Steel and Composite Structures

  • 제33권2호
  • /
  • Pages.307-318
  • /
  • 2019
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear bending analysis of porous FG thick annular/circular nanoplate based on modified couple stress and two-variable shear deformation theory using GDQM

  • 투고 : 2019.06.30
  • 심사 : 2019.09.27
  • 발행 : 2019.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

This is the first attempt to consider the nonlinear bending analysis of porous functionally graded (FG) thick annular and circular nanoplates resting on Kerr foundation. The size effects are captured based on modified couple stress theory (MCST). The material properties of the porous FG nanostructure are assumed to vary smoothly through the thickness according to a power law distribution of the volume fraction of the constituent materials. The elastic medium is modeled by Kerr elastic foundation which consists of two spring layers and one shear layer. The governing equations are extracted based on Hamilton's principle and two variables refined plate theory. Utilizing generalized differential quadrature method (GDQM), the nonlinear static behavior of the nanostructure is obtained under different boundary conditions. The effects of various parameters such as material length scale parameter, boundary conditions, and geometrical parameters of the nanoplate, elastic medium constants, porosity and FG index are shown on the nonlinear deflection of the annular and circular nanoplates. The results indicate that with increasing the material length scale parameter, the nonlinear deflection is decreased. In addition, the dimensionless nonlinear deflection of the porous annular nanoplate is diminished with the increase of porosity parameter. It is hoped that the present work may provide a benchmark in the study of nonlinear static behavior of porous nanoplates.

키워드

참고문헌

  1. Abbasi, S., Farhatnia, F. and Jazi, S.R. (2014), "A semi-analytical solution on static analysis of circular plate exposed to nonuniform axisymmetric transverse loading resting on Winkler elastic foundation", Arch. Civil Mech. Eng., 14, 476-488. https://doi.org/10.1016/j.acme.2013.09.007
  2. Alibeigloo, A. (2018), "Thermo elasticity solution of functionally graded, solid, circular, and annular plates integrated with piezoelectric layers using the differential quadrature method", Mech. Advan. Mater. Struct., 25, 766-784. https://doi.org/10.1080/15376494.2017.1308585
  3. Asemi, S.R., Farajpour, A., Asemi, H.R. and Mohammadi, M. (2014), "Influence of initial stress on the vibration of doublepiezoelectric-nanoplate systems with various boundary conditions using DQM", Physica E, 63, 169-179. https://doi.org/10.1016/j.physe.2014.05.009
  4. Barati, M.R. (2017a), "Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities", Adv. Nano Struct., Int. J., 5, 393-414. https://doi.org/10.12989/anr.2017.5.4.393
  5. Barati, M.R. (2017b), "Nonlocal microstructure-dependent dynamic stability of refined porous FG nanoplates in hygrothermal environments", Eur. Phys. J. Plus, 132, 434-444. https://doi.org/10.1140/epjp/i2017-11686-2
  6. Bahrami, A. and Teimourian, A. (2017), "Small scale effect on vibration and wave power reflection in circular annular nanoplates", Compos. Part B: Eng., 109, 214-226. https://doi.org/10.1016/j.compositesb.2016.09.107
  7. Bedroud, M., Nazemnezhad, R., Hosseini-Hashemi, Sh. and Valixani, M. (2016), "Buckling of FG circular/annular Mindlin nanoplates with an internal ring support using nonlocal elasticity", Appl. Math. Model., 40, 3185-3210. https://doi.org/10.1016/j.apm.2015.09.003
  8. Bellman, R. and Casti, J. (1971), "Differential quadrature and long-term integration", J. Math. Anal. Appl., 34, 235-238. https://doi.org/10.1016/0022-247X(71)90110-7
  9. Chakraverty, S. and Behera, L. (2016), Static and Dynamic Problems of nanobeams and nanoplates, National Institute of Technology Rourkela, India.
  10. Chan, D.Q., Anh, V.T.T. and Duc, N.D. (2019), "Vibration and nonlinear dynamic response of eccentrically stiffened functionally graded composite truncated conical shells in thermal environments", Acta Mech., 230, 157-178. https://doi.org/10.1007/s00707-018-2282-4
  11. Dastjerdi, Sh., Jabbarzadeh, M. and Aliabadi, Sh. (2016), "Nonlinear static analysis of single layer annular/circular graphene sheets embedded in Winkler-Pasternak elastic matrix based on non-local theory of Eringen", Ain Shams Eng. J., 7, 873-884. https://doi.org/10.1007/s00707-018-2282-4
  12. Duc, N.D. (2013), "Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation", Compos. Struct., 99, 88-96. https://doi.org/10.1016/j.compstruct.2012.11.017
  13. Duc, N.D. (2016), "Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory", Eur. J. Mech. - A/Solids, 58, 10-30. https://doi.org/10.1016/j.euromechsol.2016.01.004
  14. Duc, N.D., Khoa, N.D. and Thiem, H.T. (2018), "Nonlinear thermo-mechanical response of eccentrically stiffened Sigmoid FGM circular cylindrical shells subjected to compressive and uniform radial loads using the Reddy's third-order shear deformation shell theory", Mech. Adv. Mater. Struct., 25, 1157-1167. https://doi.org/10.1080/15376494.2017.1341581
  15. Ebrahimi, F. and Heidari, E. (2017), "Surface effects on nonlinear vibration of embedded functionally graded nanoplates via higher order shear deformation plate theory", Mech. Adv. Mat. Struct., 26(8), 671-699. https://doi.org/10.1080/15376494.2017.1410908
  16. Ebrahimi, F. and Heidari, E. (2018), "Vibration characteristics of advanced nanoplates in humid-thermal environment incorporating surface elasticity effects via differential quadrature method", Struct. Eng. Mech., Int. J., 68(1), 131-157. https://doi.org/10.12989/sem.2018.68.1.131
  17. Farhatnia, F., Ghanbari-Mobarakeh, M., Rasouli-Jazi, S. and Oveissi, S. (2017), "Thermal buckling analysis of functionally graded circular plate resting on the pasternak elastic foundation via the differential transform method", Facta Universitatis, Series: Mech. Eng., 15, 545-563. https://doi.org/10.22190/FUME170104004F
  18. Farhatnia, F., Babaei, J. and Foroudastan, R. (2018), "Thermo-Mechanical nonlinear bending analysis of functionally graded thick circular plates resting on Winkler foundation based on sinusoidal shear deformation theory", Arab. J. Sci. Eng., 43, 1137-1151. https://doi.org/10.1007/s13369-017-2753-2
  19. Ghadiri, M., Shafiei, N. and Alavi, H. (2017), "Thermomechanical vibration of orthotropic cantilever and propped cantilever nanoplate using generalized differential quadrature method", Mech. Adv. Mater. Struct., 24, 636-646. https://doi.org/10.1080/15376494.2016.1196770
  20. Golmakani, M.E. and Kadkhodayan, M. (2011), "Nonlinear bending analysis of annular FGM plates using higher-order shear deformation plate theories", Compos. Struct., 93, 973-982. https://doi.org/10.1016/j.compstruct.2010.06.024
  21. Golmakani, M.E. and Vahabi, H. (2017), "Nonlocal buckling analysis of functionally graded annular nanoplates in an elastic medium with various boundary conditions", Microsyst. Technol., 23, 3613-3628. https://doi.org/10.1007/s00542-016-3210-y
  22. Hajmohammad, M.H., Zarei, M.Sh., Sepehr, M. and Abtahi, N. (2018), "Bending and buckling analysis of functionally graded annular microplate integrated with piezoelectric layers based on layerwise theory using DQM", Aerosp. Sci. Technol., 79, 679-688. https://doi.org/10.1016/j.ast.2018.05.055
  23. Jung, W.Y., Han, S.Ch. and Park, W.T. (2014), "A modified couple stress theory for buckling analysis of S-FGM nanoplates embedded in Pasternak elastic medium", Compos.: Part B, 60, 746-756. https://doi.org/10.1016/j.compositesb.2013.12.058
  24. 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, 1650421, 17 pages. https://doi.org/10.1142/S0217984916504212
  25. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., Int. J., 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099
  26. Karimi, M. and Shahidi, A.R. (2017), "Thermo-mechanical vibration, buckling, and bending of orthotropic graphene sheets based on nonlocal two-variable refined plate theory using finite difference method considering surface energy effects", Proc. IMechE Part N: J. Nanomater., Nanoeng. Nanosyst., 231, 111-130. https://doi.org/10.1177/2397791417719970
  27. Karlicic, D., Murmu, T., Adhikari, S. and McCarthy, M. (2015), Non-local Structural Mechanics, John Wiley & Sons, USA.
  28. Limkatanyu, S., Prachasaree, W., Damrongwiriyanupap, N., Kwon, M. and Jung, W. (2013), "Exact stiffness for beams on Kerr-Type foundation: the virtual force approach", J. Appl. Mathemat., 13, 626287, 13 pages. http://dx.doi.org/10.1155/2013/626287
  29. Narendar, S. (2011), "Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., 93, 3093-3103. https://doi.org/10.1016/j.compstruct.2011.06.028
  30. Narendar, S. and Gopalakrishnan, S. (2012), "Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory", Acta Mech., 223, 395-413. https://doi.org/10.1007/s00707-011-0560-5
  31. Ma, L.S. and Wang, T.J. (2004), "Relationship between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory", Int. J. Solids Struct., 41, 85-101. https://doi.org/10.1016/j.ijsolstr.2003.09.008
  32. Malekzadeh, P. and Shojaee, M. (2013a), "A two-variable firstorder shear deformation theory coupled with surface and nonlocal effects for free vibration of nanoplates", J. Vib. Cont., 21, 2755-2772. https://doi.org/10.1177/1077546313516667
  33. Malekzadeh, P. and Shojaee, M. (2013b), "Free vibration of nanoplates based on a nonlocal two-variable refined plate theory", Compos. Struct., 95, 443-452. https://doi.org/10.1016/j.compstruct.2012.07.006
  34. Mecha, I., Mechab, B., Benaissa, S., Serier, B. and Bachir Bouiadjra, B. (2016), "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, 2193-2211. https://doi.org/10.1007/s40430-015-0482-6
  35. Paliwal, D.N. and Ghosh, S.K. (2014), "Stability of orthotropic plates on a Kerr foundation", AIAA J., 38, 1994-1997. https://doi.org/10.2514/2.859
  36. Phadikar, J.K. and Pradhan, S.C. (2010), "Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates", Computat. Mat. Sci., 49, 492-499. https://doi.org/10.1016/j.commatsci.2010.05.040
  37. Poodeh, F., Farhatnia, F. and Raeesi, M. (2018), "Buckling analysis of orthotropic thin rectangular plates subjected to nonlinear in-plane distributed loads using generalized differential quadrature method", Int. J. Computat. Meth. Eng. Sci. Mech., 19, 102-116. https://doi.org/10.1080/15502287.2018.1430077
  38. Quan, T.Q., Tran, P., Tuan, N.D. and Duc, N.D. (2015), "Nonlinear dynamic analysis and vibration of shear deformable eccentrically stiffened S-FGM cylindrical panels with metal-ceramic-metal layers resting on elastic foundations", Compos. Struct., 126, 16-33. https://doi.org/10.1016/j.compstruct.2015.02.056
  39. Rajasekaran, S. (2017), "Analysis of non-homogeneous orthotropic plates using EDQM", Struct. Eng. Mech., Int. J., 61(2), 295-316. https://doi.org/10.12989/sem.2017.61.2.295
  40. Rahimi Pour, H., Vossough, H., Heydari, M.M., Beygipoor, Gh. and Azimzadeh, A. (2015), "Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using Differential quadrature method", Struct. Eng. Mech., Int. J., 54(6), 1063-1071. https://doi.org/10.12989/sem.2015.54.6.1061
  41. Reddy, J.N., Wang, C.M. and Kitipornchai, S. (1999), "Axisymmetric bending of functionally graded circular and annular plates", Eur. J. Mech. A - Solids, 18, 185-199. https://doi.org/10.1016/S0997-7538(99)80011-4
  42. Rezaei, A.S. and Saidi, A.R. (2018), "An analytical study on the free vibration of moderately thick fluid-infiltrated porous annular sector plates", J. Vib. Cont., 24, 4130-4144. https://doi.org/10.1177/1077546317721416
  43. Robinson, M.T.A. (2018), "Analysis of the vibration of axially moving viscoelastic plate with free edges using differential quadrature method", J. Vib. Control, 24(17), 3908-3919. https://doi.org/10.1177/1077546317716316
  44. Saidi, A.R., Rasouli, A. and Sahraee, S. (2009), "Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory", Compos. Struct., 89, 110-119. https://doi.org/10.1016/j.compstruct.2008.07.003
  45. Shahsavari, D., Karami, B. and Li, L. (2018), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., Int. J., 29(1), 53-66. https://doi.org/10.12989/scs.2018.29.1.053
  46. Shimpi, R.P. and Patel, H.G. (2006), "A two variable refined plate theory for orthotropic plate analysis", Int. J. Solids Struct., 43, 6783-6799. https://doi.org/10.1016/j.ijsolstr.2006.02.007
  47. Shokrani, M.H., Karimi, M., Salmani Tehrani, M. and Mirdamadi, H.R. (2016), "Buckling analysis of double-orthotropic nanoplates embedded in elastic media based on non-local twovariable refined plate theory using the GDQ method", J. Brazil. Soc. Mech. Sci. Eng., 38, 2589-2606. https://doi.org/10.1007/s40430-015-0370-0
  48. Sobhy, M. (2016), "Hygrothermal vibration of orthotropic doublelayered graphene sheets embedded in an elastic medium using the two-variable plate theory", Appl. Math. Model., 40, 85-99. https://doi.org/10.1016/j.apm.2015.04.037
  49. 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. https://doi.org/10.12989/sem.2017.63.3.401
  50. Teifouet, M. and Robinson, A. (2017), "Analysis of the vibration of axially moving viscoelastic plate with free edges using differential quadrature method", J. Vib. Cont., 24, 3908-3919. https://doi.org/10.1177/1077546317716316
  51. Xu, W., Wang, L. and Jiang, J. (2016), "Strain gradient finite element analysis on the vibration of double-layered graphene sheets", Int. J. Computat. Meth., 13, 1650011, 18 pages. https://doi.org/10.1142/S0219876216500110

피인용 문헌

  1. On bending analysis of perforated microbeams including the microstructure effects vol.76, pp.6, 2020, https://doi.org/10.12989/sem.2020.76.6.765
  2. Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches vol.40, pp.2, 2021, https://doi.org/10.12989/scs.2021.40.2.157
  3. Nonlinear Analyses of Porous Functionally Graded Sandwich Piezoelectric Nano-Energy Harvesters under Compressive Axial Loading vol.11, pp.24, 2019, https://doi.org/10.3390/app112411787