Structural Engineering and Mechanics

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Nonlinear spectral collocation analysis of imperfect functionally graded plates under end-shortening

  • Ghannadpour, S. Amir M. (Aerospace Engineering Department, Faculty of New Technologies and Engineering, Shahid Beheshti University) ;
  • Kiani, Payam (Aerospace Engineering Department, Faculty of New Technologies and Engineering, Shahid Beheshti University)
  • Received : 2018.01.27
  • Accepted : 2018.03.15
  • Published : 2018.06.10
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Abstract

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.

Keywords

References

  1. Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical postbuckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., 56(1), 85-106. https://doi.org/10.12989/sem.2015.56.1.085
  2. Banic, D., Bacciocchi, M., Tornabene, F. and Ferreira, A.J. (2017), "Influence of Winkler-Pasternak foundation on the vibrational behavior of plates and shells reinforced by agglomerated carbon nanotubes", Appl. Sci., 7(12), 1-55.
  3. Belinha, J. and Dinis, L.M.J.S. (2007), "Nonlinear analysis of plates and laminates using the element free Galerkin method", Compos. Struct., 78(3), 337-350. https://doi.org/10.1016/j.compstruct.2005.10.007
  4. Dai, K.Y., Liu, G.R., Lim, K.M., Han, X. and Du, S.Y. (2004), "A mesh-free radial point interpolation method for analysis of functionally graded material (FGM) plates", Comput. Mech., 34(3), 213-223. https://doi.org/10.1007/s00466-004-0566-0
  5. Fantuzzi, N., Tornabene, F., Bacciocchi, M. and Dimitri, R. (2017), "Free vibration analysis of arbitrarily shaped functionally graded carbon nanotube-reinforced plates", Compos. Part B.-Eng., 115, 384-408. https://doi.org/10.1016/j.compositesb.2016.09.021
  6. Ferreira, A.J.M. (2013), "Bending and vibration of laminated plates by a layerwise formulation and collocation with radial basis functions", Mech. Adv. Mater. Struct., 20(8), 624-637. https://doi.org/10.1080/15376494.2011.643282
  7. Ghannadpour, S.A.M. and Alinia, M.M. (2006), "Large deflection behavior of functionally graded plates under pressure loads", Compos. Struct., 75(1), 67-71. https://doi.org/10.1016/j.compstruct.2006.04.004
  8. Ghannadpour, S.A.M. and Alinia, M.M. (2009), "Nonlinear analysis of pressure loaded FGM plates", Compos. Struct., 88(3), 354-359. https://doi.org/10.1016/j.compstruct.2008.04.013
  9. Ghannadpour, S.A.M. and Barekati, M. (2016), "Initial imperfection effects on post-buckling response of laminated plates under end-shortening strain using Chebyshev techniques", Thin. Wall. Struct., 106, 484-494. https://doi.org/10.1016/j.tws.2016.03.028
  10. Ghannadpour, S.A.M. and Ovesy, H.R. (2008), "An exact finite strip for the calculation of relative post-buckling stiffness of Isection struts", Int. J. Mech. Sci., 50(9), 1354-1364. https://doi.org/10.1016/j.ijmecsci.2008.07.010
  11. Ghannadpour, S.A.M., Kiani, P. and Reddy, J.N. (2017), "Pseudo spectral method in nonlinear analysis of relatively thick imperfect laminated plates under end-shortening strain", Compos. Struct., 182, 694-710. https://doi.org/10.1016/j.compstruct.2017.08.076
  12. Ghannadpour, S.A.M., Ovesy, H.R. and Nassirnia, M. (2012), "Buckling ana lysis of functionally graded plates under thermal loadings using the finite strip method", Comput. Struct., 108, 93-99.
  13. Gilhooley, D.F., Batra, R.C., Xiao, J.R., McCarthy, M.A. and Gillespie, J.r. (2007), "Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions", Compos. Struct., 80(4), 539-552. https://doi.org/10.1016/j.compstruct.2006.07.007
  14. Huang, B.Z. and Atluri, S.N. (1995), "A simple method to follow post-buckling paths in finite element analysis", Comput. Struct., 57(3), 477-489. https://doi.org/10.1016/0045-7949(94)00623-B
  15. Kar, V.R. and Panda, S.K. (2016), "Post-buckling behavior of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115, 318-324.
  16. Kar, V.R. and Panda, S.K. (2017), "Post-buckling analysis of shear deformable FG shallow spherical shell panel under non-uniform thermal environment", J. Therm. Stress., 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118
  17. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2017), "Effect of different temperature load on thermal post-buckling behavior of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247. https://doi.org/10.1016/j.compstruct.2016.10.125
  18. Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016), "Thermal buckling behavior of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties", Adv. Mater. Res., 5(4), 205-221. https://doi.org/10.12989/amr.2016.5.4.205
  19. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircr. Eng. Aerosp. Tec., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  20. Katariya, P.V., Panda, S.K., Hirwani, C.K., Mehar, K. and Thakare, O. (2017), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fiber", Smart. Struct. Syst., 20(5), 595-605. https://doi.org/10.12989/SSS.2017.20.5.595
  21. Kim, Y.H. and Noor, A.K. (1996), "Buckling and post-buckling of composite panels with cutouts subjected to combined loads", Fin. Elem. Anal. Des., 22(2), 163-185. https://doi.org/10.1016/0168-874X(95)00052-U
  22. Lee, Y.Y., Xin, Z. and Reddy, J.N. (2010), "Post-buckling analysis of functionally graded plates subject to compressive and thermal loads", Comput. Meth. Appl. Mech. Eng., 199(25), 1645-1653. https://doi.org/10.1016/j.cma.2010.01.008
  23. Lee, Y.Y., Zhao, X. and Liew, K.M. (2009), "Thermoelastic analysis of functionally graded plates using the element free kpritz method", Smart Mater. Struct., 18(3), 035007. https://doi.org/10.1088/0964-1726/18/3/035007
  24. Liew, K.M. and Chen, X.L. (2004), "Mesh-free radial point interpolation method for the buckling analysis of mindlin plates subjected to in‐plane point loads", Int. J. Numer. Meth. Eng., 60(11), 1861-1877. https://doi.org/10.1002/nme.1027
  25. Liu, G.R. and Chen, X.L. (2001), "A mesh-free method for static and free vibration analysis of thin plates of complicated shape", J. Sound Vibr., 241(5), 839-855. https://doi.org/10.1006/jsvi.2000.3330
  26. Liu, G.R. and Gu, Y.T. (2001), "A point interpolation method for two-dimensional solids", Int. J. Numer. Meth. Eng., 50(4), 937-951. https://doi.org/10.1002/1097-0207(20010210)50:4<937::AID-NME62>3.0.CO;2-X
  27. Liu, L., Chua, L.P. and Ghista, D.N. (2007), "Mesh-free radial basis function method for static, free vibration and buckling analysis of shear deformable composite laminates", Compos. Struct., 78(1), 58-69. https://doi.org/10.1016/j.compstruct.2005.08.010
  28. Ovesy, H.R. and Ghannadpour, S.A.M. (2007), "Large deflection finite strip analysis of functionally graded plates under pressure loads", Int. J. Struct. Stab. Dyn., 7(2), 193-211. https://doi.org/10.1142/S0219455407002241
  29. Ovesy, H.R. and Ghannadpour, S.A.M. (2009), "An exact finite strip for the calculation of relative post-buckling stiffness of isotropic plates", Struct. Eng. Mech., 31(2), 181-210. https://doi.org/10.12989/sem.2009.31.2.181
  30. Ovesy, H.R., Ghannadpour, S.A.M. and Morada, G. (2005), "Geometric non-linear analysis of composite laminated plates with initial imperfection under end shortening, using two versions of finite strip method", Compos. Struct., 71(3), 307-314. https://doi.org/10.1016/j.compstruct.2005.09.030
  31. Ovesy, H.R., Ghannadpour, S.A.M. and Nassirnia, M. (2015), "Post-buckling analysis of rectangular plates comprising functionally graded strips in thermal environments", Comput. Struct., 147, 209-215. https://doi.org/10.1016/j.compstruc.2014.09.011
  32. Ovesy, H.R., Loughlan, J. and Ghannadpour, S.A.M. (2006), "Geometric non-linear analysis of channel sections under end shortening, using different versions of the finite strip method", Comput. Struct., 84(13), 855-872. https://doi.org/10.1016/j.compstruc.2006.02.010
  33. Panda, S.K. and Katariya, P.V. (2015), "Stability and free vibration behavior of laminated composite panels under thermomechanical loading", Int. J. Appl. Comput. Math., 1(3), 475-490. https://doi.org/10.1007/s40819-015-0035-9
  34. Panda, S.K. and Singh, B.N. (2009), "Thermal post-buckling behavior of laminated composite cylindrical/hyperboloid shallow shell panel using nonlinear finite element method", Compos. Struct., 91(3), 366-374. https://doi.org/10.1016/j.compstruct.2009.06.004
  35. Panda, S.K. and Singh, B.N. (2010a), "Nonlinear free vibration analysis of thermally post-buckled composite spherical shell panel", Int. J. Mech. Mater. Des., 6(2), 175-188. https://doi.org/10.1007/s10999-010-9127-1
  36. Panda, S.K. and Singh, B.N. (2010b), "Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibers using non-linear finite element method", Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci., 224(4), 757-769. https://doi.org/10.1243/09544062JMES1809
  37. Panda, S.K. and Singh, B.N. (2011), "Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel using nonlinear FEM", Fin. Elem. Anal. Des., 47(4), 378-386. https://doi.org/10.1016/j.finel.2010.12.008
  38. Panda, S.K. and Singh, B.N. (2013a), "Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fiber", Aerosp. Sci. Technol., 29(1), 47-57. https://doi.org/10.1016/j.ast.2013.01.007
  39. Panda, S.K. and Singh, B.N. (2013b), "Post-buckling analysis of laminated composite doubly curved panel embedded with SMA fibers subjected to thermal environment", Mech. Adv. Mater. Struct., 20(10), 842-853. https://doi.org/10.1080/15376494.2012.677097
  40. Panda, S.K. and Singh, B.N. (2013c), "Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel embedded with SMA fibers", Nonlin. Dyn., 74(1-2), 395-418. https://doi.org/10.1007/s11071-013-0978-5
  41. Qian, L.F. and Batra, R.C. (2004), "Transient thermoelastic deformations of a thick functionally graded plate", J. Therm. Stress., 27(8), 705-740. https://doi.org/10.1080/01495730490440145
  42. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, CRC Press, Boca Raton, U.S.A.
  43. Sherafat, M.H., Ghannadpour, S.A.M. and Ovesy H.R. (2013), "Pressure loading, end-shortening and through-thickness shearing effects on geometrically nonlinear response of composite laminated plates using higher order finite strip method", Struct. Eng. Mech., 45(5), 677-691. https://doi.org/10.12989/sem.2013.45.5.677
  44. Sherafat, M.H., Ovesy, H.R. and Ghannadpour, S.A.M. (2013), "Buckling analysis of functionally graded plates under mechanical loading using higher order functionally graded strip", Int. J. Struct. Stab. Dyn., 13(6), 1350033. https://doi.org/10.1142/S0219455413500338
  45. Singh, S.B. and Kumar, D. (2008), "Post-buckling response and failure of symmetric laminated plates with rectangular cutouts under uniaxial compression", Struct. Eng. Mech., 29(4), 455-467. https://doi.org/10.12989/sem.2008.29.4.455
  46. Singh, S.B. and Kumar, D. (2010), "Post-buckling response and failure of symmetric laminated plates with rectangular cutouts under in-plane shear", Struct. Eng. Mech., 34(2), 175-188. https://doi.org/10.12989/sem.2010.34.2.175
  47. Sofiyev, A.H. (2007), "Vibration and stability of composite cylindrical shells containing a FG layer subjected to various loads", Struct. Eng. Mech., 27(3), 365-391. https://doi.org/10.12989/sem.2007.27.3.365
  48. Tornabene, F. and Viola, E. (2009), "Free vibration analysis of functionally graded panels and shells of revolution", Meccan., 44(3), 255-281. https://doi.org/10.1007/s11012-008-9167-x
  49. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Meth. Appl. Mech. Eng., 198(37-40), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011
  50. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2017), "Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes", Compos. Part B-Eng., 115, 449-476. https://doi.org/10.1016/j.compositesb.2016.07.011
  51. Tornabene, F., Fantuzzi, N., Bacciocchi, M., Viola, E. and Reddy, J.N. (2017), "A numerical investigation on the natural frequencies of FGM sandwich shells with variable thickness by the local generalized differential quadrature method", Appl. Sci., 7(2), 1-39.
  52. Wang, J.G. and Liu, G.R. (2002), "A point interpolation mesh-less method based on radial basis functions", Int. J. Numer. Meth. Eng., 54(11), 1623-1648. https://doi.org/10.1002/nme.489
  53. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90(2), 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005

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