. J. Struct. Stab. Dyn., 18(01), 1850014. https://doi.org/10.1142/S0219455418500141.
  32. Ouakad, H.M. and Zur, K.K. (2022), "On the snap-through buckling analysis of electrostatic shallow arch micro-actuator via meshless Galerkin decomposition technique", Eng. Anal. Bound. Elem., 134, 388-397. https://doi.org/10.1016/j.enganabound.2021.10.007.
  33. Pi, Y.L. (2020), "Non-linear in-plane multiple equilibria and buckling of pin-ended shallow circular arches under an arbitrary radial point load", Appl. Math. Model., 77(1), 115-136. https://doi.org/10.1016/j.apm.2019.07.021.
  34. Pi, Y.L. and Bradford, M.A. (2012), "Non-linear buckling and postbuckling analysis of arches with unequal rotational end restraints under a central concentrated load", Int. J. Solid. Struct., 49(26), 3762-3773. https://doi.org/10.1016/j.ijsolstr.2012.08.012.
  35. Pi, Y.L. and Trahair, N.S. (1998), "Non-linear buckling and postbuckling of elastic arches", Eng. Struct., 20(7), 571-579. https://doi.org/10.1016/S0141-0296(97)00067-9.
  36. Pi, Y.L., Bradford, M.A. and Tin-Loi, F. (2007), "Nonlinear analysis and buckling of elastically supported circular shallow arches", Int. J. Solid. Struct., 44(7-8), 2401-2425. https://doi.org/10.1016/j.ijsolstr.2006.07.011.
  37. Plaut, R.H. (1979), "Influence of load position on the stability of shallow arches", J. Appl. Math. Phys. (ZAMP), 30(3), 548-552. https://doi.org/10.1007/BF01588902.
  38. Pontecorvo, M.E., Barbarino, S., Murray, G.J. and Gandhi, F.S. (2013), "Bistable arches for morphing applications", J. Intel. Mater. Syst. Struct., 24(3), 274-286. https://doi.org/10.1177/1045389X12457252.
  39. Salonga, J. and Gauvreau, P. (2014), "Comparative study of the proportions, form, and efficiency of concrete arch bridges", J. Bridge Eng., 19(3), 04013010. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000537.
  40. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stress., 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323.
  41. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407.
  42. She, G.L., Ren, Y.R. and Yan, K.M. (2019), "On snap-buckling of porous FG curved nanobeams", Acta Astronautica, 161, 475-484. https://doi.org/10.1016/j.actaastro.2019.04.010.
  43. Shon, S., Ahn, S., Lee, S. and Ha, J. (2018), "A semianalytical approach for nonlinear dynamic system of shallow arches using higher order multistep Taylor method", Math. Prob. Eng., 2018, Article ID 9567619. https://doi.org/10.1155/2018/9567619.
  44. Simitses, G.J. and Hodges, D.H. (2006), Fundamentals of Structural Stability, Elsevier, Burlington, MA.
  45. Taghavi, N. and Nahvi, H. (2013), "Stability analysis of arch shape carbon nanotubes modeled by nonlocal elasticity theory", J. Comput. Theor. Nanosci., 10(3), 719-727. https://doi.org/10.1166/jctn.2013.2761.
  46. Tekin Atacan, A. and Yukseler, R.F. (2019), "Snap-through buckling of hinged-hinged initially imperfect beams undergoing finite deflections subjected to lateral concentrated midpoint loads", Mech. Solid., 54(7), 1119-1130. https://doi.org/10.3103/S0025654419070136.
  47. Tekin Atacan, A. and Yukseler, R.F. (2020), "Nonlinear behavior of beams having initially small imperfection subjected to sinusoidal load", Bitlis Eren u niversitesi Fen Bilimleri Dergisi, 9(1), 466-477. https://doi.org/10.17798/bitlisfen.592938.
  48. Tekin Atacan, A. and Yukseler, R.F. (2022a), "Snap-through instability of slightly curved beams under sinusoidal loading based on nonlocal elasticity theory", Mech. Bas. Des. Struct. Mach., 50(8), 2940-2960. https://doi.org/10.1080/15397734.2021.1901736.
  49. Tekin Atacan, A. and Yukseler, R.F. (2022b), "Snap-buckling and post-buckling analyses of fixed supported beams having initially circular imperfection under the effect of uniformly distributed vertical load", J. Facult. Eng. Arch. Gazi Univ., 37(2), 1091-1102. https://doi.org/10.17341/gazimmfd.845996.
  50. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability, 2nd Edition, MC Graw-Hill, New York, USA.
  51. Yan, S.T., Shen, X. and Jin, Z. (2018), "Instability of imperfect non-uniform shallow arch under uniform radial pressure for pinned and fixed boundary conditions", Thin Wall. Struct., 132, 217-236. https://doi.org/10.1016/j.tws.2018.08.018.
  52. Yan, S.T., Shen, X. and Jin, Z. (2019), "Static and dynamic symmetric snap-through of non-uniform shallow arch under a pair of end moments considering critical slowing-down effect", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 233(16), 5735-5762. https://doi.org/10.1177/0954406219855105.
  53. Yildirim, B. and Yukseler, R.F. (2011), "Effect of compressibility on nonlinear buckling of simply supported polyurethane spherical shells subjected to an apical load", J. Elastom. Plast., 43(2), 167-187. https://doi.org/10.1177/0095244310393930.
  54. Yukseler, R.F. (2015), "A theory for rubber-like rods", Int. J. Solid. Struct., 69-70, 350-359. https://doi.org/10.1016/j.ijsolstr.2015.05.015.
  55. Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stress., 45(12), 1029-1042. https://doi.org/10.1080/01495739.2022.2125137.
  56. Zhang, Y.Y., Wang, Y.X., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. http://doi.org/10.12989/scs.2021.38.3.293.
  57. Zhang, Z., Liu, A., Yang, J. and Huang, Y. (2019), "Nonlinear in-plane elastic buckling of a laminated circular shallow arch subjected to a central concentrated load", Int. J. Mech. Sci., 161-162, 105023. https://doi.org/10.1016/j.ijmecsci.2019.105023.
  58. Zhang, Z., Liu, A., Yang, J., Pi, Y.L., Huang, Y. and Fu, J. (2020), "A theoretical and experimental study on in-plane buckling of orthotropic composite arches under an arbitrary radial point load", Compos. Struct., 237(6), 111933. https://doi.org/10.1016/j.compstruct.2020.111933.