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Similarity in thermoelasticity

The develooment of similarity relationships for use in the study of transient and steady-state thermal displacements, strains and stresses between model and prototype is discussed by the authors

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Abstract

A set of similarity relationships is developed and discussed for use in the study of transient and steadystate thermal displacements, strain and stresses between model and prototype. The similarity relationships are shown to be dependent upon the existing state of stress in the thermally loaded member. Their utilization in the design or analysis of data for such experimental techniques as photoelasticity and the moiré method is cited.

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Abbreviations

u i :

displacement

ε i j :

strain

σ i j :

stress

T :

temperature

α:

coefficient of thermal expansion

ν:

Poisson's ratio

E :

modulus of elasticity

δ i j :

Kronecker delta

t :

time

K :

thermal diffusivity

Q :

heat source or sink

References

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  3. Gerard, G., and Gilbert, A. C., “Photothermoelasticity: An Exploratory Study,” Jnl. Appl. Mech., No. 57-APM-25, (August 3, 1956).

  4. Hovanesian, J. D., and Kowalski, H. C., Unpublished Research Rpt., “Photothermoelasticity,” Dept. of Engineering Mechanics, Wayne State University, (1962).

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  7. Theocaris, P. S., “The Moiré Method in Thermal Fields, Ibid. (8),223–231 (1964).

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  8. Tramposch, H. and Gerard, G., “An Exploratory Study of Three-Dimensional Photothermoelasticity,” Jnl. Appl. Mech., No. 60-WA-49.

  9. Tramposch, H. and Gerard, G., “Physical Properties of Plastics for Photothermoelastic Investigations,” Ibid., Jnl. Appl. Mech., No. 60-WA-49, (December 1958).

  10. Boley, B. A., andWeiner, J. H., “Theory of Thermal Stresses,”John Wiley and Sons, Inc., New York, 1960.

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  11. Kowalski, H. C., “Development of Thermoelastic Similarity Laws and a Theoretical and Experimental Study of Transient Thermal Stresses in a Rectangular Beam,” masters thesis, Wayne State Univ., 1963.

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Author information

Authors and Affiliations

  1. Engineering Mechanics Department, Wayne State University, Detroit, Mich

    J. D. Hovanesian (Associate Professor)

  2. Engineering Mechanics Department, Generat Motors Institute, Flint, Mich

    H. C. Kowalski (Assistant Professor)

Authors
  1. J. D. Hovanesian
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  2. H. C. Kowalski
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Hovanesian, J.D., Kowalski, H.C. Similarity in thermoelasticity. Experimental Mechanics 7, 82–84 (1967). https://doi.org/10.1007/BF02326711

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