Skip to main content
SpringerLink
Log in

Complex variable method for problems of a laminate composed of multiple isotropic layers

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

A new method of the analysis of a plate composed of thin layers of isotropic linear elastic material is developed. A general solution for displacement, resultant stress and resultant moment fields is obtained by using the complex function theory. It is proved that the complete solutions of the laminated plate subjected to tractions prescribed on its boundary can be obtained from the sum of solutions for uncoupled plates. Particular attention is devoted to the crack tip field and energy release rate for the laminated plate. A closed form solution for singular fields near the crack tip and the relation between the J-integral and the intensity factors are derived through the complex potential formula. Complete forms of the complex potentials for a crack in an infinite laminate as well as for the singularities such as a point force, a point moment and a dislocation are also obtained.

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

  • Becker, W. (1991). A complex potential method for plate problems with bending extension coupling. Archive of Applied Mechanics 61, 318–326.

    Article  MATH  Google Scholar 

  • Becker, W. (1992). Closed–form analytical solutions for a Griffith crack in a non–symmetric laminate plate. Composite Structures 21, 49–55.

    Article  Google Scholar 

  • Beom, H.G. and Earmme, Y.Y. (1997). The elastic field of an elliptic cylindrical inclusion in a laminate with multiple isotropic layers. Journal of Applied Mechanics, Accepted for Publication.

  • Eshelby, J.D., Read, W.T. and Shockley, W. (1953). Anisotropic elasticity with applications to dislocation theory. Acta Metallurgica 1, 251–259.

    Article  Google Scholar 

  • Hui, C.Y. and Zehnder, A.T. (1993). A theory for the fracture of thin plates subjected to bending and twisting moments. International Journal of Fracture 61, 211–229.

    Article  ADS  Google Scholar 

  • Irwin, G.R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate. Journal of Applied Mechanics 24, 361–364.

    Google Scholar 

  • Jones, R.M. (1975). Mechanics of Composite Materials. Scripta, Washington.

    Google Scholar 

  • Lekhnitskii, S.G. (1963). Theory of Elasticity of an Anisotropic Elastic Body.Holden–Day, San Francisco.

    MATH  Google Scholar 

  • Lu, P. and Mahrenholtz, O. (1994). Extension of the Stroh formalism to the analysis of bending of anisotropic elastic plates. Journal of the Mechanics and Physics of Solids 42, 1725–1741.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Murakami, Y. (1987). Stress Intensity Factors Handbook. Pergamon, Oxford.

    Google Scholar 

  • Muskhelishvili, N.I. (1954). Some Basic Problems of the Mathematical Theory of Elasticity.Noordhoff International Publishing, Leyden.

    MATH  Google Scholar 

  • Reismann, H. and Pawlik, P.S. (1980). Elasticity: Theory and Applications. John Wiley & Sons, New York.

    MATH  Google Scholar 

  • Rice, J.R. (1968). A path–independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 35, 379–386.

    Google Scholar 

  • Sanders, J.L., Jr. (1960). On the Griffith–Irwin fracture theory. Journal of Applied Mechanics 27, 352–353.

    MATH  MathSciNet  Google Scholar 

  • Savin, G.N. (1961). Stress Concentration Around Holes.Pergamon Press, London.

    MATH  Google Scholar 

  • Stroh, A.N. (1958). Dislocations and cracks in anisotropic elasticity. Philosophical Magazine 7, 625–646.

    Article  MathSciNet  ADS  Google Scholar 

  • Suo, Z. (1989). Singularities interacting with interfaces and cracks. International Journal of Solids and Structures 25, 1133–1142.

    Article  Google Scholar 

  • Timoshenko, S.P. and Woinowsky–Krieger, S. (1959). Theory of Plates and Shells.McGraw–Hill, London.

    MATH  Google Scholar 

  • Williams, M.L. (1961). The bending stress distribution at the base of a stationary crack. Journal of Applied Mechanics 28, 78–82.

    MATH  Google Scholar 

  • Young, W.C. (1989). Roark's Formulas for Stress and Strain.McGraw–Hill, London.

    Google Scholar 

  • Zakharov, D.D. (1995). Formulation of boundary–value problems of statics for thin elastic asymmetrically–laminated anisotropic plates and solution using functions of a complex variable. Journal of Applied Mathematics and Mechanics 59, 615–623.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering, Chonnam National University, 300, Yongbong-dong, Kwangju, 500-757, Korea; e-mail

    H.G. Beom

  2. Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Kusong-dong, Yusung-gu, Taejon, 305-701, Korea

    Y.Y. Earmme

Authors
  1. H.G. Beom
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y.Y. Earmme
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beom, H., Earmme, Y. Complex variable method for problems of a laminate composed of multiple isotropic layers. International Journal of Fracture 92, 305–324 (1998). https://doi.org/10.1023/A:1007570226527

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007570226527

Search

Navigation