Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions

  • Barati, Mohammad Reza (Aerospace Engineering Department & Center of Excellence in Computational Aerospace, AmirKabir University of Technology) ;
  • Shahverdi, Hossein (Aerospace Engineering Department & Center of Excellence in Computational Aerospace, AmirKabir University of Technology)
  • Received : 2015.12.19
  • Accepted : 2016.09.30
  • Published : 2016.11.25
⟨ Previous Next ⟩

Abstract

In this paper, thermal vibration of a nonlocal functionally graded (FG) plates with arbitrary boundary conditions under linear and non-linear temperature fields is explored by developing a refined shear deformation plate theory with an inverse cotangential function in which shear deformation effect was involved without the need for shear correction factors. The material properties of FG nanoplate are considered to be temperature-dependent and graded in the thickness direction according to the Mori-Tanaka model. On the basis of non-classical higher order plate model and Eringen's nonlocal elasticity theory, the small size influence was captured. Numerical examples show the importance of non-uniform thermal loadings, boundary conditions, gradient index, nonlocal parameter and aspect and side-to-thickness ratio on vibrational responses of size-dependent FG nanoplates.

Keywords

References

  1. Ansari, R., Ashrafi, M.A., Pourashraf, T. and Sahmani, S. (2015), "Vibration and buckling characteristics of functionally graded nanoplates subjected to thermal loading based on surface elasticity theory", Acta. Astronautica, 109, 42-51. https://doi.org/10.1016/j.actaastro.2014.12.015
  2. Barati, M.R., Zenkour, A.M. and Shahverdi, H. (2016), "Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory", Compos. Struct., 141, 203-212. https://doi.org/10.1016/j.compstruct.2016.01.056
  3. Bouiadjra, R.B., Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  4. Bourada, M., Tounsi, A. and Houari, M.S.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33. https://doi.org/10.1177/1099636211426386
  5. Daneshmehr, A. and Rajabpoor, A. (2014), "Stability of size dependent functionally graded nanoplate based on nonlocal elasticity and higher order plate theories and different boundary conditions", Int. J. Eng. Sci., 82, 84-100. https://doi.org/10.1016/j.ijengsci.2014.04.017
  6. Ebrahimi, F. and Barati, M.R. (2016), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  7. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded sizedependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  8. 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
  9. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  10. Javaheri, R. and Eslami, M.R. (2002), "Thermal buckling of functionally graded plates based on higher order theory", J. Thermal. Stress., 25(7), 603-625. https://doi.org/10.1080/01495730290074333
  11. Jung, W.Y., Han, S.C. and Park, W.T. (2014), "A modified couple stress theory for buckling analysis of SFGM nanoplates embedded in Pasternak elastic medium", Compos. Part B: Eng., 60, 746-756. https://doi.org/10.1016/j.compositesb.2013.12.058
  12. Kim, S.E., Thai, H.T. and Lee, J. (2009), "A two variable refined plate theory for laminated composite plates", Compos. Struct., 89(2), 197-205. https://doi.org/10.1016/j.compstruct.2008.07.017
  13. Kulkarni, K., Singh, B.N. and Maiti, D.K. (2015), "Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory", Compos. Struct., 134, 147-157. https://doi.org/10.1016/j.compstruct.2015.08.060
  14. Mechab, I., Atmane, H.A., Tounsi, A. and Belhadj, H.A. (2010), "A two variable refined plate theory for the bending analysis of functionally graded plates", Acta Mechanica Sinica, 26(6), 941-949. https://doi.org/10.1007/s10409-010-0372-1
  15. Nami, M.R. and Janghorban, M. (2014), "Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant", Compos. Struct., 111, 349-353. https://doi.org/10.1016/j.compstruct.2014.01.012
  16. Narendar, S. (2011), "Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., 93(12), 3093-3103. https://doi.org/10.1016/j.compstruct.2011.06.028
  17. Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Comput. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031
  18. Shen, H.S. and Wang, H. (2015), "Nonlinear bending and postbuckling of FGM cylindrical panels subjected to combined loadings and resting on elastic foundations in thermal environments", Compos. Part B. Eng., 78, 202-213. https://doi.org/10.1016/j.compositesb.2015.03.078
  19. Shimpi, R. P. (2002), "Refined plate theory and its variants", AIAA J., 40(1), 137-146. https://doi.org/10.2514/2.1622
  20. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018
  21. Sobhy, M. (2014), "Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions", Acta. Mechanica, 225(9), 2521-2538. https://doi.org/10.1007/s00707-014-1093-5
  22. Sobhy, M. (2015a), "Levy-type solution for bending of single-layered graphene sheets in thermal environment using the two-variable plate theory", Int. J. Mech. Sci., 90, 171-178. https://doi.org/10.1016/j.ijmecsci.2014.11.014
  23. Sobhy, M. (2015b), "Hygrothermal deformation of orthotropic nanoplates based on the state-space concept", Compos. Part B. Eng., 79, 224-235. https://doi.org/10.1016/j.compositesb.2015.04.042
  24. Sobhy, M. (2015c), "A comprehensive study on FGM nanoplates embedded in an elastic medium", Compos. Struct., 134, 966-980. https://doi.org/10.1016/j.compstruct.2015.08.102
  25. Sobhy, M. (2016), "An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment", Int. J. Mech. Sci., 110, 62-77. https://doi.org/10.1016/j.ijmecsci.2016.03.003
  26. Ta, H.D. and Noh, H.C. (2015), "Analytical solution for the dynamic response of functionally graded rectangular plates resting on elastic foundation using a refined plate theory", Appl. Math. Model., 39(20), 6243-6257. https://doi.org/10.1016/j.apm.2015.01.062
  27. Thai, H.T. and Choi, D.H. (2011), "A refined plate theory for functionally graded plates resting on elastic foundation", Compos. Sci.Tech., 71(16), 1850-1858. https://doi.org/10.1016/j.compscitech.2011.08.016
  28. Thai, H.T. and Kim, S.E. (2012), "Levy-type solution for free vibration analysis of orthotropic plates based on two variable refined plate theory", Appl. Math. Model., 36(8), 3870-3882. https://doi.org/10.1016/j.apm.2011.11.003
  29. Touloukian Y.S. (1967), Thermo-physical Properties Research Center. Thermo-physical properties of high temperature solid materials, Vol. 1, Elements.-Pt. 1, Macmillan.
  30. Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aero. Sci. technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  31. Zare, M., Nazemnezhad, R. and Hosseini-Hashemi, S. (2015), "Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method", Meccanica, 50(9), 2391-2408. https://doi.org/10.1007/s11012-015-0161-9
  32. Zenkour, A.M. and Sobhy, M. (2011), "Thermal buckling of functionally graded plates resting on elastic foundations using the trigonometric theory", J. Thermal. Stress., 34(11), 1119-1138. https://doi.org/10.1080/01495739.2011.606017

Cited by

  1. Hygro-thermal vibration analysis of graded double-refined-nanoplate systems using hybrid nonlocal stress-strain gradient theory vol.176, 2017, https://doi.org/10.1016/j.compstruct.2017.06.004
  2. Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions vol.73, 2017, https://doi.org/10.1016/j.jfluidstructs.2017.06.007
  3. Vibration analysis of porous functionally graded nanoplates vol.120, 2017, https://doi.org/10.1016/j.ijengsci.2017.06.008
  4. Damping vibration behavior of visco-elastically coupled double-layered graphene sheets based on nonlocal strain gradient theory 2017, https://doi.org/10.1007/s00542-017-3529-z
  5. Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions vol.40, pp.2, 2018, https://doi.org/10.1007/s40430-018-0968-0
  6. Vibration analysis of multi-phase nanocrystalline material nanoshells using strain gradient elasticity vol.4, pp.10, 2017, https://doi.org/10.1088/2053-1591/aa89fb
  7. Vibration analysis of porous FG nanoshells with even and uneven porosity distributions using nonlocal strain gradient elasticity 2017, https://doi.org/10.1007/s00707-017-2032-z
  8. Dynamic analysis of graded small-scale shells with porosity distributions under transverse dynamic loads vol.133, pp.9, 2018, https://doi.org/10.1140/epjp/i2018-12152-5
  9. Thermal buckling analysis of laminated composite beams using hyperbolic refined shear deformation theory pp.1521-074X, 2019, https://doi.org/10.1080/01495739.2018.1461042
  10. Static behavior of thermally loaded multilayered Magneto-Electro-Elastic beam vol.63, pp.4, 2016, https://doi.org/10.12989/sem.2017.63.4.481
  11. A simple analytical approach for thermal buckling of thick functionally graded sandwich plates vol.63, pp.5, 2016, https://doi.org/10.12989/sem.2017.63.5.585
  12. An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities vol.13, pp.3, 2016, https://doi.org/10.12989/eas.2017.13.3.255
  13. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  14. Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory vol.20, pp.3, 2016, https://doi.org/10.12989/sss.2017.20.3.369
  15. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  16. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2016, https://doi.org/10.12989/sem.2017.64.2.145
  17. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  18. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  19. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  20. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2016, https://doi.org/10.12989/sem.2017.64.6.737
  21. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.693
  22. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.735
  23. Vibration characteristics of advanced nanoplates in humid-thermal environment incorporating surface elasticity effects via differential quadrature method vol.68, pp.1, 2016, https://doi.org/10.12989/sem.2018.68.1.131
  24. Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory vol.65, pp.5, 2016, https://doi.org/10.12989/sem.2018.65.5.621
  25. Improved HSDT accounting for effect of thickness stretching in advanced composite plates vol.66, pp.1, 2016, https://doi.org/10.12989/sem.2018.66.1.061
  26. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2016, https://doi.org/10.12989/gae.2018.14.6.519
  27. Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory vol.15, pp.1, 2016, https://doi.org/10.12989/gae.2018.15.1.711
  28. Three dimensional finite elements modeling of FGM plate bending using UMAT vol.66, pp.4, 2018, https://doi.org/10.12989/sem.2018.66.4.487
  29. Effect of homogenization models on stress analysis of functionally graded plates vol.67, pp.5, 2018, https://doi.org/10.12989/sem.2018.67.5.527
  30. Surface effects on nonlinear vibration and buckling analysis of embedded FG nanoplates via refined HOSDPT in hygrothermal environment considering physical neutral surface position vol.5, pp.6, 2016, https://doi.org/10.12989/aas.2018.5.6.691
  31. Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation vol.27, pp.5, 2018, https://doi.org/10.12989/was.2018.27.5.311
  32. Static buckling and vibration analysis of continuously graded ceramic-metal beams using a refined higher order shear deformation theory vol.15, pp.6, 2019, https://doi.org/10.1108/mmms-03-2019-0057
  33. Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.049
  34. A novel first order refined shear-deformation beam theory for vibration and buckling analysis of continuously graded beams vol.6, pp.3, 2016, https://doi.org/10.12989/aas.2019.6.3.189
  35. The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate vol.18, pp.2, 2016, https://doi.org/10.12989/gae.2019.18.2.161
  36. Analysis of static and dynamic characteristics of strain gradient shell structures made of porous nano-crystalline materials vol.8, pp.3, 2016, https://doi.org/10.12989/amr.2019.8.3.179
  37. Vibration analysis of nonlocal porous nanobeams made of functionally graded material vol.7, pp.5, 2019, https://doi.org/10.12989/anr.2019.7.5.351
  38. Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle vol.73, pp.2, 2016, https://doi.org/10.12989/sem.2020.73.2.209
  39. Dynamic characteristics of multi-phase crystalline porous shells with using strain gradient elasticity vol.8, pp.2, 2016, https://doi.org/10.12989/anr.2020.8.2.157
  40. Buckling response of functionally graded nanoplates under combined thermal and mechanical loadings vol.22, pp.4, 2020, https://doi.org/10.1007/s11051-020-04815-9
  41. Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory vol.8, pp.4, 2020, https://doi.org/10.12989/anr.2020.8.4.293
  42. Strain gradient based static stability analysis of composite crystalline shell structures having porosities vol.36, pp.6, 2016, https://doi.org/10.12989/scs.2020.36.6.631
  43. Nonlocal strain gradient shell theory for bending analysis of FG spherical nanoshells in thermal environment vol.135, pp.10, 2016, https://doi.org/10.1140/epjp/s13360-020-00796-9
  44. Nonlinear Dynamic Behavior of Porous and Imperfect Bernoulli-Euler Functionally Graded Nanobeams Resting on Winkler Elastic Foundation vol.8, pp.4, 2020, https://doi.org/10.3390/technologies8040056
  45. A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation vol.26, pp.None, 2021, https://doi.org/10.1016/j.csite.2021.101170
  46. New higher-order shear deformation theory for bending analysis of the two-dimensionally functionally graded nanoplates vol.235, pp.16, 2016, https://doi.org/10.1177/0954406220952816
  47. Hygro-thermal buckling of porous FG nanobeams considering surface effects vol.79, pp.3, 2021, https://doi.org/10.12989/sem.2021.79.3.359