DOI QR코드

DOI QR Code

Nonlocal buckling characteristics of heterogeneous plates subjected to various loadings

  • Ebrahimi, Farzad (Department of Engineering, Imam Khomeini international university) ;
  • Babaei, Ramin (Department of Engineering, Imam Khomeini international university) ;
  • Shaghaghi, Gholam Reza (Department of Engineering, Imam Khomeini international university)
  • 투고 : 2017.06.23
  • 심사 : 2017.12.26
  • 발행 : 2018.09.25

초록

In this manuscript, buckling response of the functionally graded material (FGM) nanoplate is investigated. Two opposite edges of nanoplate is under linear and nonlinear varying normal stresses. The small-scale effect is considered by Eringen's nonlocal theory. Governing equation are derived by nonlocal theory and Hamilton's principle. Navier's method is used to solve governing equation in simply boundary conditions. The obtained results exactly match the available results in the literature. The results of this research show the important role of nonlocal effect in buckling and stability behavior of nanoplates. In order to study the FG-index effect and different loading condition effects on buckling of rectangular nanoplate, Navier's method is applied and results are presented in various figures and tables.

키워드

참고문헌

  1. Aksencer, T. and Aydogdu, M. (2011), "Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory", Physica E: Low-dimensional Syst. Nanostruct., 43(4), 954-959. https://doi.org/10.1016/j.physe.2010.11.024
  2. Analooei, H., Azhari, M. and Heidarpour, A. (2013), "Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method", Appl. Math. Modelling, 37(10-11), 6703-6717.
  3. Ansari, R., Ashrafi, M., Pourashraf, T. and Sahmani, S. (2015a), "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
  4. Ansari, R., Shojaei, M.F., Shahabodini, A. and Bazdid-Vahdati, M. (2015b), "Three-dimensional bending and vibration analysis of functionally graded nanoplates by a novel differential quadrature-based approach", Composite Struct., 131, 753-764. https://doi.org/10.1016/j.compstruct.2015.06.027
  5. Bedroud, M., Nazemnezhad, R. and Hosseini-Hashemi, S. (2015), "Axisymmetric/asymmetric buckling of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity", Meccanica, 50(7), 1791-1806. https://doi.org/10.1007/s11012-015-0123-2
  6. Cheng, C.H. and Chen, T. (2015), "Size-dependent resonance and buckling behavior of nanoplates with high-order surface stress effects", Physica E: Low-dimensional Syst. Nanostruct., 67, 12-17. https://doi.org/10.1016/j.physe.2014.10.040
  7. Daneshmehr, A., Rajabpoor, A. and Hadi, A. (2015), "Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories", J. Eng. Sci., 95, 23-35. https://doi.org/10.1016/j.ijengsci.2015.05.011
  8. Farajpour, A., Danesh, M. and Mohammadi, M. (2011), "Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics", Physica E: Low-dimensional Syst. Nanostruct., 44(3), 719-727. https://doi.org/10.1016/j.physe.2011.11.022
  9. Farajpour, A., Shahidi, A., Mohammadi, M. and Mahzoon, M. (2012), "Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics", Composite Struct., 94(5), 1605-1615. https://doi.org/10.1016/j.compstruct.2011.12.032
  10. Li, L. and Hu, Y. (2017), "Torsional vibration of bi-directional functionally graded nanotubes based on nonlocal elasticity theory", Composite Struct., 172, 242-250. https://doi.org/10.1016/j.compstruct.2017.03.097
  11. Li, L., Li, X. and Hu, Y. (2018), "Nonlinear bending of a two-dimensionally functionally graded beam", Composite Struct., 184, 1049-1061. https://doi.org/10.1016/j.compstruct.2017.10.087
  12. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metallurgica, 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  13. Naderi, A. and Saidi, A. (2013), "Modified nonlocal mindlin plate theory for buckling analysis of nanoplates", J. Nanomech. Micromech., 4(4), A4013015. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000068
  14. 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
  15. Nguyen, N.T., Hui, D., Lee, J. and Nguyen-Xuan, H. (2015), "An efficient computational approach for sizedependent analysis of functionally graded nanoplates", Comput. Methods Appl. Mech. Eng., 297, 191-218. https://doi.org/10.1016/j.cma.2015.07.021
  16. Park, J.S. and Kim, J.H. (2006), "Thermal postbuckling and vibration analyses of functionally graded plates", J. Sound Vib. 289(1-2), 77-93. https://doi.org/10.1016/j.jsv.2005.01.031
  17. Pradhan, S. (2012), "Buckling analysis and small scale effect of biaxially compressed graphene sheets using non-local elasticity theory", Sadhana, 37(4), 461-480. https://doi.org/10.1007/s12046-012-0088-y
  18. Pradhan, S. and Kumar, A. (2011), "Buckling analysis of single layered graphene sheet under biaxial compression using nonlocal elasticity theory and DQ method", J. Comput. Theoretical Nanosci., 8(7), 1325-1334. https://doi.org/10.1166/jctn.2011.1818
  19. Pradhan, S. and Murmu, T. (2009), "Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics", Comput. Mater. Sci., 47(1), 268-274. https://doi.org/10.1016/j.commatsci.2009.08.001
  20. Pradhan, S. and Murmu, T. (2010). "Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory", Physica E: Low-dimensional Syst. Nanostruct., 42(5), 1293-1301. https://doi.org/10.1016/j.physe.2009.10.053
  21. Pradhan, S. and Phadikar, J. (2011), "Nonlocal theory for buckling of nanoplates", J. Struct. Stability Dynam., 11(3), 411-429. https://doi.org/10.1142/S021945541100418X
  22. Salehipour, H., Nahvi, H. and Shahidi, A. (2015a), "Exact analytical solution for free vibration of functionally graded micro/nanoplates via three-dimensional nonlocal elasticity", Physica E: Lowdimensional Syst. Nanostruct., 66, 350-358. https://doi.org/10.1016/j.physe.2014.10.001
  23. Salehipour, H., Nahvi, H. and Shahidi, A. (2015b), "Exact closed-form free vibration analysis for functionally graded micro/nano plates based on modified couple stress and three-dimensional elasticity theories", Composite Struct., 124, 283-291. https://doi.org/10.1016/j.compstruct.2015.01.015
  24. Samaei, A., Abbasion, S. and Mirsayar, M. (2011), "Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory", Mech. Res. Commun., 38(7), 481-485. https://doi.org/10.1016/j.mechrescom.2011.06.003
  25. 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
  26. Zhu, X. and Li, L. (2017a), "Twisting statics of functionally graded nanotubes using Eringen's nonlocal integral model", Composite Struct., 178, 87-96. https://doi.org/10.1016/j.compstruct.2017.06.067
  27. Zhu, X. and Li, L. (2017b), "Longitudinal and torsional vibrations of size-dependent rods via nonlocal integral elasticity", J. Mech. Sci., 133, 639-650. https://doi.org/10.1016/j.ijmecsci.2017.09.030
  28. Zhu, X. and Li, L. (2017c), "Closed form solution for a nonlocal strain gradient rod in tension", J. Eng. Sci., 119, 16-28. https://doi.org/10.1016/j.ijengsci.2017.06.019