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Buckling analysis of functionally graded material grid systems

  • Darilmaz, K. (Civil Engineering Department, Istanbul Technical University) ;
  • Aksoylu, M. Gunhan (Civil Engineering Department, Istanbul Technical University) ;
  • Durgun, Yavuz (Civil Engineering Department, Istanbul Technical University)
  • Received : 2014.03.24
  • Accepted : 2014.11.15
  • Published : 2015.06.10

Abstract

This paper aims to fill the technical gap on the elastic buckling behavior of functionally graded material (FGM) grid systems under inplane loads on which few research has been done. Material properties of an FG beam are assumed to vary smoothly in the thickness direction according to power and exponential laws. Based on a hybrid-stress finite element formulation, buckling solutions for FGM grid systems consisting of various aspect ratios and material gradation are provided. The numerical results demonstrate that the aspect ratio and material gradation play an important role in the buckling behavior of FGM grid systems. We believe that the new results obtained from this study, will be very useful to designers and researchers in this field.

Keywords

References

  1. ANSYS (1997), Swanson Analysis Systems, Swanson J. ANSYS 5.4, U.S.A.
  2. Akgoz, B. and Civalek, O. (2014), "Shear deformation beam models for functionally graded microbeams with new shear correction factors", Compos. Struct., 112, 214-225. https://doi.org/10.1016/j.compstruct.2014.02.022
  3. Aydogdu, M. and Taskin, V. (2007), "Free vibration analysis of functionally graded beams with simply supported edges", Mater. Des., 28(5),1651-6. https://doi.org/10.1016/j.matdes.2006.02.007
  4. Atmane, H.A., Tounsi, A., Ziane, N. and Mechab, I. (2011), "Mathematical solution for free vibration of sigmoid functionally graded beams with varying cross-section", Steel Compos. Struct., 11(6), 489-504. https://doi.org/10.12989/scs.2011.11.6.489
  5. Bouremana, M., Houari, M.S.A., Tounsi, A., Kaci, A. and Bedia, E.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel Compos. Struct., 15(5), 467-479. https://doi.org/10.12989/scs.2013.15.5.467
  6. Cetin, D. and Simsek, M. (2011), "Free vibration of an axially functionally graded pile with pinned ends embedded in Winkler-Pasternak elastic medium", Struct. Eng. Mech., 40(4), 583-594. https://doi.org/10.12989/sem.2011.40.4.583
  7. Chakraborty, A., Gopalakrishnan, S. and Reddy, J.N. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45, 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4
  8. Chakraborty, A. and Gopalakrishnan, S. (2003), "A spectrally formulated finite element for wave propagation analysis in functionally graded beams", Int. J. Solid. Struct., 40(10), 2421-2448. https://doi.org/10.1016/S0020-7683(03)00029-5
  9. Ching, H.K. and Yen, S.C. (2005), "Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads", J. Compos. Part B. Eng., 36, 223-240. https://doi.org/10.1016/j.compositesb.2004.09.007
  10. Darilmaz, K. (2012), "Analysis of sandwich plates: a three-dimensional assumed stress hybrid finite element", J. Sandw. Struct. Mater., 14(4), 487-501. https://doi.org/10.1177/1099636212443916
  11. Darilmaz, K. (2011), "Influence of aspect ratio and fibre orientation on the stability of simply supported orthotropic skew plates", Steel Compos. Struct., 11(5), 359-374. https://doi.org/10.12989/scs.2011.11.5.359
  12. Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., 18(2), 395-408. https://doi.org/10.12989/scs.2015.18.2.395
  13. Giunta, G., Koutsawa, Y., Belouettar, S. and Calvi, A. (2014), "A dynamic analysis of three-dimensional functionally graded beams by hierarchical models", Smart Struct. Syst., 13(4), 637-657. https://doi.org/10.12989/sss.2014.13.4.637
  14. Kapuria, S., Bhattacharyya, M. and Kumar, A.N. (2008), "Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation", Compos. Struct., 82(3), 390-402. https://doi.org/10.1016/j.compstruct.2007.01.019
  15. Kim, J. and Paulino, G.H. (2002), "Finite element evaluation of mixed mode stress intensity factors in functionally graded materials", Int. J. Numer. Meth. Eng., 53(8), 1903-1935. https://doi.org/10.1002/nme.364
  16. Kocaturk, T. and Akbas, S.D. (2013), "Thermal post-buckling analysis of functionally graded beams with temperature-dependent physical properties", Steel Compos. Struct., 15(5), 481-505. https://doi.org/10.12989/scs.2013.15.5.481
  17. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib., 318(4-5), 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056
  18. Li, S.R. and Batra, R.C. (2013), "Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams", Compos. Struct., 95, 5-9. https://doi.org/10.1016/j.compstruct.2012.07.027
  19. Lu, C.F. and Chen, W.Q. (2005), "Free vibration of orthotropic functionally graded beams with various end conditions", Struct. Eng. Mech., 20(4), 465-476. https://doi.org/10.12989/sem.2005.20.4.465
  20. Lu, C.F., Chen, W.Q., Xu, R.Q. and Lim, C.W. (2008), "Semi-analytical elasticity solutions for bi-directional functionally graded beams", Int. J. Solid. Struct., 45, 258-275. https://doi.org/10.1016/j.ijsolstr.2007.07.018
  21. Pian, T.H.H. and Chen, D.P. (1983), "On the suppression of zero energy deformation modes", Int. J. Numer. Meth. Eng., 19, 1741-1752. https://doi.org/10.1002/nme.1620191202
  22. Qian, L.F. and Ching, H.K. (2004), "Static and dynamic analysis of 2D functionally graded elasticity by using meshless local Petrov-Galerkin method", J. Chinese Inst. Eng., 27, 491-503. https://doi.org/10.1080/02533839.2004.9670899
  23. Sanjay Anandrao, K., Gupta, R.K., Ramchandran, P. and Venkateswara Rao, G. (2012), "Non-linear free vibrations and post- buckling analysis of shear flexible functionally graded beams", Struct. Eng. Mech., 44(3), 339-361. https://doi.org/10.12989/sem.2012.44.3.339
  24. Sankar, B.V. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0
  25. Simsek, M. and Reddy, J.N. (2013), "A unified higher order beam theory for buckling of a functionally graded microbeam embedded in elastic medium using modified couple stress theory", Compos. Struct., 101, 47-58. https://doi.org/10.1016/j.compstruct.2013.01.017
  26. Simsek, M. (2009), "Static analysis of a functionally graded beam under a uniformly distributed load by Ritz method", Int. J. Eng. Appl. Sci., 1(3), 1-11.
  27. Simsek, M. and Kocaturk, T. (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90, 465-473. https://doi.org/10.1016/j.compstruct.2009.04.024
  28. Simsek, M. (2010), "Vibration analysis of a functionally graded beam under a moving mass by using different beam theories", Compos. Struct., 92, 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030
  29. Tajalli, S.A., Rahaeifard, M., Kahrobaiyan, M.H., Movahhedy, M.R., Akbari, J. and Ahmadian, M.T. (2013), "Mechanical behavior analysis of size-dependent micro-scaled functionally graded Timoshenko beams by strain gradient elasticity theory", Compos. Struct., 102, 72-80. https://doi.org/10.1016/j.compstruct.2013.03.001
  30. Wakashima, K., Hirano, T. and Niino, M. (1990), "Space applications of advanced structural materials", ESA, SP-303, 97.
  31. Xiang, H.J. and Yang, J. (2007), "Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction", J. Compos. Part B, 39(2), 292-303.
  32. Ying, J., Lu, C.F. and Chen, W.Q. (2008), "Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations", Compos. Struct., 84(3), 209-219. https://doi.org/10.1016/j.compstruct.2007.07.004
  33. Yang, J. and Chen, Y. (2008), "Free vibration and buckling analyses of functionally graded beams with edge cracks", Compos. Struct., 83(1), 48-60. https://doi.org/10.1016/j.compstruct.2007.03.006
  34. Yang, J., Chen, Y., Xiang, Y. and Jia, X.L. (2008), "Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load", J. Sound Vib., 312(1-2), 166-181. https://doi.org/10.1016/j.jsv.2007.10.034
  35. Zhong, Z. and Yu, T. (2007), "Analytical solution of a cantilever functionally graded beam", Compos. Sci. Technol., 67(3-4), 481-488. https://doi.org/10.1016/j.compscitech.2006.08.023

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