Skip to main content
SpringerLink
Log in

Nonstationary Problem of Torsion for an Elastic Cone with Spherical Crack

  • Published:
Materials Science Aims and scope

Abstract

We solve the problem of torsion of an elastic cone weakened by a spherical crack under the action of an impact moment applied to the vertex. For the solution of the problem, we use an approach based on the method of discontinuous solutions. The problem is reduced to a one-dimensional integrodifferential equation for the unknown jump of displacements in the space of Laplace transforms. An approximate solution of this equation is obtained by applying the procedure of discretization of the investigated equation in time in combination with the method of orthogonal polynomials. As a result, we deduce a formula for finding the stress intensity factor.

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

  1. V. V. Bozhydarnyk and G. T. Sulym, Elements of the Theory of Elasticity [in Ukrainian], Svit, Lviv (1994).

    Google Scholar 

  2. G. Ya. Popov, Concentration of Elastic Stresses Near Stamps, Cuts, Thin Inclusions, and Reinforcements [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  3. G. Ya. Popov, “Some integral transformations and their application to the solution of boundary-value problems of mathematical physics,” 53, No. 6, 810–819 (2001).

    Google Scholar 

  4. N. N. Lebedev, I. P. Skal'skaya, and Ya. S. Uflyand, Collection of Problems in Mathematical Physics [in Russian], Gostekhteorizdat, Moscow (1955).

    Google Scholar 

  5. G. Ya. Popov, Yu. A. Morozov, and N. D. Vaisfel'd, “Solution of dynamical problems of concentration of elastic stresses near defects on cylindrical surfaces,” Prikl. Mekh., No. 1, 50–59 (1999).

  6. H. Bateman and A. Erdélyi, Higher Transcendental Functions, MacGrow-Hill, New York etc. (1953).

    Google Scholar 

  7. M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, Appl. Mathematics Series-55 (1964).

  8. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  9. F. Oberhettinger and L. Badii, Tables of Laplace Transforms, Springer Verlag, New-York, etc. (1972).

    Google Scholar 

  10. G. Bateman and A. Erdélyi, Tables of Integral Transforms, MacGrow-Hill, New York etc. (1954).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechnikov Odessa National University, Odessa

    N. D. Vaisfel'd

Authors
  1. N. D. Vaisfel'd
    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

Vaisfel'd, N.D. Nonstationary Problem of Torsion for an Elastic Cone with Spherical Crack. Materials Science 38, 698–708 (2002). https://doi.org/10.1023/A:1024266524535

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024266524535

Keywords

Search

Navigation