Skip to main content
SpringerLink
Log in

Elasticity Solution of a Cantilever Functionally Graded Beam

  • Published:
Applied Composite Materials Aims and scope Submit manuscript

Abstract

This paper considers the plane stress problem of a cantilever functionally graded beam subjected to linearly distributed load. 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 numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a functionally graded cantilever beam.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Timoshenko, S.P., Goodier, J.N.: Theory of elasticity, 3rd edn. McGraw-Hill, New York (1970)

    Google Scholar 

  2. Lekhnitskii, S.G.: Anisotropic plate. Gordon and Breach, New York (1968)

    Google Scholar 

  3. Silverman, I.K.: Orthotropic beams under polynomial loads. Proceeding ASCE. J. Eng. Mech. Div. 90, 293–319 (1964)

    Google Scholar 

  4. Ding, H.J., Huang, D.J., Wang, H.M.: Analytical solution for fixed-end beam subjected to uniform load. J. Zhejiang Univ. Sci. 6A(8), 779–783 (2005)

    Article  Google Scholar 

  5. Ahmed, S.R., Idris, B.M., Uddin, M.W.: Numerical solution of both ends fixed deep beams. Comput. Struct. 61(1), 21–29 (1996)

    Article  Google Scholar 

  6. Shi, Z.F.: General solution of a density functionally gradient piezoelectric cantilever and its applications. Smart Mater. Struct. 11, 122–129 (2002)

    Article  CAS  Google Scholar 

  7. Shi, Z.F., Chen, Y.: Functionally graded piezoelectric cantilever beam under load. Arch. Appl. Mech. 74, 237–247 (2004)

    Google Scholar 

  8. Zhang, L.N., Shi, Z.F.: Analytical solution of a simply supported piezoelectric beam subjected to a uniformly distributed loading. Appl. Math Mech. 24, 1215–1223 (2003)

    Article  Google Scholar 

  9. Sankar, B.V.: An elasticity solution for functionally graded beams. Compos Sci. Technol. 61, 689–696 (2001)

    Article  Google Scholar 

  10. Sankar, B.V., Taeng, J.T.: Thermal stresses in functionally graded beams. AIAA J. 40, 1228–1232 (2002)

    Article  Google Scholar 

  11. Venkataraman, S., Sankar, B.V.: Elasticity solution for stresses in a sandwich beam with functionally graded core. AIAA J. 41, 2501–2505 (2003)

    Article  Google Scholar 

  12. Zhu, H., Sankar, B.V.: A combined Fourier series-Galerkin method for the analysis of functionally graded beams. ASME J. Appl. Mech. 71, 421–424 (2004)

    Article  Google Scholar 

  13. Ding, H.J., Huang, D.J., Chen, W.Q.: Elasticity solutions for plane anisotropic functionally graded beams. Int. J. Solids. Struct. 44(1), 176–196 (2007)

    Article  Google Scholar 

  14. Huang, D.J., Ding, H.J., Chen, W.Q.: Piezoelasticity solutions for functionally graded piezoelectric beams. Smart. Mater. Struct. 16(3), 387–395 (2007)

    Google Scholar 

  15. Huang, D.J., Ding, H.J., Chen, W.Q.: Analytical solution for functionally graded anisotropic cantilever beam subjected to linearly distributed load. J. Appl. Math. Mech. 28(7), 855–860 (2007)

    Article  Google Scholar 

  16. Sallai, B.-O., Tounsi, A., Mechab, I., Bachir Bouiadjra, M., Meradjah, M., Adda Bedia, E.A.: A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams. Comput. Mater. Sci. 44, 1344–1350 (2009)

    Article  Google Scholar 

  17. Benatta, M.A., Mechab, I., Tounsi, A., Adda bedia, E.A.: Static analysis of functionally graded short beams including warping and shear deformation effects. Comput. Mater. Sci. 44, 765–773 (2008)

    Article  CAS  Google Scholar 

  18. Zhong, Zheng, Yu, Tao: Analytical solution of a cantilever functionally graded beam. Compos. Sci. Tech. 67, 481–488 (2007)

    Article  Google Scholar 

  19. Delale, F., Erdogan, F.: The crack problem for a nonhomogeneous plane. ASME J. Appl. Mech. 50, 609–614 (1983)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Ibn Khaldoun, BP 78 Zaaroura, 14000, Tiaret, Algérie

    Tahar Hassaine Daouadji & Abdelaziz Hadj Henni

  2. Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, BP 89 Cité Ben M’hidi, 22000, Sidi Bel Abbes, Algérie

    Tahar Hassaine Daouadji, Abdelaziz Hadj Henni, Abdelouahed Tounsi & Adda Bedia El Abbes

Authors
  1. Tahar Hassaine Daouadji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdelaziz Hadj Henni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdelouahed Tounsi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Adda Bedia El Abbes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tahar Hassaine Daouadji.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Daouadji, T.H., Henni, A.H., Tounsi, A. et al. Elasticity Solution of a Cantilever Functionally Graded Beam. Appl Compos Mater 20, 1–15 (2013). https://doi.org/10.1007/s10443-011-9243-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10443-011-9243-6

Keywords

Search

Navigation