DOI QR코드

DOI QR Code

Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations

  • She, Gui-Lin (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University) ;
  • Ren, Yi-Ru (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University) ;
  • Xiao, Wan-Shen (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University) ;
  • Liu, Haibo (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University)
  • Received : 2018.02.23
  • Accepted : 2018.04.01
  • Published : 2018.06.25

Abstract

This paper studies thermal buckling and post-buckling behaviors of functionally graded materials (FGM) tubes subjected to a uniform temperature rise and resting on elastic foundations via a refined beam model. Compared to the Timoshenko beam theory, the number of unknowns of this model are the same and no correction factors are required. The material properties of the FGM tube vary continuously in the radial direction according to a power function. Two ends of the tube are assumed to be simply supported and in-plane boundary conditions are immovable. Energy variation principle is employed to establish the governing equations. A two-step perturbation method is adopted to determine the critical thermal buckling loads and post-buckling paths of the tubes with arbitrary radial non-homogeneity. Through detailed parametric studies, it can be found that the tube has much higher buckling temperature and post-buckling strength when it is supported by an elastic foundation.

Acknowledgement

Supported by : National Natural Science Foundation of China, Central Universities

References

  1. Amar, L.H.H., Kaci, A. and Tounsi, A. (2017), "On the size-dependent behavior of functionally graded micro-beams with porosities", Struct. Eng. Mech., 64(5), 527-541. https://doi.org/10.12989/SEM.2017.64.5.527
  2. Barati, M.R. (2017a), "On non-linear vibrations of flexoelectric nanobeams", Int. J. Eng. Sci., 121, 143-153. https://doi.org/10.1016/j.ijengsci.2017.09.001
  3. Barati, M.R. (2017b), "On wave propagation in nanoporous materials", Int. J. Eng. Sci., 116, 1-11. https://doi.org/10.1016/j.ijengsci.2017.03.007
  4. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  5. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  6. Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A. and Bedia, E.A.A. (2016), "Thermo-mechanical postbuckling of symmetric s-fgm plates resting on pasternak elastic foundations using hyperbolic shear deformation theory", Struct. Eng. Mech., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617
  7. Dai, H.L. and Dai, T. (2014), "Analysis for the thermoelastic bending of a functionally graded material cylindrical shell", Meccan., 49(5), 1069-1081. https://doi.org/10.1007/s11012-013-9853-1
  8. Dai, T. and Dai, H.L. (2015), "Investigation of mechanical behavior for a rotating FGM circular disk with a variable angular speed", J. Mech. Sci. Technol., 29(9), 3779-3787. https://doi.org/10.1007/s12206-015-0824-4
  9. Dai, T. and Dai, H.L. (2016), "Thermo-elastic analysis of a functionally graded rotating hollow circular disk with variable thickness and angular speed", Appl. Math. Model., 40(17-18), 7689-7707. https://doi.org/10.1016/j.apm.2016.03.025
  10. Dai, T. and Dai, H.L. (2017), "Analysis of a rotating FGMEE circular disk with variable thickness under thermal environment", Appl. Math. Model., 45, 900-924. https://doi.org/10.1016/j.apm.2017.01.007
  11. Dehrouyeh-Semnani, A.M. (2018), "On the thermally induced non-linear response of functionally graded beams", Int. J. Eng. Sci., 125, 53-74. https://doi.org/10.1016/j.ijengsci.2017.12.001
  12. Dehrouyeh-Semnani, A.M. (2017), "On boundary conditions for thermally loaded FG beams", Int. J. Eng. Sci., 119, 109-127. https://doi.org/10.1016/j.ijengsci.2017.06.017
  13. Dehrouyeh-Semnani, A.M., Mostafaei, H. and Dehrouyeh, M. (2017), "Thermal pre- and post-snap-through buckling of a geometrically imperfect doubly-clamped microbeam made of temperature-dependent functionally graded materials", Compos. Struct., 170, 122-134. https://doi.org/10.1016/j.compstruct.2017.03.003
  14. Ebrahimi, F. and Barati, M.R. (2016), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", Int. J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001
  15. Ebrahimi, F. and Daman, M. (2017a), "Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment", Struct. Eng. Mech., 64(1),121-133.
  16. Ebrahimi, F. and Daman, M. (2017b), "Nonlocal thermo-electromechanical vibration analysis of smart curved FG piezoelectric Timoshenko nanobeam", Smart Struct. Syst., 20(3), 351-368. https://doi.org/10.12989/SSS.2017.20.3.351
  17. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205
  18. Ebrahimi, F. and Javari, A. (2016), "Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., 59(2), 343-371. https://doi.org/10.12989/sem.2016.59.2.343
  19. Ebrahimi, F. and Zia, M. (2015), "Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities", Acta Astronaut., 116, 117-125. https://doi.org/10.1016/j.actaastro.2015.06.014
  20. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008
  21. Ebrahimi, F., Daman, M. and Fardshad, R.E. (2017), "Surface effects on vibration and buckling behavior of embedded nanoarches", Struct. Eng. Mech., 64(1), 1-10.
  22. Ebrahimi, F., Daman, M. and Jafari, A. (2017), "Nonlocal strain gradient-based vibration analysis of embedded curved porous piezoelectric nano-beams in thermal environment", Smart Struct. Syst., 20(6), 709-728. https://doi.org/10.12989/SSS.2017.20.6.709
  23. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/SEM.2017.63.5.585
  24. Elmossouess, B., Kebdani, S., Bouiadjra, M.B. and Tounsi, A. (2017), "A novel and simple hsdt for thermal buckling response of functionally graded sandwich plates", Struct. Eng. Mech., 62(4), 401-415. https://doi.org/10.12989/sem.2017.62.4.401
  25. Fu, Y., Zhong, J., Shao, X. and Chen, Y. (2015), "Thermal postbuckling analysis of functionally graded tubes based on a refined beam model", Int. J. Mech. Sci., 96, 58-64.
  26. Gan, B.S. (2016), "Post-buckling responses of elastoplastic FGM beams on nonlinear elastic foundation", Struct. Eng. Mech., 58(3), 515-532. https://doi.org/10.12989/sem.2016.58.3.515
  27. Hadji, L. and Bedia, E.A.A. (2015), "Influence of the porosities on the free vibration of FGM beams", Wind Struct., 21(3), 273-287. https://doi.org/10.12989/was.2015.21.3.273
  28. Hadji, L., Daouadji, T.H., Meziane, M.A.A., Tlidji, Y. and Bedia, E.A.A. (2016), "Analysis of functionally graded beam using a new first-order shear deformation theory", Struct. Eng. Mech., 57(2), 315-325. https://doi.org/10.12989/sem.2016.57.2.315
  29. Hadji, L., Zouatnia, N. and Kassoul, A. (2016), "Bending analysis of FGM plates using a sinusoidal shear deformation theory", Wind Struct., 23(6), 543-558. https://doi.org/10.12989/was.2016.23.6.543
  30. Hadji, L., Zouatnia, N. and Kassoul, A. (2017), "Wave propagation in functionally graded beams using various higher-order shear deformation beams theories", Struct. Eng. Mech., 62(2), 143-149. https://doi.org/10.12989/sem.2017.62.2.143
  31. Heydari, A., Jalali, A. and Nemati, A. (2016), "Buckling analysis of circular functionally graded plate under uniform radial compression including shear deformation with linear and quadratic thickness variation on the Pasternak elastic foundation", Appl. Math. Model., 41, 494-507.
  32. Huang, H., Zhang, Y. and Han, Q. (2017), "Stability of hydrostatic-pressured fgm thick rings with material nonlinearity", Appl. Math. Model., 45, 55-64. https://doi.org/10.1016/j.apm.2016.12.007
  33. Huang, Y. and Li, X.F. (2010), "Buckling of functionally graded circular columns including shear deformation", Mater. Des., 31(7), 3159-3166. https://doi.org/10.1016/j.matdes.2010.02.032
  34. Ji, X., Li, A. and Zhou, S. (2017), "A comparison of strain gradient theories with applications to the functionally graded circular micro-plate", Appl. Math. Model., 49, 124-143. https://doi.org/10.1016/j.apm.2017.04.021
  35. Karami, B., Janghorban, M. and Li, L. (2018), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronaut., 143, 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011
  36. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/SCS.2017.25.3.361
  37. Kiani, Y. (2016), "Thermal postbuckling of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets", J. Therm. Stress., 39(9), 1098-1110. https://doi.org/10.1080/01495739.2016.1192856
  38. Kiani, Y. and Eslami, M.R. (2010 a), "Thermal buckling analysis of functionally graded material beams", Int. J. Mech. Mater. Des., 6(3), 229-238. https://doi.org/10.1007/s10999-010-9132-4
  39. Kiani, Y. and Eslami, M.R. (2010b), "The GDQ approach to thermally nonlinear generalized thermoelasticity of a hollow sphere", Int. J. Mech. Sci., 118(1),195-204.
  40. Lal, A., Shegokar, N.L. and Singh, B.N. (2016), "Finite element based nonlinear dynamic response of elastically supported piezoelectric functionally graded beam subjected to moving load in thermal environment with random system properties", Appl. Math. Model., 44, 274-295.
  41. Mouaici, F., Benyoucef, S. and Atmane, H.A. (2016), "Effect of porosity on vibrational characteristics of non-homogeneous plates using hyperbolic shear deformation theory", Wind Struct., 22(4), 429-454. https://doi.org/10.12989/was.2016.22.4.429
  42. Nejad, M.Z., Hadi, A. and Rastgoo, A. (2016), "Buckling analysis of arbitrary two-directional functionally graded euler-bernoulli nano-beams based on nonlocal elasticity theory", Int. J. Eng. Sci., 103, 1-10. https://doi.org/10.1016/j.ijengsci.2016.03.001
  43. Nejad, M.Z. and Hadi, A. (2016a), "Non-local analysis of free vibration of bi-directional functionally graded euler-bernoulli nano-beams", Int. J. Eng. Sci., 105, 1-11. https://doi.org/10.1016/j.ijengsci.2016.04.011
  44. Nejad, M.Z. and Hadi, A. (2016b), "Eringen's non-local elasticity theory for bending analysis of bi-directional functionally graded euler-bernoulli nano-beams", Int. J. Eng. Sci., 106, 1-9. https://doi.org/10.1016/j.ijengsci.2016.05.005
  45. Nejad, M.Z., Hadi, A. and Farajpour, A. (2017). "Consistent couple-stress theory for free vibration analysis of euler-bernoulli nano-beams made of arbitrary bi-directional functionally graded materials", Struct. Eng. Mech., 63(2), 161-169. https://doi.org/10.12989/SEM.2017.63.2.161
  46. Rajasekaran, S. and Khaniki, H.B. (2017), "Bending, buckling and vibration of small-scale tapered beams", Int. J. Eng. Sci., 120, 172-188. https://doi.org/10.1016/j.ijengsci.2017.08.005
  47. Reddy, J.N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6), 593-626. https://doi.org/10.1080/01495739808956165
  48. Shahverdi, H. and Barati, M.R. (2017), "Vibration analysis of porous functionally graded nanoplates", Int. J. Eng. Sci., 120, 82-99. https://doi.org/10.1016/j.ijengsci.2017.06.008
  49. She, G.L., Ren, Y.R., Yuan, F.G. and Xiao, W.S. (2018), "On vibrations of porous nanotubes", Int. J. Eng. Sci., 125, 23-35. https://doi.org/10.1016/j.ijengsci.2017.12.009
  50. She, G.L., Yuan, F.G. and Ren, Y.R. (2017a), "Nonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory", Compos. Struct., 165, 74-82. https://doi.org/10.1016/j.compstruct.2017.01.013
  51. She, G.L., Yuan, F.G., Ren, Y.R. and Xiao, W.S. (2017), "On buckling and postbuckling behavior of nanotubes", Int. J. Eng. Sci., 121, 130-142. https://doi.org/10.1016/j.ijengsci.2017.09.005
  52. She, G.L., Shu, X. and Ren, Y.R. (2017), "Thermal buckling and postbuckling analysis of piezoelectric FGM beams based on high-order shear deformation theory", J. Therm. Stress., 40(6), 783-797. https://doi.org/10.1080/01495739.2016.1261009
  53. She, G.L., Yuan, F.G. and Ren, Y.R. (2017b), "Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory", Appl. Math. Model., 47, 340-357. https://doi.org/10.1016/j.apm.2017.03.014
  54. She, G.L., Yuan, F.G. and Ren, Y.R. (2017c), "Research on nonlinear bending behaviors of FGM infinite cylindrical shallow shells resting on elastic foundations in thermal environments", Compos. Struct., 170, 111-121. https://doi.org/10.1016/j.compstruct.2017.03.010
  55. Shen, H.S. (2013), A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells, John Wiley & Sons Inc., Singapore.
  56. Shen, H.S. (2014), "Postbuckling of FGM cylindrical panels resting on elastic foundations subjected to axial compression under heat conduction", Int. J. Mech. Sci., 89, 453-461. https://doi.org/10.1016/j.ijmecsci.2014.10.010
  57. Shvartsman, B. and Majak, J. (2016), "Numerical method for stability analysis of functionally graded beams on elastic foundation", Appl. Math. Model., 40(5-6), 3713-3719. https://doi.org/10.1016/j.apm.2015.09.060
  58. Simsek, M. (2016), "Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach", Int. J. Eng. Sci., 105, 12-27. https://doi.org/10.1016/j.ijengsci.2016.04.013
  59. Song, Q., Shi, J. and Liu, Z. (2017), "Vibration analysis of functionally graded plate with a moving mass", Appl. Math. Model., 46, 141-160. https://doi.org/10.1016/j.apm.2017.01.073
  60. Sun, Y., Li, S.R. and Batra, R.C. (2016), "Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation", J. Therm. Stress., 39(1), 11-26. https://doi.org/10.1080/01495739.2015.1120627
  61. Tossapanon, P. and Wattanasakulpong, N. (2016), "Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation", Compos. Struct., 142, 215-225. https://doi.org/10.1016/j.compstruct.2016.01.085
  62. Tu, T.M., Quoc, T.H. and Long, N.V. (2017), "Bending analysis of functionally graded plates using new eight-unknown higher order shear deformation theory", Struct. Eng. Mech., 62(3), 311-324. https://doi.org/10.12989/sem.2017.62.3.311
  63. Tuna, M. and Kirca, M. (2016), "Exact solution of eringen's nonlocal integral model for vibration and buckling of euler-bernoulli beam", Int. J. Eng. Sci., 107, 54-67. https://doi.org/10.1016/j.ijengsci.2016.07.004
  64. Wang, Y., Ding, H. and Xu, R. (2016), "Three-dimensional analytical solutions for the axisymmetric bending of functionally graded annular plates", Appl. Math. Model., 40(9-10), 5393-5420. https://doi.org/10.1016/j.apm.2015.11.051
  65. Wattanasakulpong, N., Gangadhara, P.B. and Kelly, D.W. (2011), "Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams", Int. J. Mech. Sci., 53(9), 734-743. https://doi.org/10.1016/j.ijmecsci.2011.06.005
  66. Wu, H., Kitipornchai, S. and Yang, J. (2016), "Imperfection sensitivity of thermal post-buckling behaviour of functionally graded carbon nanotube-reinforced composite beams", Appl. Math. Model., 42, 735-752.
  67. Zhang, P. and Fu, Y. (2013), "A higher-order beam model for tubes", Eur. J. Mech. A-Sol., 38(3), 12-19. https://doi.org/10.1016/j.euromechsol.2012.09.009
  68. Zhao, L., Zhu, J. and Wen, X.D. (2016), "Exact analysis of bidirectional functionally graded beams with arbitrary boundary conditions via the symplectic approach", Struct. Eng. Mech., 59(1),101-122. https://doi.org/10.12989/sem.2016.59.1.101
  69. Zhong, J., Fu, Y., Wan, D. and Li, Y. (2016), "Nonlinear bending and vibration of functionally graded tubes resting on elastic foundations in thermal environment based on a refined beam model", Appl. Math. Model., 40(17-18), 7601-7614. https://doi.org/10.1016/j.apm.2016.03.031
  70. Zhu, X., Wang, Y. and Dai, H.H. (2017), "Buckling analysis of euler-bernoulli beams using eringen's two-phase nonlocal model", Int. J. Eng. Sci., 116, 130-140. https://doi.org/10.1016/j.ijengsci.2017.03.008
  71. Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., 64(2), 145-153.
  72. Zouatnia, N., Hadji, L. and Kassoul, A. (2017), "A refined hyperbolic shear deformation theory for bending of functionally graded beams based on neutral surface position", Struct. Eng. Mech., 63(5), 683-689. https://doi.org/10.12989/SEM.2017.63.5.683

Cited by

  1. Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals vol.5, pp.9, 2018, https://doi.org/10.1088/2053-1591/aad4c3