Steel and Composite Structures

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Thermal buckling of FGM beams having parabolic thickness variation and temperature dependent materials

  • Arioui, Othman (Department of Civil Engineering, University of Oran of Science and Technology) ;
  • Belakhdar, Khalil (Department of Science and Technology, University Centre of Tamanrasset) ;
  • Kaci, Abdelhakim (Department of Civil Engineering and Hydraulics, University of Saida) ;
  • Tounsi, Abdelouahed (Laboratory of Materials and Hydrology, University of Sidi Bel Abbes)
  • Received : 2018.02.26
  • Accepted : 2018.04.06
  • Published : 2018.06.25
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Abstract

An investigation on the thermal buckling resistance of simply supported FGM beams having parabolic-concave thickness variation and temperature dependent material properties is presented in this paper. An analytical formulation based on the first order beam theory is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. a function of thickness variation is introduced which controls the parabolic variation intensity of the beam thickness without changing its original material volume. The results showed the high importance of taking into account the temperature-dependent material properties in the thermal buckling analysis of such critical beam sections. Different Influencing parametric on the thermal stability are studied which may help in design guidelines of such complex structures.

Keywords

References

  1. Abdelaziz, H.H., Ait Amar Meziane, M., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., Int. J., 25(6), 693-704.
  2. Abualnour, M., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047
  3. Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil, Struct. Envir., 4(2), 59-64.
  4. Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  5. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  6. Akavci, S.S. (2015), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676.
  7. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  8. Anandrao, K., Gupta, R., Ramachandran, P. and Rao, G. (2013), "Thermal buckling and free vibration analysis of heated functionally graded material beams", Defence Sci. J., 63(3), 315-322. https://doi.org/10.14429/dsj.63.2370
  9. Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567
  10. Atmane H., Tounsi A., Ziane N. and Mechab I., (2011), "Mathematical Solution For Free Vibration of Sigmoid Functionally Graded Beams With Varying Cross-Section", Steel Compos. Struct., Int. J., 11(6), 489-504. https://doi.org/10.12989/scs.2011.11.6.489
  11. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., Int. J., 65(4), 453-464.
  12. Aydogdu, M. (2006), "Buckling analysis of cross-ply laminated beams with general boundary conditions by ritz method", Compos. Sci. Technol., 66(10), 1248-1255. https://doi.org/10.1016/j.compscitech.2005.10.029
  13. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher-order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  14. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. https://doi.org/10.12989/EAS.2018.14.2.103
  15. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  16. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(3), 257-270.
  17. Bennai, R., Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  18. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  19. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053
  20. Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Adda-Bedia, E.A. (2014), "Hygrothermal effects on the postbuckling response of composite beams", Am. J. Mater. Res., 1(2), 35-43.
  21. Bouderba, B., Houari, M.S.A. and Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., Int. J., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  22. Bouguenina, O., Belakhdar, K., Tounsi, A. and Adda-Bedia, E.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., Int. J., 19(3), 679-695. https://doi.org/10.12989/scs.2015.19.3.679
  23. 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., Int. J., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  24. De Faria, A. and De Almeida, S.M. (2004), "Buckling optimization of variable thickness composite plates subjected to non uniform loads", AIAA J., 42(2), 228-231. https://doi.org/10.2514/1.1422
  25. 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., Int. J., 63(5), 585-595.
  26. Fallah, A. and Aghdam, M. (2012), "Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation", Compos. Part B-Eng., 43(3), 1523-1530.
  27. Ghayesh, M.H. and Farokhi, H. (2018), "Bending and vibration analyses of coupled axially functionally graded tapered beams", Nonlinear Dyn., 91(1), 17-28. https://doi.org/10.1007/s11071-017-3783-8
  28. Ghomshei, M. and Abbasi, V. (2013), "Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method", J. Mech. Sci. Technol., 27(4), 1031-1039. https://doi.org/10.1007/s12206-013-0211-y
  29. Hadji, L., Zouatnia, N. and Kassoul, A. (2017), "Wave propagation in functionally graded beams using various higherorder shear deformation beams theories", Struct. Eng. Mech., Int. J., 62(2), 143-149. https://doi.org/10.12989/sem.2017.62.2.143
  30. Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally graded-carbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., 1099636217720373.
  31. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  32. Huang, Y. and Li, X. (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
  33. Jabbarzadeh, M., Eskandari, J. and Khosravi, M. (2013), "The analysis of thermal buckling of circular plates of variable thickness from functionally graded materials", Modares Mech. Eng., 12(5), 59-73.
  34. Janghorban, M. and Rostamsowlat, I. (2012), "Free vibration analysis of functionally graded plates with multiple circular and non-circular cutouts", Chinese J. Mech. Eng., 25(2), 277-284. https://doi.org/10.3901/CJME.2012.02.277
  35. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory", Struct. Eng. Mech., Int. J., 65(5), 621-631.
  36. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  37. Kar, V.R. and Panda, S.K. (2016), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115, 318-324.
  38. Kar, V.R. and Panda, S.K. (2017), "Postbuckling analysis of shear deformable FG shallow spherical shell panel under nonuniform thermal environment", J. Therm. Stress., 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118
  39. Karami, B., Shahsavari, D. and Janghorban, M. (2017a), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 1-11.
  40. Karami, B., Shahsavari, D. and Li, L. (2017b), "Temperature-dependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Therm. Stress., 1-17.
  41. Karami, B., Janghorban, M. and Li, L. (2018a), "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
  42. Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2018b) "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proc. Inst. Mech. Eng. Part C - J. Mech. Eng. Sci., 954406218756451. https://doi.org/10.1177/0954406218756451
  43. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircr. Eng. Aerosp. Technol. An Int. J., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  44. Katariya, P.V., Panda, S.K., Hirwani, C.K., Mehar, K. and Thakare, O. (2017), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", SMART Struct. Syst., 20(5), 595-605. https://doi.org/10.12989/SSS.2017.20.5.595
  45. Kiani, Y. and Eslami, M.R. (2010), "Thermal buckling analysis of functionally graded material beams", Int. J. Mech. Sci. Mater. Des., 6(3), 229-238. https://doi.org/10.1007/s10999-010-9132-4
  46. Kiani, Y. and Eslami, M. (2013), "Thermomechanical buckling of temperature-dependent FGM beams", Latin Am. J. Solids Struct., 10(2), 223-246. https://doi.org/10.1590/S1679-78252013000200001
  47. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016
  48. Kolahchi, R. and Bidgoli, A.M.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37(2), 265-274. https://doi.org/10.1007/s10483-016-2030-8
  49. Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlinear Dyn., 90(1), 479-492. https://doi.org/10.1007/s11071-017-3676-x
  50. Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032
  51. Kolahchi, R., Safari, M. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
  52. Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2017a), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater., 1099636217731071. https://doi.org/10.1177/1099636217731071
  53. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017b), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016
  54. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017c), "Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039
  55. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., Int. J., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  56. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel. Compos. Struct., Int. J., 25(2), 157-175.
  57. Mohammadabadi, M., Daneshmehr, A. and Homayounfard, M. (2015), "Size-dependent thermal buckling analysis of micro composite laminated beams using modified couple stress theory", Int. J. Eng. Sci., 92, 47-62. https://doi.org/10.1016/j.ijengsci.2015.03.005
  58. Mozafari, H. and Ayob, A. (2012), "Effect of thickness variation on the mechanical buckling load in plates made of functionally graded materials", Procedia Tech, 1, 496-504. https://doi.org/10.1016/j.protcy.2012.02.108
  59. Mozafari, H., Ayob, A. and Alias, A. (2010), "Influence of thickness variation on the buckling load in plates made of functionally graded materials", Eur. J. Sci. Res., 47(3), 422-435.
  60. Nami, M.R., Janghorban, M. and Damadam, M. (2015), "Thermal buckling analysis of functionally graded rectangular nanoplates based on nonlocal third-order shear deformation theory", Aerosp. Sci. Technol., 41, 7-15. https://doi.org/10.1016/j.ast.2014.12.001
  61. Panda, S.K. and Katariya, P.V. (2015), "Stability and free vibration behaviour of laminated composite panels under thermo-mechanical loading", Int. J. Appl. Comput. Math., 1(3), 475-490. https://doi.org/10.1007/s40819-015-0035-9
  62. Panda, S.K. and Singh, B.N. (2009), "Thermal post-buckling behaviour of laminated composite cylindrical/hyperboloid shallow shell panel using nonlinear finite element method", Compos. Struct., 91(3), 366-374. https://doi.org/10.1016/j.compstruct.2009.06.004
  63. Panda, S.K. and Singh, B.N. (2010), "Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibres using non-linear finite element method", Proc. Inst. Mech. Eng. Part C - J. Mech. Eng. Sci., 224(4), 757-769. https://doi.org/10.1243/09544062JMES1809
  64. Panda, S.K. and Singh, B.N. (2013a), "Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel embedded with SMA fibers", Nonlinear Dyn., 74(1-2), 395-418. https://doi.org/10.1007/s11071-013-0978-5
  65. Panda, S.K. and Singh, B.N. (2013b), "Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre", Aerosp. Sci. Technol., 29(1), 47-57. https://doi.org/10.1016/j.ast.2013.01.007
  66. Panda, S.K. and Singh, B.N. (2013c), "Post-buckling analysis of laminated composite doubly curved panel embedded with SMA fibers subjected to thermal environment", Mech. Adv. Mater. Struct., 20(10), 842-853. https://doi.org/10.1080/15376494.2012.677097
  67. Panda, S.K. and Singh, B.N. (2013d), "Thermal Postbuckling Behavior of Laminated Composite Spherical Shell Panel Using NFEM#", Mech. Based Des. Struct. Mach., 41(4), 468-488. https://doi.org/10.1080/15397734.2013.797330
  68. Pouladvand, M. (2009), "Thermal stability of thin rectangular plates with variable thickness made of functionally graded material", J. Solid. Mech., 1(3), 171-189.
  69. Rajasekaran, S. and Wilson, A. (2013), "Buckling and vibration of rectangular plates of variable thickness with different end conditions by finite difference technique", Struct. Eng. Mech., Int. J., 46(2), 269-294. https://doi.org/10.12989/sem.2013.46.2.269
  70. Robert, M.J. (2006), "Buckling of bars plates and shells", Bull Ridge.
  71. Shahsavari, D., Shahsavarib, M., Li, L. and Karami, B. (2018), "A novel quasi-3D hyperbolic theory for free vibration of FG-plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004
  72. Shahsiah, R., Nikbin, K.M. and Eslami, M.R. (2009), "Thermal buckling of functionally graded beams", Iran J. Mech. Eng., 10(2), 64-80.
  73. Shen, H. (2009), Functionally Graded Materials: Non-linear Analysis of Plates and Shells, CRC Press, New York, NY, USA.
  74. Shokravi, M. (2017a), "Buckling analysis of embedded laminated plates with agglomerated CNT-reinforced composite layers using FSDT and DQM", Geomech. Eng., Int. J., 12(2), 327-346. https://doi.org/10.12989/gae.2017.12.2.327
  75. Shokravi, M. (2017b), "Buckling of sandwich plates with FGCNT-reinforced layers resting on orthotropic elastic medium using Reddy plate theory", Steel Compos. Struct., Int. J., 23(6), 623-631.
  76. Shokravi, M. (2017c), "Dynamic pull-in and pull-out analysis of viscoelastic nanoplates under electrostatic and Casimir forces via sinusoidal shear deformation theory", Microelectron. Reliab., 71, 17-28. https://doi.org/10.1016/j.microrel.2017.02.006
  77. Shokravi, M. (2017d), "Vibration analysis of silica nanoparticles-reinforced concrete beams considering agglomeration effects", Comput. Concrete, 19(3), 333-338. https://doi.org/10.12989/cac.2017.19.3.333
  78. Siddiqui, F. (2015), "Extended higher order theory for sandwich plates of arbitrary aspect ratio", Thesis; Georgia Institute of Technology.
  79. Sun, Y., Li, S. and Batra, R. (2016), "Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation", J. Therm. Stresses, 39(1), 11-26. https://doi.org/10.1080/01495739.2015.1120627
  80. Szilard, R. (2004), Theories and Applications of Plate Analysis: Classical Numerical and Engineering Methods, John Wiley & Sons, USA.
  81. Wattanasakulpong, N., Gangadhara, P.B. and Kelly, D. (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
  82. Yazdani, S., Kiani, Y., Jabbari, M. and Eslami, M. (2011), "Thermal buckling of piezoelectric composite beam", ISRN Mech. Eng., 2011, 1-11.
  83. Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with $SiO_2$ nano-particles", Wind Struct., Int. J., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043

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