Skip to main content
SpringerLink
Log in

Stress analysis of functionally gradient beam using effective principal axes

  • Original Paper
  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

The mechanical model is established for the functionally gradient material (FGM) beam with rectangular cross section. A new method of effective principal axes is put forth, based on which the normal stress formula is derived for the FGM beam. The method is verified to be correct by the retrogression of it to the centroidal principal axes method of the traditional beam made of homogeneous elastic material. For several different loading cases, the␣effects of the non-homogeneity parameter on the distribution of the normal stress and on the position of the neutral axis are discussed. It is indicated that, with the increase of the absolute value of the non-homogeneity parameter, the normal stress at the more rigid region in the cross section increases, the normal stress at the less rigid region decreases, and the neutral axis moves toward the more rigid region.

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

Similar content being viewed by others

References

  • Chen, Y.F., Erdogan, F.: The interface crack problem for a non-homogeneous coating bonded to a homogeneous substrate. J. Mech. Phys. Solids 44, 771–787 (1996)

    Article  Google Scholar 

  • Erdogan, F., Ozturk, M.: Periodic cracking of functionally graded coatings. Int. J. Engng. Sci. 33(15), 2179–2195 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  • Erdogan, F., Wu, B.H.: The surface crack problem for a plate with functionally graded properties. J. Appl. Mech. 64(2), 449–456 (1997)

    Article  MATH  Google Scholar 

  • Huang, G.Y., Wang, Y.S., Dietmar, G.: Fracture analysis of functionally graded coatings: antiplane deformation. Eur. J. Mech. A/Solids 21, 391–400 (2002)

    Article  MATH  Google Scholar 

  • Huang, G.Y., Wang, Y.S., Yu, S.W.: Fracture analysis of a functionally graded interfacial zone under plane deformation. Int. J. Solids Struct. 41(3–4), 731–743 (2004)

    Article  MATH  Google Scholar 

  • Konda, N., Erdogan, F.: The mixed-mode crack problem in a nonhomogeneous elastic medium. Engng. Fract. Mech. 47(3), 533–545 (1994)

    Article  Google Scholar 

  • Li, Y.D., Jia, B., Zhang, N., Tang, L.Q., Dai, Y.: Dynamic stress intensity factor of the weak/micro-discontinuous interface crack of a FGM coating. Int. J. Solids Struct. 43(16), 4795–4809 (2006)

    Google Scholar 

  • Li, C.Y., Weng, G.J.: Dynamic stress intensity factors of a cylindrical interface crack with a functionally graded interlayer. Mech. Mater. 33, 325–333 (2001)

    Article  Google Scholar 

  • Wang, Y.S., Huang, G.Y., Gross, D.: On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: anti-plane deformation. J. Appl. Mech. 70(3), 676–680 (2003a)

    Article  MATH  Google Scholar 

  • Wang, B.L., Mai, Y.W., Sun, Y.G.: Anti-plane fracture of a functionally graded material strip. Eur. J. Mech. A/Solids 22(3), 357–368 (2003b)

    Article  MATH  Google Scholar 

  • Wang, X.Y., Zou, Z.Z., Wang, D.: On the penny-shaped crack in a nonhomogeneous interlayer of adjoining two different elastic materials. Int. J. Solids Struct. 34(30), 3911–3921 (1997)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Engineering Mechanics, Department of Mechanical Engineering, Armored Force Engineering Institute, No. 21, Du Jia Kan, Chang Xin Dian, Beijing, 100072, P.R. China

    Li Yongdong, Zhang Hongcai, Zhang Nan & Dai Yao

Authors
  1. Li Yongdong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhang Hongcai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhang Nan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dai Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li Yongdong.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yongdong, L., Hongcai, Z., Nan, Z. et al. Stress analysis of functionally gradient beam using effective principal axes. Int J Mech Mater Des 2, 157–164 (2005). https://doi.org/10.1007/s10999-006-9000-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10999-006-9000-4

Keywords

Search

Navigation