Skip to main content
SpringerLink
Log in

Partially stiffened elastic half-plane with an edge crack

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

Abstract

In the present paper two contact problems referring to the partially stiffened elastic half-plane along its edge with a reinforcement (or stringer) either in the form of a rigid plate or a smooth rigid stamp, are considered. The half-plane contains an edge crack which is arbitrarily pressurized, and is perpendicular to the bounding edge of the half-space. It is assumed that the mid-point of the stringer is located in the axis of the crack. Each of the above two half-plane contact problems is first reduced to a system of two singular integral equations with fixed singularities. Then by employing the generalized method of integral transforms, this system is further reduced to a system of Wiener–Hopf equations that is equivalent to the Riemann matrix boundary value problem. Exact analytical solutions of the two problems are presented in series form. Asymptotic approximations for the stress intensity factor and the energy release rate at the crack tip are also given. Finally, numerical results for the contact stresses, crack opening displacements, stress intensity factor and crack energy are displayed.

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

  • Antipov, Y.A. and Arutyunyan, N.K. (1991). Contact problems of the theory of elasticity in the presence of friction and adhesion. PMM 55, 1005–1017.

    MATH  MathSciNet  Google Scholar 

  • Arutyunyan, N.Kh. (1968). Contact problem for a half plane with elastic reinforcement. Journal of Applied Mathematics and Mechanics (PMM) 32, 665.

    Google Scholar 

  • Bardzokas, D. and Exadaktylos, G. (1995). Plane contact of a cylindrical opening stiffened by a thin shell. Engineering Transactions 43(1–2), 27–44.

    Google Scholar 

  • Bardzokas, D., Exadaktylos, G. and Anastaselos, G. (1996). The effect of stringers and patches on the stress intensities around cracks in plates. Engineering Fracture Mechanics 55(6), 935–955.

    Article  Google Scholar 

  • Buffler, H. (1961). Scheibe mit endlicher, elastischer Versteifung. VDI-Forschungsheft, 485.

  • Chaplygin, S.A. (1950). Pressure of a rigid die on an elastic foundation. (in Russian). Collected Works 3, 317–323.

    Google Scholar 

  • Delale, F. and Erdogan, F. (1982). The crack problem for a half plane stiffened by elastic cover plates. International Journal of Solids Structures 18(5), 381–395.

    Article  MATH  Google Scholar 

  • Doran, H.E. and Buchwald, V.T. (1969). The half-plane with edge crack in plane elastostatics. Journal of Instantaneous Mathematics and Application 5(1), 91–112.

    MATH  Google Scholar 

  • Emery, A.F., Walker, Jr., G.E. and Williams, J.A. (1966). A Green's function for the stress-intensity factors of edge cracks and its application to thermal stresses. Transaction ASME, Series D, Journal of Basic Engineering 88, 45.

    Google Scholar 

  • Erdogan, F. (1971). Analysis of elastic cover plates. Developments in Mechanics 6, 817–830. Proc. 12th Midwestern Mechanics Conference.

    Google Scholar 

  • Gradshteyn, I.S. and Ryzhik, I.M. (1980). Tables of Integrals, Series and Products. Academic Press Inc.

  • Hasebe, N. (1979). Uniform tension of a semi-infinite plate with a crack at an end of a stiffened edge. Ingenieur-Archiv 48, 141.

    Article  MATH  Google Scholar 

  • Jones, D.S. Wiener-Hopf splitting of a 2×2 matrix. Proceedings of the Royal Society of London A 434, 419.

  • Koiter, W.T. (1956). On the flexural rigidity of a beam, weakened by transverse saw cuts. Proceedings of Royal Netherlands Academy of Sciences B59(4), 354–374.

    MathSciNet  Google Scholar 

  • Koiter, W.T. (1965). Note on the stress intensity factors for sheet strips with cracks under tensile loads. University of Technology; Laboratory of Engineering Mechanical Rep. nr. 314, Delft, Netherlands.

  • Muskhelishvili, N.I. (1965). Some basic problems of the mathematical theory of elasticity. Groningen: P. Noordhoff.

    Google Scholar 

  • Sadowski, M. (1928). Zweidimensionale probleme der elastizitatstheorie. ZAMM 8, 107–121.

    Google Scholar 

  • Sneddon, I.N. and Lowengrub, M. (1969). Crack Problems in the Classical Theory of Elasticity. John Wiley and Sons, Inc., 221.

  • Theocaris, P.S. and Bardzokas, D. (1981). The influence of a finite stringer on the stress intensities around cracks in plates. Engineering Fracture Mechanics 14(3), 493–507.

    Article  MathSciNet  Google Scholar 

  • Theocaris, P.S. and Bardzokas, D. (1983). The frictionless contact of cracked elastic bodies. ZAMM 63(2), 80–102.

    MathSciNet  Google Scholar 

  • Titchmarsh, E.C. (1948). An Introduction of the Theory of Fourier Integrals. University of Oxford (2nd edition).

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics A, stuttgart University, Pfaffenwqaldring 57, D-70569, Stuttgart, Germany

    Y.A. Antipov

  2. Department of Engineering Science, Section of Mechanics, National Technical University of Athens, 5 Heroes of Polytechnion Avenue, GR-157 73, Athens, Greece

    D. Bardzokas

  3. Department of Mineral Resources Engineering, Laboratory of Rock Mechanics, Akrotiri, Technical University of Crete, GR-73 100, Chania, Greece

    G.E. Exadaktylos

Authors
  1. Y.A. Antipov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Bardzokas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G.E. Exadaktylos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G.E. Exadaktylos.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Antipov, Y., Bardzokas, D. & Exadaktylos, G. Partially stiffened elastic half-plane with an edge crack. International Journal of Fracture 85, 241–263 (1997). https://doi.org/10.1023/A:1007428813410

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007428813410

Search

Navigation