Structural Engineering and Mechanics

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Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material

  • Nguyen, Dinh-Kien (Department of Solid Mechanics, Institute of Mechanics, Vietnam Academy of Science and Technology) ;
  • Gan, Buntara S. (Department of Architecture, College of Engineering, Nihon University) ;
  • Trinh, Thanh-Huong (Department of Solid Mechanics, Institute of Mechanics, Vietnam Academy of Science and Technology)
  • Received : 2013.02.10
  • Accepted : 2014.02.01
  • Published : 2014.03.25
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Abstract

Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material (FGM) by using the finite element method is presented. The material property of the structures is assumed to be graded in the thickness direction by a power law distribution. A nonlinear beam element based on Bernoulli beam theory, taking the shift of the neutral axis position into account, is formulated in the context of the co-rotational formulation. The nonlinear equilibrium equations are solved by using the incremental/iterative procedure in a combination with the arc-length control method. Numerical examples show that the formulated element is capable to give accurate results by using just several elements. The influence of the material inhomogeneity in the geometrically nonlinear behavior of the FGM beam and frame structures is examined and highlighted.

Keywords

References

  1. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration chatacteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  2. Belytschko, T., Liu, W.K. and Moran, B. (2000), Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, Chichester, USA.
  3. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", Appl. Mech. Rev., 60(5), 195-216. https://doi.org/10.1115/1.2777164
  4. Chakraborty, A., Gopalakrishnan, S. and Reddy, J.R. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45(3), 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4
  5. Cichon, C. (1984), "Large displacement in-plane analysis of elastic-plastic frames", Comput. Struct., 19(5- 6), 737-745. https://doi.org/10.1016/0045-7949(84)90173-1
  6. Crisfield, M.A. (1981), "A fast incremental/iterative solution procedure that handles 'snap-through'", Comput. Struct., 13(1-3), 55-62. https://doi.org/10.1016/0045-7949(81)90108-5
  7. Crisfield, M.A. (1991), Nonlinear Finite Element Analysis of Solids and Structures, Volume 1, Essentials, John Wiley & Sons, Chichester, USA.
  8. Fallah, A. and Aghdam, M.M. (2011), "Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation", Eur. J. Mech. A/Solids, 30(4), 571-583. https://doi.org/10.1016/j.euromechsol.2011.01.005
  9. Gere, G.M. and Timoshenko, S.P. (1991), Mechanics of Materials, Third SI Edition, Chapman & Hall, London, UK.
  10. Hsiao, K.M. and Huo, F.Y. (1987), "Nonlinear finite element analysis of elastic frames", Comput. Struct., 26(4), 693-701. https://doi.org/10.1016/0045-7949(87)90016-2
  11. Hsiao, K.M., Huo, F.Y. and Spiliopoulos, K.V. (1988), "Large displacement analysis of elasto-plastic frames", Comput. Struct., 28(5), 627-633. https://doi.org/10.1016/0045-7949(88)90007-7
  12. Huang, Y. and Li, X.F. (2011), "Buckling analysis of non-uniform and axially graded beams with varying flexural rigidity", ASCE J. Eng. Mech., 137(1), 73-81. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000206
  13. Jafari, V., Vahdani, S.H. and Rahimian, M. (2010), "Derivation of the consistent flexibility matrix for geometrically nonlinear Timoshenko frame finite element", Finite Elem. Anal. Des., 46(12), 1077-1085. https://doi.org/10.1016/j.finel.2010.07.015
  14. Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation beam theory", Appl. Math. Model., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015
  15. Kang, Y.A. and Li, X.F. (2009), "Bending of functionally graded cantilever beam with power-law nonlinearity subjected to an end force", Int. J. Nonlin. Mech., 44(6), 696-703. https://doi.org/10.1016/j.ijnonlinmec.2009.02.016
  16. Kang, Y.A. and Li, X.F. (2010), "Large deflection of a nonlinear cantilever functionally graded beam", J. Reinf. Plast. Comp., 29(4), 1761-1774. https://doi.org/10.1177/0731684409103340
  17. Kocaturk, T. and Akbas, S.D. (2012), "Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading", Struct. Eng. Mech., 41(6), 775-789. https://doi.org/10.12989/sem.2012.41.6.775
  18. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B Eng., 28(1-2), 1-4.
  19. Lee, Y.Y., Zhao, X. and Reddy, J.N. (2010), "Postbuckling analysis of functionally graded plates subjected to compressive and thermal loads", Comput. Meth. Appl. Mech. Eng., 199(25-28), 1645-1653. https://doi.org/10.1016/j.cma.2010.01.008
  20. Mattiasson, K. (1981), "Numerical results for large deflection beam and frame problems analyzed by meams of elliptic integrals", Int. J. Numer. Eng., 17(1), 145-153. https://doi.org/10.1002/nme.1620170113
  21. Meek, J.L. and Xue, Q. (1996), "A study on the instability problem for 2D-frames", Comput. Meth. Appl. Mech. Eng., 136(3-4), 347-361. https://doi.org/10.1016/0045-7825(96)00995-4
  22. Nanakorn, P. and Vu, L.N. (2006), "A 2D field-consistent beam element for large displacement analysis using the total Lagrangian formulation", Finite Elem. Anal. Des., 42(14), 1240-1247. https://doi.org/10.1016/j.finel.2006.06.002
  23. Nguyen, D.K. (2004), "Post-buckling behavior of beam on two-parameter elastic foundation", Int. J. Struct. Stab. Dyn., 4(1), 21-43. https://doi.org/10.1142/S0219455404001082
  24. Nguyen, D.K. (2012), "A Timoshenko beam element for large displacement analysis of planar beams and frames", Int. J. Struct. Stab. Dyn., 12(6), 1-9. https://doi.org/10.1142/S0219455412004628
  25. Pacoste, C. and Eriksson, A. (1997), "Beam elements in instability problems", Comput. Methods Appl. Mech. Eng., 144(1-2), 163-197. https://doi.org/10.1016/S0045-7825(96)01165-6
  26. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solids Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  27. Shahba, A., Attarnejad, R., Marvi, M.T. and Hajila, S. (2011), "Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions", Compos. Part B Eng., 42(4), 801-808.
  28. Simsek, M. and Kocatürk, T. (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90(4), 465-473. https://doi.org/10.1016/j.compstruct.2009.04.024
  29. Singh, K.V. and Li, G. (2009), "Buckling of functionally graded and elastically restrained nonuniform column", Compos. Part B Eng., 40(5), 393-403. https://doi.org/10.1016/j.compositesb.2009.03.001
  30. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability, McGraw-Hill, New York, USA.

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