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Thermo-Elastic Similarity Laws

  • A. E. Green
  • J. R. M. Radok
  • R. S. Rivlin

Abstract

In a book edited by Hetényi [1], Mindlin and Salvadori have discussed certain similarity laws for thermo-elastic problems. They were, however, primarily concerned with the replacement of thermo-elastic problems by purely elastic problems involving dislocations. In the present paper we are concerned with the conditions which must be satisfied by the physical parameters describing the properties of a body and a scale model (scaled both in linear dimensions and time) in order that the stress in the original body may be determined from that at the corresponding position and time in the scale model by means of the multiplier M (= rigidity modulus of body/ rigidity modulus of model). It will be seen that the conditions for the stresses in the body to be an arbitrary constant C times those in the model are then easily obtained. In deriving these conditions much of the mathematical analysis of Mindlin and Salvadori could have been used. However, we have preferred to obtain them by somewhat different methods.

Keywords

Stress Component Scale Model Displacement Component Surface Traction Average Stress Distribution 
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References

  1. 1.
    M. Hetényi, Handbook of experimental stress analysis, John Wiley and Sons, New York, 1950, Chap. 16Google Scholar
  2. 2.
    A. E. H. Love, The mathematical theory of elasticity, 4th ed., Cambridge Univ. Press, 1927Google Scholar
  3. 3.
    A. E. Green and W. Zerna, Theoretical elasticity, The Clarendon Press, Oxford, 1954Google Scholar
  4. 4.
    I. N. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, Nordhoff, Holland, 1953Google Scholar
  5. 5.
    E. G. Coker and L. N Filon, Photo-elasticity, Cambridge Univ. Press, 1931Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • A. E. Green
    • 1
  • J. R. M. Radok
    • 1
  • R. S. Rivlin
    • 1
  1. 1.Brown UniversityUSA

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