Steel and Composite Structures

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Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation

  • Karami, Behrouz (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Shahsavari, Davood (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Nazemosadat, Seyed Mohammad Reza (Sama Technical and Vocational Training College, Islamic Azad University) ;
  • Li, Li (State Key Lab of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology) ;
  • Ebrahimi, Arash (Faculty of Computer Science and Electrical Engineering, University of Rostock)
  • Received : 2018.04.03
  • Accepted : 2018.09.25
  • Published : 2018.11.10
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Abstract

Thermal buckling behavior of porous functionally graded nanobeam integrated with piezoelectric sensor and actuator based on the nonlocal higher-order shear deformation beam theory is investigated for the first time. Its material properties are assumed to be temperature-dependent and varying along the thickness direction according to the modified power-law rule. Note that the porosity with even type is considered herein. The equations of motion are obtained through Hamilton's principle. The influences of several parameters (such as type of temperature distribution, external electric voltage, material composition, porosity, small-scale effect, Ker foundation parameters, and beam thickness) on the thermal buckling of FG nanobeam are investigated in detail.

Keywords

References

  1. Ansari, R., Pourashraf, T., Gholami, R. and Shahabodini, A. (2016), "Analytical solution for nonlinear postbuckling of functionally graded carbon nanotube-reinforced composite shells with piezoelectric layers", Compos. Part B: Eng., 90, 267-277. https://doi.org/10.1016/j.compositesb.2015.12.012
  2. Arash, B. and Wang, Q. (2012), "A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes", Computat. Mater. Sci., 51(1), 303-313. https://doi.org/10.1016/j.commatsci.2011.07.040
  3. Atmane, H.A., Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x
  4. Barati, M.R. and Zenkour, A.M. (2017), "Investigating postbuckling of geometrically imperfect metal foam nanobeams with symmetric and asymmetric porosity distributions", Compos. Struct., 182, 91-98. https://doi.org/10.1016/j.compstruct.2017.09.008
  5. Barati, M.R., Shahverdi, H. and Zenkour, A.M. (2017), "Electromechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory", Mech. Adv. Mater. Struct., 24(12), 987-998. https://doi.org/10.1080/15376494.2016.1196799
  6. Barretta, R., Feo, L., Luciano, R. and de Sciarra, F.M. (2016), "Application of an enhanced version of the Eringen differential model to nanotechnology", Compos. Part B: Eng., 96, 274-280. https://doi.org/10.1016/j.compositesb.2016.04.023
  7. Barretta, R., Diaco, M., Feo, L., Luciano, R., de Sciarra, F.M. and Penna, R. (2018a), "Stress-driven integral elastic theory for torsion of nano-beams", Mechanics Research Communications, 87, 35-41. https://doi.org/10.1016/j.mechrescom.2017.11.004
  8. Barretta, R., Canadija, M., Luciano, R. and de Sciarra, F.M. (2018b), "Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams", Int. J. Eng. Sci., 126, 53-67. https://doi.org/10.1016/j.ijengsci.2018.02.012
  9. Challamel, N. and Wang, C. (2008), "The small length scale effect for a non-local cantilever beam: a paradox solved", Nanotech., 19(34), 345703. https://doi.org/10.1088/0957-4484/19/34/345703
  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. Dai, H.-L., Rao, Y.-N. and Dai, T. (2016), "A review of recent researches on FGM cylindrical structures under coupled physical interactions, 2000-2015", Compos. Struct., 152, 199-225. https://doi.org/10.1016/j.compstruct.2016.05.042
  12. Ebrahimi, F. and Daman, M. (2017), "Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment", Struct. Eng. Mech., Int. J., 64(1), 121-133.
  13. Ebrahimi, F. and Barati, M.R. (2017), "Porosity-dependent vibration analysis of piezo-magnetically actuated heterogeneous nanobeams", Mech. Syst. Signal Process., 93, 445-459. https://doi.org/10.1016/j.ymssp.2017.02.021
  14. Eltaher, M., Emam, S.A. and Mahmoud, F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Computat., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  15. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803
  16. Ghorbanpour Arani, A., Mosayyebi, M., Kolahdouzan, F., Kolahchi, R. and Jamali, M. (2017), "Refined zigzag theory for vibration analysis of viscoelastic functionally graded carbon nanotube reinforced composite microplates integrated with piezoelectric layers", Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 231(13), 2464-2478. https://doi.org/10.1177/0954410016667150
  17. Gupta, A. and Talha, M. (2017), "Influence of Porosity on the Flexural and Free Vibration Responses of Functionally Graded Plates in Thermal Environment", Int. J. Struct. Stabil. Dyn., 1850013.
  18. Hu, Y.G., Liew, K.M., Wang, Q., He, X.Q. and Yakobson, B.I. (2008), "Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes", J. Mech. Phys. Solids, 56(12), 3475-3485. https://doi.org/10.1016/j.jmps.2008.08.010
  19. Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Modern Phys. Lett. B, 30(36), 1650421. https://doi.org/10.1142/S0217984916504212
  20. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., Int. J., 25(3), 361-374.
  21. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018a), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., Int. J., 28(1), 99-110.
  22. Karami, B., Shahsavari, D., Karami, M. and Li, L. (2018b), "Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 0954406218781680.
  23. Karami, B., Shahsavari, D. and Li, L. (2018c), "Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimensional Syst. Nanostruct., 97, 317-327. https://doi.org/10.1016/j.physe.2017.11.020
  24. Karami, B., Janghorban, M. and Tounsi, A. (2018d), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., Int. J., 27(2), 201-216.
  25. Karami, B., Janghorban, M. and Li, L. (2018e), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronautica, 143, 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011
  26. Karami, B., Shahsavari, D. and Li, L. (2018f), "Temperaturedependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Therm. Stress., 41(4), 483-499. https://doi.org/10.1080/01495739.2017.1393781
  27. Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2018g), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.
  28. Karami, B., Janghorban, M. and Tounsi, A. (2018h), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025
  29. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2018i), "Wave dispersion of mounted graphene with initial stress", Thin-Wall. Struct., 122, 102-111. https://doi.org/10.1016/j.tws.2017.10.004
  30. Karami, B., Shahsavari, D. and Janghorban, M. (2018j), "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
  31. Khdeir, A. and Reddy, J. (1999), "Free vibrations of laminated composite plates using second-order shear deformation theory", Comput. Struct., 71(6), 617-626. https://doi.org/10.1016/S0045-7949(98)00301-0
  32. Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., Int. J., 64(4), 391-402.
  33. Kneifati, M.C. (1985), "Analysis of plates on a Kerr foundation model", J. Eng. Mech., 111(11), 1325-1342. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:11(1325)
  34. Kolahchi, R., Safari, M. and Esmailpour, M. (2016), "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
  35. Li, L. and Hu, Y. (2017a), "Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects", Int. J. Mech. Sci., 120, 159-170. https://doi.org/10.1016/j.ijmecsci.2016.11.025
  36. Li, L. and Hu, Y. (2017b), "Torsional vibration of bi-directional functionally graded nanotubes based on nonlocal elasticity theory", Compos. Struct., 172, 242-250. https://doi.org/10.1016/j.compstruct.2017.03.097
  37. Li, J.F., Takagi, K., Ono, M., Pan, W., Watanabe, R., Almajid, A. and Taya, M. (2003), "Fabrication and evaluation of porous piezoelectric ceramics and porosity-graded piezoelectric actuators", J. Am. Ceramic Soc., 86(7), 1094-1098. https://doi.org/10.1111/j.1151-2916.2003.tb03430.x
  38. Li, C., Yao, L., Chen, W. and Li, S. (2015), "Comments on nonlocal effects in nano-cantilever beams", Int. J. Eng. Sci., 87, 47-57. https://doi.org/10.1016/j.ijengsci.2014.11.006
  39. Li, L., Tang, H. and Hu, Y. (2018), "Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature", Compos. Struct., 184, 1177-1188. https://doi.org/10.1016/j.compstruct.2017.10.052
  40. Lim, C.W., Li, C. and Yu, J.-l. (2010), "Free vibration of pretensioned nanobeams based on nonlocal stress theory", J. Zhejiang Univ.-SCIENCE A, 11(1), 34-42. https://doi.org/10.1631/jzus.A0900048
  41. Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, B. B. (2016a), "Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories", J. Brazil. Soc. Mech. Sci. Eng., 38(8), 2193-2211. https://doi.org/10.1007/s40430-015-0482-6
  42. Mechab, B., Mechab, I., Benaissa, S., Ameri, M. and Serier, B. (2016b), "Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler-Pasternak elastic foundations", Appl. Math. Model., 40(2), 738-749. https://doi.org/10.1016/j.apm.2015.09.093
  43. Mirzavand, B. and Eslami, M. (2011), "A closed-form solution for thermal buckling of piezoelectric FGM rectangular plates with temperature-dependent properties", Acta Mechanica, 218(1), 87-101. https://doi.org/10.1007/s00707-010-0402-x
  44. Murmu, T. and Adhikari, S. (2012), "Nonlocal frequency analysis of nanoscale biosensors", Sensors and Actuators A: Physical, 173(1), 41-48. https://doi.org/10.1016/j.sna.2011.10.012
  45. 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
  46. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41(3), 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  47. Pradhan, S. and Murmu, T. (2010), "Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever", Physica E: Low-dimensional Syst. Nanostruct., 42(7), 1944-1949. https://doi.org/10.1016/j.physe.2010.03.004
  48. Pradhan, S. and Kumar, A. (2011), "Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method", Compos. Struct., 93(2), 774-779. https://doi.org/10.1016/j.compstruct.2010.08.004
  49. Rad, A.B. and Shariyat, M. (2015), "Three-dimensional magnetoelastic analysis of asymmetric variable thickness porous FGM circular plates with non-uniform tractions and Kerr elastic foundations", Compos. Struct., 125, 558-574. https://doi.org/10.1016/j.compstruct.2015.02.049
  50. Romano, G. and Barretta, R. (2017), "Nonlocal elasticity in nanobeams: the stress-driven integral model", Int. J. Eng. Sci., 115, 14-27. https://doi.org/10.1016/j.ijengsci.2017.03.002
  51. Romano, G., Barretta, R., Diaco, M. and de Sciarra, F.M. (2017a), "Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams", Int. J. Mech. Sci., 121, 151-156. https://doi.org/10.1016/j.ijmecsci.2016.10.036
  52. Romano, G., Barretta, R. and Diaco, M. (2017b), "On nonlocal integral models for elastic nano-beams", Int. J. Mech. Sci., 131, 490-499.
  53. Romano, G., Luciano, R., Barretta, R. and Diaco, M. (2018), "Nonlocal integral elasticity in nanostructures, mixtures, boundary effects and limit behaviours", Continuum Mech. Thermodyn., 30, 641-655. https://doi.org/10.1007/s00161-018-0631-0
  54. Rouzegar, J. and Abad, F. (2015), "Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory", Thin-Wall. Struct., 89, 76-83. https://doi.org/10.1016/j.tws.2014.12.010
  55. Shafiei, N. and Kazemi, M. (2017), "Nonlinear buckling of functionally graded nano-/micro-scaled porous beams", Compos. Struct., 178, 483-492. https://doi.org/10.1016/j.compstruct.2017.07.045
  56. Shafiei, N., Mousavi, A. and Ghadiri, M. (2016), "On sizedependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams", Int. J. Eng. Sci., 106, 42-56. https://doi.org/10.1016/j.ijengsci.2016.05.007
  57. Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Brazil. Soc. Mech. Sci. Eng., 39(10), 3849-3861. https://doi.org/10.1007/s40430-017-0863-0
  58. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2017a), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol.
  59. Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017b), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Express, 4(8), 085013. https://doi.org/10.1088/2053-1591/aa7d89
  60. Shahsavari, D., Karami, B., Fahham, H.R. and Li, L. (2018a), "On the shear buckling of porous nanoplates using a new sizedependent quasi-3D shear deformation theory", Acta Mechanica, 1-25.
  61. Shahsavari, D., Karami, B. and Mansouri, S. (2018b), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech.-A/Solids, 67, 200-214. https://doi.org/10.1016/j.euromechsol.2017.09.004
  62. 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
  63. 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
  64. She, G.-L., Yuan, F.-G., Ren, Y.-R. and Xiao, W.-S. (2017c), "On buckling and postbuckling behavior of nanotubes", Int. J. Eng. Sci., 121, 130-142. https://doi.org/10.1016/j.ijengsci.2017.09.005
  65. She, G.-L., Yuan, F.-G., Ren, Y.-R., Liu, H.-B. and Xiao, W.-S. (2018a), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063
  66. She, G.-L., Ren, Y.-R., Yuan, F.-G. and Xiao, W.-S. (2018b), "On vibrations of porous nanotubes", Int. J. Eng. Sci., 125, 23-35. https://doi.org/10.1016/j.ijengsci.2017.12.009
  67. She, G.-L., Yuan, F.-G. and Ren, Y.-R. (2018c), "On wave propagation of porous nanotubes", Int. J. Eng. Sci., 130, 62-74. https://doi.org/10.1016/j.ijengsci.2018.05.002
  68. She, G.-L., Ren, Y.-R., Xiao, W.-S. and Liu, H. (2018d), "Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations", Struct. Eng. Mech., Int. J., 66(6), 729-736.
  69. She, G.-L., Yan, K.-M., Zhang, Y.-L., Liu, H.-B. and Ren, Y.-R. (2018e), "Wave propagation of functionally graded porous nanobeams based on nonlocal strain gradient theory", Eur. Phys. J. Plus, 133(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5
  70. Sobhy, M. (2017), "Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory", Struct. Eng. Mech., Int. J., 63(3), 401-415.
  71. Touloukian, Y. and Buyco, E. (1970), Thermophysical Properties of Matter, The TPRC Data Series, Specific Heat of Metallic Elements and Alloys, (Volume 4), and Specific Heat of Nonmetallic Solids, (Volume 5), IFI: Plenum, New York, NY, USA.
  72. Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  73. Wang, C. and Duan, W. (2008), "Free vibration of nanorings/arches based on nonlocal elasticity", J. Appl. Phys., 104(1), 014303. https://doi.org/10.1063/1.2951642
  74. Wang, L. and Hu, H. (2008), "Flexural Wave Propagation in Single-Walled Carbon Nanotubes", J. Computat. Theor. Nanosci., 5(4), 581-586. https://doi.org/10.1166/jctn.2008.019
  75. Wang, Q. and Wang, C.M. (2007), "The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes", Nanotechnology, 18(7), 075702. https://doi.org/10.1088/0957-4484/18/7/075702
  76. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  77. Yahia, S.A., Atmane, H.A., 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
  78. Yang, H. and Yu, L. (2017), "Feature extraction of wood-hole defects using wavelet-based ultrasonic testing", J. Forest. Res., 28(2), 395-402. https://doi.org/10.1007/s11676-016-0297-z
  79. Yang, J., Ke, L. and Kitipornchai, S. (2010), "Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", Physica E: Low-dimensional Syst. Nanostruct., 42(5), 1727-1735. https://doi.org/10.1016/j.physe.2010.01.035
  80. Zhu, X. and Li, L. (2017a), "Closed form solution for a nonlocal strain gradient rod in tension", Int. J. Eng. Sci., 119, 16-28. https://doi.org/10.1016/j.ijengsci.2017.06.019
  81. Zhu, X. and Li, L. (2017b), "Twisting statics of functionally graded nanotubes using Eringen's nonlocal integral model", Compos. Struct., 178, 87-96. https://doi.org/10.1016/j.compstruct.2017.06.067
  82. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO 2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68(1), 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2

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