Structural Engineering and Mechanics

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Large deformation bending analysis of functionally graded spherical shell using FEM

  • Received : 2014.01.24
  • Accepted : 2014.09.18
  • Published : 2015.02.25
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Abstract

In this article, nonlinear finite element solutions of bending responses of functionally graded spherical panels are presented. The material properties of functionally graded material are graded in thickness direction according to a power-law distribution of volume fractions. A general nonlinear mathematical shallow shell model has been developed based on higher order shear deformation theory by taking the geometric nonlinearity in Green-Lagrange sense. The model is discretised using finite element steps and the governing equations are obtained through variational principle. The nonlinear responses are evaluated through a direct iterative method. The model is validated by comparing the responses with the available published literatures. The efficacy of present model has also been established by demonstrating a simulation based nonlinear model developed in ANSYS environment. The effects of power-law indices, support conditions and different geometrical parameters on bending behaviour of functionally graded shells are obtained and discussed in detail.

Keywords

References

  1. Alijani, F. and Amabili, M. (2014), "Non-linear vibrations of shells: a literature review from 2003 to 2013", Int. J. Nonlin. Mech., 58, 233-257. https://doi.org/10.1016/j.ijnonlinmec.2013.09.012
  2. Bian, Z.G., Ying, J., Chen, W.Q. and Ding, H.J. (2006), "Bending and free vibration analysis of a smart functionally graded plate", Struct. Eng. Mech., 23(1), 97-113. https://doi.org/10.12989/sem.2006.23.1.097
  3. Bich, D.H. and Tung, H.V. (2011), "Non-linear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects", Int. J. Nonlin. Mech., 46, 1195-1204. https://doi.org/10.1016/j.ijnonlinmec.2011.05.015
  4. Bich, D.H., Dung, D.V. and Hoa, L.K. (2012), "Nonlinear static and dynamic buckling analysis of functionally graded shallow spherical shells including temperature effects", Compos. Struct., 94, 2952-2960. https://doi.org/10.1016/j.compstruct.2012.04.012
  5. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", Appl. Mech. Rev., 60, 195-216. https://doi.org/10.1115/1.2777164
  6. Cook, R.D., Malkus, D.S., Plesha, M.E. and Witt, R.J. (2009), Concepts and applications of finite element analysis, 4th Edition, John Wiley & Sons Pvt. Ltd., Singapore.
  7. Jha, D.K., Kant, T., Singh, R.K. (2013), "A critical review of recent research on functionally graded plates", Compos. Struct., 96, 833-849. https://doi.org/10.1016/j.compstruct.2012.09.001
  8. Lei, Z.X., Zhang, L.W., Liew, K.M. and Yu, J.L. (2014), "Dynamic stability analysis of carbon nanotubereinforced functionally graded cylindrical panels using the element-free kp-Ritz method", Compos. Struct., 113, 328-338. https://doi.org/10.1016/j.compstruct.2014.03.035
  9. Liew, K.M., Lei, Z.X., Yu, J.L. and Zhang, L.W. (2014), "Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach", Comput. Meth. Appl. Mech. Eng., 268, 1-17. https://doi.org/10.1016/j.cma.2013.09.001
  10. Liew, K.M., Zhao, X., Ferreira, A.J.M. (2011), "A review of meshless methods for laminated and functionally graded plates and shells", Compos. Struct., 93(8), 2031-2041. https://doi.org/10.1016/j.compstruct.2011.02.018
  11. Mantari, J.L., Oktem, A.S. and Soares, C.G. (2012), "Bending response of functionally graded plates by using a new higher order shear deformation theory", Compos. Struct., 94, 714-723. https://doi.org/10.1016/j.compstruct.2011.09.007
  12. Mao, Y.Q., Fu, Y.M., Chen, C.P. and Li, Y.L. (2011), "Nonlinear dynamic response for functionally graded shallow shell under low velocity impact in thermal environment", Appl. Math. Model., 35, 2887-2900. https://doi.org/10.1016/j.apm.2010.12.012
  13. Navazi, H.M. and Haddadpour, H. (2008), "Nonlinear cylindrical bending analysis of shear deformable functionally graded plates under different loadings using analytical methods", "Int. J. Mech. Sci., 50, 1650-1657. https://doi.org/10.1016/j.ijmecsci.2008.08.010
  14. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2011), "Bending of FGM plates by a sinusoidal plate formulation and collocation with radial basis functions", Mech. Res. Commun., 38, 368-371. https://doi.org/10.1016/j.mechrescom.2011.04.011
  15. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2012), "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94, 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005
  16. Oktem, A.S., Mantari, J.L. and Soares, C.G. (2012), "Static response of functionally graded plates and doubly-curved shells based on a higher order shear deformation theory", Eur. J. Mech. A-Solid., 36, 163-172. https://doi.org/10.1016/j.euromechsol.2012.03.002
  17. Reddy, J.N. (2003), Mechanics of laminated composite: Plates and shells-Theory and analysis, 2nd Edition, CRC press, Boca Raton, FL.
  18. Santos, H., Soares, C.M.M., Soares, C.A.M. and Reddy, J.N. (2009), "A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials", Compos. Struct., 91, 427-432. https://doi.org/10.1016/j.compstruct.2009.04.008
  19. Shen H.S. (2009), Functionally graded material: Nonlinear analysis of plates & shells, CRC press, Boca Raton, FL.
  20. Shen, H.S. (2002), "Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments", Int. J. Mech. Sci., 44, 561-584. https://doi.org/10.1016/S0020-7403(01)00103-5
  21. Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34, 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034
  22. Thai, H.T. and Kim, S.E. (2013), "A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates", Compos. Struct., 96, 165-173. https://doi.org/10.1016/j.compstruct.2012.08.025
  23. Woo, J. and Meguid, S.A. (2001), "Nonlinear analysis of functionally graded plates and shallow shells", Int. J. Solid. Struct., 38, 7409-7421. https://doi.org/10.1016/S0020-7683(01)00048-8
  24. Xiang, S. and Kang G. (2013), "A nth-order shear deformation theory for the bending analysis on the functionally graded plates", Eur. J. Mech. A-Solid., 37, 336-343. https://doi.org/10.1016/j.euromechsol.2012.08.005
  25. Zenkour, A.M. and Sobhy, M. (2013), "Dynamic bending response of thermoelastic functionally graded plates resting on elastic foundations", Aerosp. Sci. Technol., 29, 7-17. https://doi.org/10.1016/j.ast.2013.01.003
  26. Zhang, L.W., Lei, Z.X., Liew, K.M. and Yu, J.L. (2014a), "Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels", Compos. Struct., 111, 205-212. https://doi.org/10.1016/j.compstruct.2013.12.035
  27. Zhang, L.W., Lei, Z.X., Liew, K.M. and Yu, J.L. (2014b), "Large deflection geometrically nonlinear analysis of carbon nanotube-reinforced functionally graded cylindrical panels", Comput. Meth. Appl. Mech. Eng., 273, 1-18. https://doi.org/10.1016/j.cma.2014.01.024
  28. Zhang, L.W., Zhu, P. and Liew, K.M. (2014), "Thermal buckling of functionally graded plates using a local Kriging meshless method", Compos. Struct., 108, 472-492. https://doi.org/10.1016/j.compstruct.2013.09.043
  29. Zhao, X. and Liew, K.M. (2009a), "Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method", Comput. Meth. Appl. Mech. Eng., 198, 2796-2811. https://doi.org/10.1016/j.cma.2009.04.005
  30. Zhao, X. and Liew, K.M. (2009b), "Geometrically nonlinear analysis of functionally graded shells", Int. J. Mech. Sci., 51, 131-144. https://doi.org/10.1016/j.ijmecsci.2008.12.004
  31. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Thermoelastic and vibration analysis of functionally graded cylindrical shells", Int. J. Mech. Sci., 51, 694-707. https://doi.org/10.1016/j.ijmecsci.2009.08.001
  32. Zhu, P., Zhang, L.W. and Liew, K.M. (2014), "Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov-Galerkin approach with moving Kriging interpolation", Compos. Struct., 107, 298-314. https://doi.org/10.1016/j.compstruct.2013.08.001

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