Advances in materials Research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Theoretical analysis of composite beams under uniformly distributed load

  • Received : 2016.03.20
  • Accepted : 2016.04.28
  • Published : 2016.03.25
⟨ Previous Next ⟩

Abstract

The bending problem of a functionally graded cantilever beam subjected to uniformly distributed load is investigated. The material properties of the functionally graded beam are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. A practical example is presented to show the application of the method.

Keywords

References

  1. Ahmed, S.R., Idris, B.M. and Uddin, M.W. (1996), "Numerical solution of both ends fixed deep beams", Comput. Struct., 61(1), 21-29. https://doi.org/10.1016/0045-7949(96)00029-6
  2. 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
  3. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  4. 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
  5. Ben-Oumrane, S., Abedlouahed, T., Ismail, M., Mohamed, B.B., Mustapha, M. and El Abbas, A.B. (2009), "A theoretical analysis of flexional bending of Al/Al 2 O 3 S-FGM thick beams", Comput. Mater. Sci., 44(4), 1344-1350. https://doi.org/10.1016/j.commatsci.2008.09.001
  6. Daouadji, T.H. (2015), "Analytical solution of nonlinear cylindrical bending for functionally graded plates", Geomech. Eng., 9(5), 631-644. https://doi.org/10.12989/gae.2015.9.5.631
  7. Ding, H.J., Huang, D.J. and Chen, W.Q. (2007), "Elasticity solutions for plane anisotropic functionally graded beams", Int. J. Solid. Struct., 44(1), 176-196. https://doi.org/10.1016/j.ijsolstr.2006.04.026
  8. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  9. Huang, D.J., Ding, H.J. and Chen, W.Q. (2007), "Piezoelasticity solutions for functionally graded piezoelectric beams", Smart Mater. Struct., 16(3), 687. https://doi.org/10.1088/0964-1726/16/3/015
  10. Lekhnitskii, S.G. (1968), Anisotropic plate, Gordon and Breach, New York.
  11. Lin-nan, Z. and Zhi-fei, S. (2003), "Analytical solution of a simply supported piezoelectric beam subjected to a uniformly distributed loading", Appl. Math. Mech., 24(10), 1215-1223. https://doi.org/10.1007/BF02438110
  12. Sankar, B.V. and Tzeng, J.T. (2002), "Thermal stresses in functionally graded beams", AIAA J., 40(6), 1228-1232. https://doi.org/10.2514/2.1775
  13. Shi, Z.F. and Chen, Y. (2004), "Functionally graded piezoelectric cantilever beam under load", Arch. Appl. Mech., 74(3-4), 237-247. https://doi.org/10.1007/s00419-004-0346-5
  14. Silverman, I.K. (1964), "Orthotropic beams under polynomial loads", J. Eng. Mech., 90(5), 293-320.
  15. Timoshenko, S.P. and Goodier, J.N. (1970), Theory of elasticity, 3rd Ed., McGraw-Hill, New York.
  16. Tlidji, Y., Daouadji, T.H., Hadji, L., Tounsi, A. and Bedia, E.A.A. (2014), "Elasticity solution for bending response of functionally graded sandwich plates under thermomechanical loading", J. Therm. Stresses, 37(7), 852-869. https://doi.org/10.1080/01495739.2014.912917
  17. Tounsi, A., Bourada, M., Kaci, A. and Houari, M.S.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
  18. Venkataraman, S. and Sankar, B.V. (2003), "Elasticity solution for stresses in a sandwich beam with functionally graded core", AIAA J., 41(12), 2501-2505. https://doi.org/10.2514/2.6853
  19. Zhu, H. and Sankar, B.V. (2004), "A combined fourier series-glerkin method for the analysis of functionally graded beams", J. Appl. Mech., 71(3), 421-424. https://doi.org/10.1115/1.1751184
  20. Zoubida, K., Daouadji, T.H., Hadji, L., Tounsi, A. and El Abbes, A.B. (2015), "A new higher order shear deformation model of functionally graded beams based on neutral surface position", Transactions of the Indian Institute of Metals, 1-9.

Cited by

  1. Elastic-plastic fracture of functionally graded circular shafts in torsion vol.5, pp.4, 2016, https://doi.org/10.12989/amr.2016.5.4.299
  2. Transient thermo-mechanical response of a functionally graded beam under the effect of a moving heat source vol.6, pp.1, 2016, https://doi.org/10.12989/amr.2017.6.1.027
  3. Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates vol.7, pp.2, 2016, https://doi.org/10.12989/amr.2018.7.2.119
  4. Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix vol.70, pp.3, 2019, https://doi.org/10.12989/sem.2019.70.3.269
  5. Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate vol.16, pp.5, 2016, https://doi.org/10.12989/eas.2019.16.5.601
  6. Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions vol.70, pp.5, 2019, https://doi.org/10.12989/sem.2019.70.5.535
  7. Flexural behaviour of steel beams reinforced by carbon fibre reinforced polymer: Experimental and numerical study vol.72, pp.4, 2019, https://doi.org/10.12989/sem.2019.72.4.409
  8. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2016, https://doi.org/10.12989/amr.2020.9.4.265
  9. Thermo-mechanical behavior of porous FG plate resting on the Winkler-Pasternak foundation vol.9, pp.6, 2016, https://doi.org/10.12989/csm.2020.9.6.499
  10. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575
  11. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity vol.77, pp.2, 2016, https://doi.org/10.12989/sem.2021.77.2.217
  12. Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity vol.10, pp.1, 2016, https://doi.org/10.12989/csm.2021.10.1.061
  13. Analysis on the buckling of imperfect functionally graded sandwich plates using new modified power-law formulations vol.77, pp.6, 2016, https://doi.org/10.12989/sem.2021.77.6.797
  14. Multilevel Analysis of Strain Rate Effect on Visco-Damage Evolution in Short Random Fiber Reinforced Polymer Composites vol.36, pp.2, 2016, https://doi.org/10.1515/ipp-2020-4045