DOI QR코드

DOI QR Code

Buckling analysis of nanocomposite cut out plate using domain decomposition method and orthogonal polynomials

  • Jamali, M. (School of Mechanical Engineering, Iran University of Science and Technology) ;
  • Shojaee, T. (School of Mechanical Engineering, Iran University of Science and Technology) ;
  • Kolahchi, R. (Faculty of Mechanical Engineering University of Kashan) ;
  • Mohammadi, B. (School of Mechanical Engineering, Iran University of Science and Technology)
  • Received : 2016.06.21
  • Accepted : 2016.10.24
  • Published : 2016.10.30

Abstract

In this editorial, buckling analytical investigation of the nanocomposite plate with square cut out reinforced by carbon nanotubes (CNTs) surrounded by Pasternak foundation is considered. The plate is presumed has square cut out in center and resting on Pasternak foundation. CNTs are used as amplifier in plate for diverse distribution, such as uniform distribution (UD) and three patterns of functionally graded (FG) distribution types of CNTs (FG-X, FG-A and FG-O). Moreover, the effective mechanical properties of nanocomposite plate are calculated from the rule of mixture. Domain decomposition method and orthogonal polynomials are applied in order to define the shape function of nanocomposite plate with square cut out. Finally, Rayleigh-Ritz energy method is used to obtain critical buckling load of system. A detailed parametric study is conducted to explicit the effects of the dimensions of plate, length of square cut out, different distribution of CNTs, elastic medium and volume fraction of CNTs. It is found from results that increase the dimensions of plate and length of square cut out have negative impact on buckling behavior of system but considering CNTs in plate has positive influence.

Keywords

References

  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 Systems and Nanostructures, 43(4), 954-959. https://doi.org/10.1016/j.physe.2010.11.024
  2. Asadi, E. and Jam, J.E. (2014), "Analytical and numerical buckling analysis of carbon nanotube reinforced annular composite plates", Int. J. Adv. Des. Manuf. Technol., 7(2), 35-44.
  3. Ashoori Movassagh, A. and Mahmoodi, M.J. (2013), "A micro-scale modeling of Kirchhoff plate based on modified strain-gradient elasticity theory", Eur. J. Mech. - A/Solids, 40, 50-59. https://doi.org/10.1016/j.euromechsol.2012.12.008
  4. Baseri, V., Soleimani Jafari, G. and Kolahchi, R. (2016), "Analytical solution for buckling of embedded laminated plates based on higher order shear deformation plate theory", Steel Compos. Struct., Int. J., 21(4), 883-919. https://doi.org/10.12989/scs.2016.21.4.883
  5. Bhat, R.B. (1985), "Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method", J. Sound Vib., 102(4), 493-499. https://doi.org/10.1016/S0022-460X(85)80109-7
  6. Farajpour, A., Danesh, M. and Mohammadi, M. (2011), "Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics", Physica E: Low-dimensional Systems and Nanostructures, 44(3), 719-727. https://doi.org/10.1016/j.physe.2011.11.022
  7. Farajpour, A., Shahidi, A.R., Mohammadi, M. and Mahzoon, M. (2012), "Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics", Compos. Struct., 94(5), 1605-1615. https://doi.org/10.1016/j.compstruct.2011.12.032
  8. Ghorbanpour Arani, A. and Shokravi, M. (2014), "Vibration response of visco-elastically coupled double-layered visco-elastic graphene sheet systems subjected to magnetic field via strain gradient theory considering surface stress effects", Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems, 229(4), 180-190. https://doi.org/10.1177/1740349914529102
  9. Ghorbanpour Arani, A.G., Maghamikia, S., Mohammadimehr, M. and Arefmanesh, A. (2011), "Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods", J. Mech. Sci. Technol., 25(3), 809-820. https://doi.org/10.1007/s12206-011-0127-3
  10. Ghorbanpour Arani, A., Kolahchi, R. and Vossough, H. (2012), "Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory", Physica B: Condensed Matter, 407(22), 4458-4465. https://doi.org/10.1016/j.physb.2012.07.046
  11. Ghorbanpour Arani, A., Kolahchi, R., Mosayyebi, M. and Jamali, M. (2014), "Pulsating fluid induced dynamic instability of visco-double-walled carbon nano-tubes based on sinusoidal strain gradient theory using DQM and Bolotin method", Int. J. Mech. Mater. Des., 12(1), 17-38.
  12. Ghorbanpour Arani, A., Jamali, M., Mosayyebi, M. and Kolahchi, R. (2015), "Analytical modeling of wave propagation in viscoelastic functionally graded carbon nanotubes reinforced piezoelectric microplate under electro-magnetic field", Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems. [In press]
  13. Ghorbanpour Arani, A., Jamali, M., Ghorbanpour-Arani, A., Kolahchi, R. and Mosayyebi, M. (2016a), "Electro-magneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. [In press]
  14. Ghorbanpour Arani, A., Jamali, M., Mosayyebi, M. and Kolahchi, R. (2016b), "Wave propagation in FGCNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory", Composites Part B: Engineering, 95, 209-224. https://doi.org/10.1016/j.compositesb.2016.03.077
  15. Golmakani, M.E. and Rezatalab, J. (2015), "Nonuniform biaxial buckling of orthotropic nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory", Composite Structures, 119, 238-250. https://doi.org/10.1016/j.compstruct.2014.08.037
  16. Hashemi, S.H. and Samaei, A.T. (2011), "Buckling analysis of micro/nanoscale plates via nonlocal elasticity theory", Physica E: Low-dimensional Systems and Nanostructures, 43(7), 1400-1404. https://doi.org/10.1016/j.physe.2011.03.012
  17. Jam, J.E. and Maghamikia, S. (2011), "Elastic buckling of composite plate reinforced with carbon nano tubes", Int. J. Eng. Sci. Technol., 3, 4090-4101.
  18. 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
  19. Lam, K.Y. and Hung, K.C. (1990a), "Orthogonal polynomials and sub-sectioning method for vibration of plates", Comput. Struct., 34(6), 827-834. https://doi.org/10.1016/0045-7949(90)90353-4
  20. Lam, K.Y. and Hung, K.C. (1990b), "Vibration study on plates with stiffened openings using orthogonal polynomials and partitioning method", Comput. Struct., 37(3), 295-301. https://doi.org/10.1016/0045-7949(90)90321-R
  21. Lam, K.Y., Hung, K.C. and Chow, S.T. (1989), "Vibration analysis of plates with cutouts by the modified Rayleigh-Ritz method", Appl. Acoust., 28(1), 49-60. https://doi.org/10.1016/0003-682X(89)90030-3
  22. Liew, K.M., Hung, K.C. and Lim, M.K. (1993), "Method of domain decomposition in vibrations of mixed edge anisotropic plates", Int. J. Solid. Struct., 30(23), 3281-3301. https://doi.org/10.1016/0020-7683(93)90114-M
  23. Liew, K.M., Hung, K.C. and Sum, Y.K. (1995), "Flexural vibration of polygonal plates: treatments of sharp re-entrant corners", J. Sound Vib., 183(2), 221-238. https://doi.org/10.1006/jsvi.1995.0251
  24. Liew, K.M., Ng, T.Y. and Kitipornchai, S. (2001), "A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation", Int. J. Solid. Struct., 38(28-29), 4937-4954. https://doi.org/10.1016/S0020-7683(00)00329-2
  25. Liew, K.M., Kitipornchai, S., Leung, A.Y.T. and Lim, C.W. (2003), "Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method", Int. J. Mech. Sci., 45(5), 941-959. https://doi.org/10.1016/S0020-7403(03)00109-7
  26. Mohammadimehr, M., Mohandes, M. and Moradi, M. (2014a), "Size dependent effect on the buckling and vibration analysis of double-bonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory", J. Vib. Control, 22(7), 1790-1807. https://doi.org/10.1177/1077546314544513
  27. Mohammadimehr, M., Rousta-Navi, B. and Ghorbanpour-Arani, A. (2014b), "Biaxial Buckling and Bending of Smart Nanocomposite Plate Reinforced by CNTs using Extended Mixture Rule Approach", Mech. Adv. Compos. Struct., 1(1), 17-26.
  28. Mosallaie Barzoki, A.A., Loghman, A. and Ghorbanpour Arani, A. (2015), "Temperature-dependent nonlocal nonlinear buckling analysis of functionally graded SWCNT-reinforced microplates embedded in an orthotropic elastomeric medium", Struct. Eng. Mech., Int. J., 53(3), 479-517.
  29. Murmu, T. and Pradhan, S.C. (2009), "Buckling of biaxially compressed orthotropic plates at small scales", Mech. Res. Commun., 36(8), 933-938. https://doi.org/10.1016/j.mechrescom.2009.08.006
  30. Murmu, T., Sienz, J., Adhikari, S. and Arnold, C. (2013), "Nonlocal buckling of double-nanoplate-systems under biaxial compression", Compos. Part B: Eng., 44(1), 84-94. https://doi.org/10.1016/j.compositesb.2012.07.053
  31. Pan, Z., Cheng, Y. and Liu, J. (2013), "A semi-analytical analysis of the elastic buckling of cracked thin plates under axial compression using actual non-uniform stress distribution", Thin-Wall. Struct., 73, 229-241. https://doi.org/10.1016/j.tws.2013.08.007
  32. Pradhan, S.C. (2009), "Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory", Physics Letters A, 373(45), 4182-4188. https://doi.org/10.1016/j.physleta.2009.09.021
  33. Pradhan, S.C. and Murmu, T. (2009), "Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics", Computat. Mater. Sci., 47(1), 268-274. https://doi.org/10.1016/j.commatsci.2009.08.001
  34. Pradhan, S.C. and Phadikar, J.K. (2009), "Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory", Struct. Eng. Mech., Int. J., 33(2), 193-213. https://doi.org/10.12989/sem.2009.33.2.193
  35. Radic, N., Jeremic, D., Trifkovic, S. and Milutinovic, M. (2014), "Buckling analysis of double-orthotropic nanoplates embedded in Pasternak elastic medium using nonlocal elasticity theory", Compos. Part B: Eng., 61, 162-171. https://doi.org/10.1016/j.compositesb.2014.01.042
  36. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
  37. Samaei, A.T., Abbasion, S. and Mirsayar, M.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
  38. Sandler, J., Shaffer, M.S.P., Prasse, T., Bauhofer, W., Schulte, K. and Windle, A.H. (1999), "Development of a dispersion process for carbon nanotubes in an epoxy matrix and the resulting electrical properties", Polymer, 40(21), 5967-5971. https://doi.org/10.1016/S0032-3861(99)00166-4
  39. Shams, S. and Soltani, B. (2015), "The effects of carbon nanotube waviness and aspect ratio on the buckling behavior of functionally graded nanocomposite plates using a meshfree method", Polym. Compos.
  40. Shams, S. and Soltani, B. (2016), "Buckling of laminated carbon nanotube-reinforced composite plates on elastic foundations using a meshfree method", Arab. J. Sci. Eng., 41(5), 1981-1993.
  41. Tagrara, S.H., Benachour, A., Bouiadjra, M.B. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., Int. J., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259
  42. Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation", Appl. Math. Model., 39(18), 5459-5472. https://doi.org/10.1016/j.apm.2014.12.058
  43. Zhu, P., Lei, Z.X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010

Cited by

  1. A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations 2017, https://doi.org/10.1177/1099636217727577
  2. Isogeometric buckling analysis of composite variable-stiffness panels vol.165, 2017, https://doi.org/10.1016/j.compstruct.2017.01.016
  3. Vibration of size-dependent functionally graded sandwich microbeams with different boundary conditions based on the modified couple stress theory 2017, https://doi.org/10.1177/1099636217738909
  4. Differential transform method and Adomian decomposition method for free vibration analysis of fluid conveying Timoshenko pipeline vol.62, pp.1, 2016, https://doi.org/10.12989/sem.2017.62.1.065
  5. Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter vol.28, pp.1, 2016, https://doi.org/10.12989/scs.2018.28.1.013
  6. Cut out effect on nonlinear post-buckling behavior of FG-CNTRC micro plate subjected to magnetic field via FSDT vol.7, pp.6, 2016, https://doi.org/10.12989/anr.2019.7.6.405
  7. Damping and vibration response of viscoelastic smart sandwich plate reinforced with non-uniform Graphene platelet with magnetorheological fluid core vol.33, pp.6, 2016, https://doi.org/10.12989/scs.2019.33.6.891