Skip to main content
SpringerLink
Log in

Steady state thermal stresses in an elastic solid bounded by two cones

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Zusammenfassung

Es wird für das Problem der Wärmespannungen in einem kegelförmig begrenzten elastischen Körper eine Ähnlichkeitstransformation entwickelt. Ist die Temperatur an der freien Oberfläche als Potenz des Abstandes von der Spitze vorgeschrieben, so lässt sich ein Satz von Ähnlichkeitsvariablen angeben, welcher die thermoelastischen Beziehungen auf Legendre-Gleichungen reduziert und damit der Lösung leicht zugänglich macht. Die Rechnung ist für den Sonderfall konstant gehaltener Oberflächentemperatur im einzelnen durchgeführt.

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

References

  1. Abbott, D. E., andKline, S. J.,Simple Methods of Classification and Construction of Similarity of Partial Differential Equations, AFOSR-TN-60-1163, October 1960.

  2. Birkhoff, G.,Hydrodynamics (Princeton Univ. Press, 1960).

  3. Manohar, R.,Some Similarity Solutions of Partial Differential Equations of Boundary Layers, MRC Tech. Rep. 375 (January 1963).

  4. Morgan, A. J. A.,The Reduction by One of the Number of Independent Variables in Some System of Partial Differential Equations, Quart. J. Math.2, 250 (1952).

    Google Scholar 

  5. Morgan, A. J. A.,Stress Distribution in Semi-infinite Solids of Revolution, Z. angew. Math. Phys.5, 330 (1954).

    Google Scholar 

  6. Morgan, A. J. A.,Stress Distribution Within Solids Bounded by One or Two Cones, Z. angew. Math. Phys.7, 130 (1956).

    Google Scholar 

  7. Muki, R., andSternberg, E.,Steady State Heat Conduction in a Circular Cone, Z. angew. Math. Phys.11, 306 (1960).

    Google Scholar 

  8. Muki, R., andSternberg, E.,Steady State Thermal Stresses in an Elastic Cone, Z. angew. Math. Phys.11, 471 (1960).

    Google Scholar 

  9. Nowacki, W.,Zagadnienia Termosprezystosci (Polish) (Warszawa 1960), p. 22–24.

  10. Singh, A.,The distribution of Stresses in Transversely Isotropic Bodies of Revolution Bounded by One or Two Cones, J. S. E. R.5, 7 (1961).

    Google Scholar 

  11. Singh, A.,Thermal Stresses Within Isotropic Bodies Bounded by One or Two Cones, J. S. E. R.6, 201 (1962).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Rensselaer Polytechnic Institute, Troy, N. Y., USA

    Subhendu K. Datta

Authors
  1. Subhendu K. Datta
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work has been done at the Mathematics Research Center, University of Wisconsin, under the U.S. Army Contract DA-11-022-ORD-2059.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Datta, S.K. Steady state thermal stresses in an elastic solid bounded by two cones. Journal of Applied Mathematics and Physics (ZAMP) 15, 175–183 (1964). https://doi.org/10.1007/BF01602659

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01602659

Keywords

Search

Navigation