Advances in materials Research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Static deflection and dynamic behavior of higher-order hyperbolic shear deformable compositionally graded beams

  • Bensaid, Ismail (Department of Mechanical Engineering, IS2M Laboratory, Faculty of Technology, University of Tlemcen) ;
  • Cheikh, Abdelmadjid (Department of Mechanical Engineering, IS2M Laboratory, Faculty of Technology, University of Tlemcen) ;
  • Mangouchi, Ahmed (Department of Mechanical Engineering, IS2M Laboratory, Faculty of Technology, University of Tlemcen) ;
  • Kerboua, Bachir (EOLE Laboratory, Faculty of Technology, University of Tlemcen)
  • Received : 2016.12.24
  • Accepted : 2017.03.07
  • Published : 2017.03.25
⟨ Previous Next ⟩

Abstract

In this work we introduce a higher-order hyperbolic shear deformation model for bending and frees vibration analysis of functionally graded beams. In this theory and by making a further supposition, the axial displacement accounts for a refined hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the beam boundary surfaces, so no need of any shear correction factors (SCFs). The material properties are continuously varied through the beam thickness by the power-law distribution of the volume fraction of the constituents. Based on the present refined hyperbolic shear deformation beam model, the governing equations of motion are obtained from the Hamilton's principle. Analytical solutions for simply-supported beams are developed to solve the problem. To verify the precision and validity of the present theory some numerical results are compared with the existing ones in the literature and a good agreement is showed.

Keywords

References

  1. Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  2. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  3. Allahverdizadeh, A., Eshraghi, I., Mahjoob, M.J. and Nasrollahzadeh, N. (2014), "Nonlinear vibration analysis of FGER sandwich beams", J. Mech. Sci., 78(1), 167-176. https://doi.org/10.1016/j.ijmecsci.2013.11.012
  4. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  5. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  6. Benatta, M.A, Tounsi, A., Mechab, I. and Bachir Bouiadjra, M. (2009), "Mathematical solution for bending of short hybrid composite beams with variable fibers spacing", Appl. Math. Comput., 212(2), 337-348. https://doi.org/10.1016/j.amc.2009.02.030
  7. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  8. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  9. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  10. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  11. Bouremana, M, Houari, M.S.A., Tounsi, A., Kaci, A. and Adda 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
  12. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", J. Comput. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  13. Ebrahimi, F. and Barati, M.R. (2016), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A., 122(9), 1-14.
  14. Hadji, L., Daouadji, T.H., Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519. https://doi.org/10.12989/scs.2014.16.5.507
  15. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  16. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  17. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  18. Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015
  19. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B: Eng., 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9
  20. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vibr., 318(4-5), 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056
  21. Li, X.F., Wang, B.L. and Han, J.C. (2010), "A higher-order theory for static and dynamic analyses of functionally graded beams", Arch. Appl. Mech., 80(10), 1197-1212. https://doi.org/10.1007/s00419-010-0435-6
  22. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  23. Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793
  24. Nareen, K. and Shimpi, R.P. (2014), "Refined hyperbolic shear deformation plate theory", J. Mech. Eng. Sci., 229(15), 2675-2686.
  25. Nguyen, T.K. (2015), "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", J. Mech. Mater. Des., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3
  26. Nguyen, T.K., Vo, T.P. and Thai, H.T. (2013), "Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory", Compos. Part B: Eng., 55, 147-157. https://doi.org/10.1016/j.compositesb.2013.06.011
  27. Ould, L.L., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Bas. Des. Struct., 41(4), 421-433. https://doi.org/10.1080/15397734.2013.763713
  28. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons Inc., New York, U.S.A.
  29. Sallai, B.O., Tounsi, A., Mechab, I., Bachir, B.M., Meradjah, M. and Adda, B.E.A. (2009), "A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams", Comput. Mater. Sci., 44(4), 1344-1350. https://doi.org/10.1016/j.commatsci.2008.09.001
  30. 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
  31. Simsek, M. (2010a), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nucl. Eng. Des., 240(4), 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013
  32. Simsek, M. (2010b), "Vibration analysis of a functionally graded beam under a moving mass by using different beam theories", Compos. Struct., 92(4), 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030
  33. Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
  34. Thai, H.T., Nguyen, T.K., Vo, T.P. and Lee, J. (2014), "Analysis of functionally graded sandwich plates using a new first-order shear deformation theory", Eur. J. Mech., 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008
  35. Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", J. Mech. Sci., 62(1), 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014
  36. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547
  37. Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015), "A quasi-3D theory for vibration and buckling of functionally graded sandwich beams", Compos. Struct., 119, 1-12. https://doi.org/10.1016/j.compstruct.2014.08.006
  38. 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

Cited by

  1. Non-linear delamination in two-dimensional functionally graded multilayered beam vol.9, pp.5, 2018, https://doi.org/10.1108/IJSI-12-2017-0079
  2. Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities vol.6, pp.1, 2017, https://doi.org/10.12989/amr.2017.6.1.045
  3. Thermal stability analysis of temperature dependent inhomogeneous size-dependent nano-scale beams vol.7, pp.1, 2017, https://doi.org/10.12989/amr.2018.7.1.001
  4. Eigenfrequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory vol.22, pp.1, 2018, https://doi.org/10.12989/sss.2018.22.1.121
  5. A novel first order refined shear-deformation beam theory for vibration and buckling analysis of continuously graded beams vol.6, pp.3, 2017, https://doi.org/10.12989/aas.2019.6.3.189
  6. A GN-based modified model for size-dependent coupled thermoelasticity analysis in nano scale, considering nonlocality in heat conduction and elasticity: An analytical solution for a nano beam with ene vol.73, pp.3, 2017, https://doi.org/10.12989/sem.2020.73.3.287
  7. Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects vol.234, pp.18, 2017, https://doi.org/10.1177/0954406220916481