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Influence of porosity on thermal buckling behavior of functionally graded beams

  • Bellifa, Hichem (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Selim, Mahmoud M. (Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University) ;
  • Chikh, Abdelbaki (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdeldjebbar (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benrahou, Kouider Halim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Al-Zahrani, Mesfer Mohammad (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2020.11.17
  • Accepted : 2020.12.20
  • Published : 2021.04.25
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Abstract

The interest of this work is the analysis of the effect of porosity on the nonlinear thermal stability response of power law functionally graded beam with various boundary conditions. The modelling was done according to the Euler-Bernoulli beam model where the distribution of material properties is imitated polynomial function. The thermal loads are assumed to be not only uniform but linear as well non-linear and the temperature rises through the thickness direction. The effects of the porosity parameter, slenderness ratio and power law index on the thermal buckling of P-FG beam are discussed.

Keywords

References

  1. Abdulrazzaq, M.A. Kadhim, Z.D., Faleh, N.M. and Moustafa, N.M. (2020a), "A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads", Struct. Monitor. Maint., 7(1), 27-42. https://doi.org/10.12989/smm.2020.7.1.027
  2. Abdulrazzaq, M.A., Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020b), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos. Struct., Int. J., 35(1), 147-157. https://doi.org/10.12989/scs.2020.35.1.147
  3. Abrate, S. (2008), "Functionally graded plates behave like homogeneous plates", Compos. Part B, 39(1), 151-158. https://doi.org/10.1016/j.compositesb.2007.02.026
  4. Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B-Eng., 96, 136-152. https://doi.org/10.1016/j.compositesb.2016.04.035
  5. 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
  6. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta Mechanica, 224(9), 2185-2201. https://doi.org/10.1007/s00707-013-0883-5
  7. Arefi, M. (2015a), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., Int. J., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659
  8. Arefi, M. (2015b), "Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation", Smart Struct. Syst., Int. J., 16(1), 195-211. https://doi.org/10.12989/sss.2015.16.1.195
  9. Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. J. Eng. Sci., 115, 73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011
  10. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  11. Boulal, A., Bensattalah, T., Karas, A., Zidour, M., Heireche, H. and Adda Bedia, E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle", Struct. Eng. Mech., Int. J., 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209
  12. Cao, Y., Musharavati, F., Baharom, S., Talebizadehsardari, P., Sebaey, T.A., Eyvazian, A. and Zain, A.M. (2020), "Vibration response of FG-CNT-reinforced plates covered by magnetic layer utilizing numerical solution", Steel Compos. Struct., Int. J., 37(2), 253-258. https://doi.org/10.12989/scs.2020.37.2.253
  13. Celebi, K., Yarimpabuc, D. and Keles, I. (2016), "A unified method for stresses in FGM sphere with exponentially-varying properties", Struct. Eng. Mech., Int. J., 57(5), 823-835. https://doi.org/10.12989/sem.2016.57.5.823
  14. Chami, K, Messafer, T. and Hadji, L. (2020), "Analytical modeling of bending and free vibration of thick advanced composite beams resting on Winkler-Pasternak elastic foundation", Earthq. Struct., Int. J., 19(2), 91-101. https://doi.org/10.12989/eas.2020.19.2.091
  15. Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052
  16. Chikh, A. (2019), "Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory", Strojnicky casopis-J. Mech. Eng., 69(4), 9-24. https://doi.org/10.2478/scjme-2019-0039
  17. Chikh, A. (2020), "Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations", Frattura ed Integrita Strutturale., 14(51), 115-126. https://doi.org/10.3221/IGF-ESIS.51.09
  18. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2020), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Composite Structures, 113216. https://doi.org/10.1016/j.compstruct.2020.113216
  19. Darabi, A. and Vosoughi, A.R. (2016), "Hybrid inverse method for small scale parameter estimation of FG nanobeams", Steel Compos. Struct., Int. J., 20(5), 1119-1131. https://doi.org/10.12989/scs.2016.20.5.1119
  20. Daraei, B., Shojaee, S. and Hamzehei-Javaran, S. (2020), "Free vibration analysis of axially moving laminated beams with axial tension based on 1D refined theories using Carrera unified formulation", Steel Compos. Struct., Int. J., 37(1), 37-49. https://doi.org/10.12989/scs.2020.37.1.037
  21. Ebrahimi, F. and Barati, M.R. (2016), "Thermal buckling analysis of size-dependent FG nanobeams based on the third-order shear deformation beam theory", Acta Mechanica Solida Sinica., 29(5), 547-554. https://doi.org/10.1016/s0894-9166(16)30272-5
  22. Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., Int. J., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837
  23. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions", J. Thermal Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  24. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccanica, 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y
  25. Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.A. (2014), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Comput., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072
  26. Fallah, A. and Aghdam, M.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. https://doi.org/10.1016/j.compositesb.2011.08.041
  27. Farokhian, A. and Salmani-Tehrani, M. (2020), "Surface and small scale effects on the dynamic buckling of carbon nanotubes with smart layers assuming structural damping", Steel Compos. Struct., Int. J., 37(2), 229-251. https://doi.org/10.12989/scs.2020.37.2.229
  28. Feldman, E. and Aboudi, J. (1997), "Buckling analysis of functionally graded plates subjected to uniaxial loading", Compos. Struct., 38(1-4), 29-36. https://doi.org/10.1016/s0263-8223(97)00038-x
  29. Fenjan, R.M., Moustafa, N.M. and Faleh, N.M. (2020), "Scale-dependent thermal vibration analysis of FG beams having porosities based on DQM", Adv. Nano Res., Int. J., 8(4), 283-292. https://doi.org/10.12989/anr.2020.8.4.283
  30. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., Int. J., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037
  31. Hadji, L. (2020a), "Vibration analysis of FGM beam: Effect of the micromechanical models", Coupl. Syst. Mech., Int. J., 9(3), 265-280. https://doi.org/10.12989/csm.2020.9.3.265
  32. Hadji, L. (2020b), "Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model", Smart Struct. Syst., Int. J., 26(2), 253-262. https://doi.org/10.12989/sss.2020.26.2.253
  33. Hadji, L. and Avcar, M. (2021), "Free Vibration Analysis of FG Porous Sandwich Plates under Various Boundary Conditions", J. Appl. Comput. Mech., 7(2), 505-519. https://doi.org/10.22055/JACM.2020.35328.2628
  34. Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., Int. J., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231
  35. Jabbari, M., Mojahedin, A., Khorshidvand, A.R. and Eslami, M.R. (2013), "Buckling analysis of a functionally graded thin circular plate made of saturated porous materials", J. Eng. Mech., 140(2), 287-295. https://doi.org/10.1061/(asce)em.1943-7889.0000663
  36. Jabbari, M., Hashemitaheri, M., Mojahedin, A. and Eslami, M.R. (2014), "Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials", J. Therm. Stress., 37(2), 202-220. https://doi.org/10.1080/01495739.2013.839768
  37. Javaheri, R. and Eslami, M.R. (2002), "Thermal buckling of functionally graded plates", AIAA J., 40(1), 162-169. https://doi.org/10.2514/2.1626
  38. 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
  39. Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016), "Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties", Adv. Mater. Res., 5(4), 205-221. https://doi.org/10.12989/amr.2016.5.4.205
  40. Karami, B., Shahsavari, D. and Janghorban, M. (2018), "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., 25(12), 1047-1057. https://doi.org/10.1080/15376494.2017.1323143
  41. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2019), "Influence of homogenization schemes on vibration of functionally graded curved microbeams", Compos. Struct., 216, 67-79. https://doi.org/10.1016/j.compstruct.2019.02.089
  42. Karami, B., Shahsavari, D., Ordookhani, A., Gheisari, P., Li, L. and Eyvazian, A. (2020), "Dynamics of graphene-nanoplatelets reinforced composite nanoplates including different boundary conditions", Steel Compos. Struct., Int. J., 36(6), 689-702. https://doi.org/10.12989/scs.2020.36.6.689
  43. Khadimallah, M.A. and Hussain, M. (2020), "Effect of power law index for vibration of armchair and zigzag single walled carbon nanotubes", Steel Compos. Struct., Int. J., 37(5), 621-632. https://doi.org/10.12989/scs.2020.37.5.621
  44. Kiani, Y. and Eslami, M.R. (2010), "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
  45. Levyakov, S.V. (2013), "Elastica solution for thermal bending of a functionally graded beam", Acta Mechanica, 224(8), 1731- 1740. https://doi.org/10.1007/s00707-013-0834-1
  46. Levyakov, S. (2015), "Thermal elastica of shear-deformable beam fabricated of functionally graded material", Acta Mechanica, 226(3), 723-733. https://doi.org/10.1007/s00707-014-1218-x
  47. Ma, L.S. and Lee, D.W. (2011), "A further discussion of nonlinear mechanical behavior for FGM beams under in-plane thermal loading", Compos. Struct., 93(2), 831-842. https://doi.org/10.1016/j.compstruct.2010.07.011
  48. Ma, L.S. and Lee, D.W. (2012), "Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading", Eur. J. Mech. - A/Solids, 31(1), 13-20. https://doi.org/10.1016/j.euromechsol.2011.06.016
  49. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., Int. J., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427
  50. Madenci, E. and Ozutok, A. (2020), "Variational approximate for high order bending analysis of laminated composite plates", Struct. Eng. Mech., Int. J., 73(1), 97-108. https://doi.org/10.12989/sem.2020.73.1.097
  51. Merzoug, M., Bourada, M., Sekkal, M., Ali Chaibdra, A., Belmokhtar, C., Benyoucef, S. and Benachour, A. (2020), "2D and quasi 3D computational models for thermoelastic bending of FG beams on variable elastic foundation: Effect of the micromechanical models", Geomech. Eng., Int. J., 22(4), 361-374. https://doi.org/10.12989/gae.2020.22.4.361
  52. Mohammadi, M., Saidi, A.R. and Jomehzadeh, E. (2010), "A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges", Mech. Eng. Sci., 224, 1831-1841. https://doi.org/10.1243/09544062jmes1804
  53. Najafizadeh, M.M. and Eslami, M.R. (2002), "First-Order-Theory-Based Thermo Elastic Stability of Functionally Graded Material Circular Plates", AIAA J., 40(7), 1444-1450. https://doi.org/10.2514/2.1807
  54. Najafizadeh, M.M. and Heydari, H.R. (2004), "Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory", Eur. J. Mech. - A/Solids, 23(6), 1085-1100. https://doi.org/10.1016/j.euromechsol.2004.08.004
  55. Nebab, M., Ait Atmane, H., Bennai, R. and Tahar, B. (2019), "Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory", Earthq. Struct., Int. J., 17(5), 447-462. https://doi.org/10.12989/eas.2019.17.5.447
  56. Nebab, M., Benguediab, S., Ait Atmane, H and Bernard, F. (2020), "A simple quasi-3D HDST for dynamic behavior of advanced composite plates with the effect of variables elastic foundations", Geomechanics and Engineering, 22(5), 415-431. DOI: http://dx.doi.org/10.12989/gae.2020.22.5.415
  57. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bachir Bouiadjra, R., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., Int. J., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065
  58. Rahmani, M., Mohammadi, Y., Kakavand, F. and Raeisifard, H. (2020), "Vibration analysis of different types of porous FG conical sandwich shells in various thermal surroundings", J. Appl. Computat. Mech., 6(3), 416-432. https://doi.org/10.22055/jacm.2019.29442.1598
  59. Ramteke, P.M., Panda, S.K. and Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., Int. J., 33(6), 865-875. https://doi.org/10.12989/scs.2019.33.6.865
  60. Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams Using an efficient shear deformation beam theory", Earthq. Struct., Int. J., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.3.329
  61. Selmi, A. (2020), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam", Smart Struct. Syst., Int. J., 26(3), 361-371. https://doi.org/10.12989/sss.2020.26.3.361
  62. She, G.-L., Liu, H.-B. and Karami, B. (2020), "On resonance behavior of porous FG curved nanobeams", Steel Compos. Struct., Int. J., 36(2), 179-186. https://doi.org/10.12989/scs.2020.36.2.179
  63. Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nuclear Eng. Des., 240(4), 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013
  64. Tabasi, H.M., Jam, J.E., Fard, K.M. and Beni, M.H. (2020), "Buckling and Free Vibration Analysis of Fiber Metal-laminated Plates Resting on Partial Elastic Foundation", J. Appl. Computat. Mech., 6(1), 37-51. https://doi.org/10.22055/jacm.2019.28156.1489
  65. Tayeb, T.S., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Bedia, E.A. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle", Adv. Nano Res., Int. J., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135
  66. Thanh, C.L., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput. https://doi.org/10.1007/s00366-020-01154-0
  67. Timesli, A. (2020), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, Int. J., 26(1), 53-62. https://doi.org/10.12989/cac.2020.26.1.053
  68. Ton-That, H.L. (2020), "Finite Element Analysis of Functionally Graded Skew Plates in Thermal Environment based on the New Third-order Shear Deformation Theory", J. Appl. Computat. Mech., 6(4), 1044-1057. https://doi.org/10.22055/jacm.2019.31508.1881
  69. Turan, M., Adiyaman, G., Kahya, V. and Birinci, A. (2016), "Axisymmetric analysis of a functionally graded layer resting on elastic substrate", Struct. Eng. Mech., Int. J., 58(3), 423-442. https://doi.org/10.12989/sem.2016.58.3.423
  70. Vinyas, M. (2020), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044
  71. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends GM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  72. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90(2), 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005

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