Skip to main content
SpringerLink
Log in

Inverse transient thermoelastic deformations in thin circular plates

  • Published:
Sadhana Aims and scope Submit manuscript

Abstract

This paper deals with the determination of unknown heating temperatures and temperature distributions on the upper surface of a thin circular plate, defined as 0 ≤ r ≤a, —b/2 ≤z ≤b/2. The expressions of unknown heating temperatures and temperature distributions are obtained in series form, involving Bessel’s functions with the help of the integral transform technique. Thermoelastic deformations are discussed with the help of temperature and are illustrated numerically.

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

  • Boley B A, Weiner J H 1960Theory of thermal stresses (New York: John Wiley and Sons)

    MATH  Google Scholar 

  • Deshmukh K C, Wankhede P C 1998 An inverse transient problem of a quasi-static thermal deflection of a thin clamped circular plate.Bull. Pure Appl. Sci. 17: 1, 165–172

    MATH  Google Scholar 

  • Grysa K W, Cialkowski M J 1980 On a certain inverse problem of temperature and thermal stress field.Acta Mech. 36: 169–185

    Article  MATH  MathSciNet  Google Scholar 

  • Grysa K W, Kozlowski Z 1982 One dimensional problems of temperature and heat flux determination at the surfaces of a thermoelastic slab, Part 1: The analytical solutions.Nucl. Engrg. Des. 74: 1–14

    Article  Google Scholar 

  • Ishihara M, Noda N 1997 Theoretical analysis of thermoelastoplastic deformation of a circular plate due to a partially distributed heat supply.J. Thermal Stresses 20: 203–225

    Article  Google Scholar 

  • Khobragade N L, Deshmukh K C 2003 An inverse quasi-static thermal deflection problem for a thin clamped circular plate.J. Thermal Stresses (accepted)

  • Nowinski J L 1978Theory of thermoelasticity with application (Alphen aan den Rijn: Sijthof Noordhoff) p. 407

    Google Scholar 

  • özisik M N 1968Boundary value problem of the heat conduction (Scranton, PA: Int. Textbook Co.)

    Google Scholar 

  • Roychoudhuri S K 1973 A note on the quasi-static thermal deflection of a thin clamped circular plate due to ramp-type of heating of a concentric circular region of the upper face.J. Franklin Inst. 296: 3: 213–219

    Article  Google Scholar 

  • Sneddon I N 1972The use of integral transforms (New York: McGraw-Hill)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Late KZS Science College, Bramhani 441 501 (Kalmeshwar), India

    A. K. Tikhe

  2. Department of Mathematics, Post Graduate Department of Teaching, Nagpur University, 440 010, Nagpur, India

    K. C. Deshmukh

Authors
  1. A. K. Tikhe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. C. Deshmukh
    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

Tikhe, A.K., Deshmukh, K.C. Inverse transient thermoelastic deformations in thin circular plates. Sadhana 30, 661–671 (2005). https://doi.org/10.1007/BF02703513

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02703513

Keywords

Search

Navigation