Structural Engineering and Mechanics

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Hygro-thermal buckling of porous FG nanobeams considering surface effects

  • Li, Y.S. (College of Architecture and Civil Engineering, Guangdong University of Petrochemical Technology) ;
  • Liu, B.L. (College of Architecture and Civil Engineering, Guangdong University of Petrochemical Technology) ;
  • Zhang, J.J. (College of Mechanical and Equipment Engineering, Hebei University of Engineering)
  • Received : 2020.10.14
  • Accepted : 2021.06.11
  • Published : 2021.08.10
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Abstract

Hygro-thermal buckling of the porous FG nanobeam incorporating the surface effect is investigated. The even distribution of porosities is assumed in this paper. Various porous FG nanobeam models including classical beam theory (CBT), Timoshenko beam theory (TBT), Reddy beam theory (RBT), sinusoidal beam theory (SBT), hyperbolic beam theory (HBT) and exponential beam theory (EBT) are developed in this paper. The nonlocal strain gradient theory with material length scale and nonlocal parameters is adopted to examine the buckling behavior. The governing equations of the porous FG nanobeam are derived from principle of minimum potential energy. In the numerical examples, the effect of the nonlocal parameter, material length scale parameter, the temperature rise, the moisture concentration, surface effect, material gradient index, and porosity volume fraction on the buckling temperature and moisture are analyzed and discussed in detail. The results show that the stiffness of the beam depends on the relation of size between nonlocal parameter and length scale parameter. The paper will be helpful for the design and manufacture of the FG nanobeam under complex environments.

Keywords

Acknowledgement

This work is funded by National Natural Science Foundation of China (11572113), Natural Science Foundation of Hebei Province (A2018402158) and the Project of Introduction of Returned Overseas Chinese Scholar (C201805).

References

  1. Alzahrani, E.O., Zenkour, A.M. and Sobhy, M. (2013), "Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium", Compos. Struct., 105, 163-172. https://doi.org/10.1016/j.compstruct.2013.04.045.
  2. Aria, A.I. and Friswell, M.I. (2019), "Computational hygrothermal vibration and buckling analysis of functionally graded sandwich microbeams", Compos. B Eng., 165, 785-797. https://doi.org/10.1016/j.compositesb.2019.02.028.
  3. Baghani, M., Mohammadi, M. and Farajpour, A. (2016), "Dynamic and stability analysis of the rotating nanobeam in a nonuniform magnetic field considering the surface energy", Int. J. Appl. Mech., 8, 1650048. https://doi.org/10.1142/S1758825116500484.
  4. Barati, M.R. (2018), "A general nonlocal stress-strain gradient theory for forced vibration analysis of heterogeneous porous nanoplates", Eur. J. Mech. A/Solid., 67, 215-230. https://doi.org/10.1016/j.euromechsol.2017.09.001.
  5. Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., 60, 707-727. https://doi.org/10.12989/sem.2016.60.4.707.
  6. Barati, M.R. and Zenkour, A.M. (2019), "Analysis of postbuckling behavior of general higher-order functionally graded nanoplates with geometrical imperfection considering porosity distributions", Mech. Adv. Mater. Struct., 26, 1081-1088. https://doi.org/10.1080/15376494.2018.1430280.
  7. Brischetto, S. (2013), "Hygrothermoelastic analysis of multilayered composite and sandwich shells", J. Sandw. Struct. Mater., 15, 168-202. https://doi.org/10.1177/1099636212471358.
  8. Chakraborty, A., Gopalakrishnan, S. and Reddy, J.N. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45, 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4.
  9. Chang, W.J., Chen, T.C. and Weng, C.I. (1991), "Transient hygrothermal stresses in an infinitely long annular cylinder: coupling of heat and moisture", J. Therm. Stress., 14, 439-454. https://doi.org/10.1080/01495739108927078.
  10. 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.
  11. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aeros. Sci. Technol., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020.
  12. Ebrahimi, F. and Barati, M.R. (2016), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A, 122, 792. https://doi.org/10.1007/s00339-016-0322-2.
  13. Ebrahimi, F. and Jafari, A. (2018), "A four-variable refined shear-deformation beam theory for thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities", Mech. Adv. Mater. Struct., 25, 212-224. https://doi.org/10.1080/15376494.2016.1255820.
  14. Ebrahimi, F. and Salari. E. (2016), "Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams", Mech. Adv. Mater. Struct., 23, 1379-1397. https://doi.org/10.1080/15376494.2015.1091524.
  15. Emam, S. and Eltaher, M.A. (2016), "Buckling and postbuckling of composite beams in hygrothermal environments", Compos. Struct., 152, 665-675. https://doi.org/10.1016/j.compstruct.2016.05.029.
  16. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803.
  17. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibration of porous nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
  18. Fallah, A. and Aghdam, M.M. (2012), "Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation", Compos. B Eng., 43, 1523-1530. https://doi.org/10.1016/j.compositesb.2011.08.041.
  19. Farajpour, A., Farokhi, H. and Ghayesh, M.H. (2019), "Chaotic motion analysis of fluid-conveying viscoelastic nanotubes" Eur. J. Mech./A Solid., 74, 281-296. https://doi.org/10.1016/j.euromechsol.2018.11.012.
  20. Ghayesh, M.H. and Farajpour, A. (2020), "Nonlinear coupled mechanics of nanotubes incorporating both nonlocal and strain gradient effects", Mech. Adv. Mater. Struct., 27, 373-382. https://doi.org/10.1080/15376494.2018.1473537.
  21. Giunta, G., Belouettar, S. and Ferreira, A.J.M. (2016), "A static analysis of three-dimensional functionally graded beams by hierarchical modelling and a collocation meshless solution method", Acta Mech., 227, 969-991. https://doi.org/10.1007/s00707-015-1503-3.
  22. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Ration. Mech. Anal., 57, 291-323. https://doi.org/10.1007/BF00261375.
  23. Heshmati, M. and Daneshmand, F. (2018), "A study on the vibrational properties of weight-efficient plates made of material with functionally graded porosity", Compos. Struct., 200, 229-238. https://doi.org/10.1016/j.compstruct.2018.05.099.
  24. Heshmati, M. and Jalali, S.K. (2019), "Effect of radially graded porosity on the free vibration behavior of circular and annular sandwich plates", Eur. J. Mech. A/Solid., 74, 417-430. https://doi.org/10.1016/j.euromechsol.2018.12.009.
  25. Karamanli, A. and Aydogdu, M. (2019), "Size dependent flapwise vibration analysis of rotating two-directional functionally graded sandwich porous microbeams based on a transverse shear and normal deformation theory", Int. J. Mech. Sci., 159, 165-181. https://doi.org/10.1016/j.ijmecsci.2019.05.047.
  26. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2020), "Free vibration analysis of FG nanoplate with poriferous imperfection in hygrothermal environment", Struct. Eng. Mech., 73, 191-207. https://doi.org/10.12989/sem.2020.73.2.191.
  27. Ke, L.L., Yang, J., Kitipornchai, S. and Xiang, Y. (2009), "Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials", Mech. Adv. Mater. Struct., 16, 488-502. https://doi.org/10.1080/15376490902781175.
  28. Koizumi, M. (1997), "FGM activities in Japan", Compos. B Eng., 28, 1-4. https://doi.org/10.1016/s1359-8368(96)00016-9.
  29. Komai, K., Minoshima, K. and Shiroshita, S. (1991), "Hygrothermal degradation and fracture process of advanced fibre-reinforced plastics", Mater. Sci. Eng. A, 143, 155-166. https://doi.org/10.1016/0921-5093(91)90735-6.
  30. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solid., 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  31. Liu, Y.J., Su, S.K., Huang, H.W. and Liang, Y.J. (2019), "Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane", Compos. B Eng., 168, 236-242. https://doi.org/10.1016/j.compositesb.2018.12.063.
  32. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (1999), Functionally Graded Materials: Design, Processing and Applications, Springer, Boston, MA, USA.
  33. Muller, E., Drasar, C., Schilz, J. and Kaysser, W.A. (2003), "Functionally graded materials for sensor and energy applications", Mater. Sci. Eng. A, 362, 17-39. https://doi.org/10.1016/S0921-5093(03)00581-1
  34. Nguyen, T.K., Nguyen, B.D., Vo, T.P. and Thai, H.T. (2017), "Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams", Compos. Struct., 176, 1050-1060. https://doi.org/10.1016/j.compstruct.2017.06.036.
  35. Niino, M., Kisara, K. and Mori, M. (2005), "Feasibility study of FGM technology in space solar power systems (SSPS)", Mater. Sci. Forum, 492-493, 163-170. https://doi.org/10.4028/www.scientific.net/MSF.492-493.163.
  36. Polit, O., Anant, C., Anirudh, B. and Ganapathi, M. (2019), "Functionally graded graphene reinforced porous nanocomposite curved beams: bending and elastic stability using a higher-order model with thickness stretch effect", Compos. B Eng., 166, 310-327. https://doi.org/10.1016/j.compositesb.2018.11.074.
  37. Radic, N. (2018), "On buckling of porous double-layered FG nanoplates in the Pasternak elastic foundation based on nonlocal strain gradient elasticity", Compos. B Eng., 153, 465-479. https://doi.org/10.1016/j.compositesb.2018.09.014.
  38. Rossit, C.A., Bambill, D.V. and Gilardi, G.J. (2017), "Free vibrations of afg cantilever tapered beams carrying attached masses", Struct. Eng. Mech., 61, 685-691. https://doi.org/10.12989/sem.2017.61.5.685.
  39. Safarabadi, M., Mohammadi, M., Farajpour, A. and Goodarzi, M. (2015), "Effect of surface energy on the vibration analysis of rotating nanobeam", J. Solid Mech., 7, 299-311.
  40. Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory", Compos. Struct., 186, 68-78. https://doi.org/10.1016/j.compstruct.2017.11.082.
  41. Shafiei, N. and Kazemi, M. (2017), "Buckling analysis on the bi-dimensional functionally graded porous tapered nano/micro-scale beams", Aerosp. Sci. Technol., 66, 1-11. https://doi.org/10.1016/j.ast.2017.02.019.
  42. Sharma, J.N., Sharma, P.K. and Mishra, K.C. (2016), "Dynamic response of functionally graded cylinders due to time-dependent heat flux", Meccanica, 51, 139-154. https://doi.org/10.1007/s11012-015-0191-3.
  43. Shen, H.S. (2015), "Nonlinear analysis of functionally graded fiber reinforced composite laminated beams in hygrothermal environments, Part I: Theory and solutions", Compos. Struct., 125, 698-705. https://doi.org/10.1016/j.compstruct.2014.12.024.
  44. Shen, H.S. (2015), "Nonlinear analysis of functionally graded fiber reinforced composite laminated beams in hygrothermal environments, part ii: Numerical results", Compos. Struct., 125, 706-712. https://doi.org/10.1016/j.compstruct.2014.12.023.
  45. Simsek, M. and Kocaturk, T. (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90, 465-473. https://doi.org/10.1016/j.compstruct.2009.04.024.
  46. Thang, P.T., Nguyen, T.T., Lee, D.K., Kang, J.W. and Lee, J.H. (2018), "Elastic buckling and free vibration analyses of porous-cellular plates with uniform and non-uniform porosity distributions", Aeros. Sci. Technol., 79, 278-287. https://doi.org/10.1016/j.ast.2018.06.010.
  47. Tian, J.J., Zhang, Z.G. and Hua, H.X. (2019), "Free vibration analysis of rotating functionally graded double-tapered beam including porosities", Int. J. Mech. Sci., 150, 526-538. https://doi.org/10.1016/j.ijmecsci.2018.10.056.
  48. Wu, D., Liu, A., Huang, Y., Huang, Y., Pi, Y. and Gao, W. (2018), "Dynamic analysis of functionally graded porous structures through finite element analysis", Eng. Struct., 165, 287-301. https://doi.org/10.1016/j.engstruct.2018.03.023.
  49. Xue, Y.Q., Jin, G.Y., Ma, X.L., Chen, H.L., Ye, T.G., Chen, M.F. and Zhang, Y.T. (2019), "Free vibration analysis of porous plates with porosity distributions in the thickness and in-plane directions using isogeometric approach", Int. J. Mech. Sci., 152, 346-362. https://doi.org/10.1016/j.ijmecsci.2019.01.004.
  50. Zenkour, A.M. and Radwan, A.F. (2019), "Bending response of FG plates resting on elastic foundations in hygrothermal environment with porosities", Compos. Struct., 213, 133-143. https://doi.org/10.1016/j.compstruct.2019.01.065.
  51. Zhang, L.W., Zhu, P. and Liew, K.M. (2014), "Thermal buckling of functionally graded plates using a local Kriging meshless method", Compos. Struct., 108, 472-492. https://doi.org/10.1016/j.compstruct.2013.09.043.