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Thermal stresses in a thin circular disc of orthotropic material due to an instantaneous point heat source

Wärmespannungen in einer dünnen Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle

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Summary

In this paper, we have analysed the transient plane thermal stress problem of a circular disc of orthotropic material with instantaneous point heat source. The variation of σθθ with time along different radius vectors is exhibited graphically and compared with that of the isotropic case.

Zusammenfassung

In dieser Arbeit wurde das instationäre ebene Wärmespannungsproblem einer Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle untersucht. Die Veränderung von σθθ über die Zeit für verschiedene Radien ist graphisch dargestellt und wird mit dem isotropen Fall verglichen.

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Abbreviations

r, θ:

polar coordinates

T :

temperature rise

α2 :

ratio of conductivities

β2 :

thermal diffusivity in θ-direction

J nα :

Bessel function ofnα-th order

t :

time

p :

introduced in equation (2)

h :

heat transfer coefficient

a :

radius of circular disc

f(r, θ) :

temperature distribution at initial state

r 0, θ0 :

a point on the disc

T 0 :

strength of point heat source

δ:

Dirac delta function

F :

stress function in two dimensions

α1, α2 :

coefficient of thermal expansion

a 11,a 12,a 22,a 66 :

elastic constants

References

  1. Takeuti, Y.: Bulletin of JSME10, 423 (1967).

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  2. Carslaw, H. S., andJ. C. Jaeger: Conduction of Heat in Solids. Oxford University Press. 1959.

  3. Lekhnitskii, S. G.: Theory of Elasticity of an Anisotropic Elastic Body. San Francisco: Holden-Day Inc. 1963.

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Authors and Affiliations

  1. Department of Mathematics, Regional Engineering College, Rourkela-8, Orissa, India

    J. Parida &  A. K. Das

Authors
  1. J. Parida
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  2. A. K. Das
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Parida, J., Das, A.K. Thermal stresses in a thin circular disc of orthotropic material due to an instantaneous point heat source. Acta Mechanica 13, 205–214 (1972). https://doi.org/10.1007/BF01586793

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  • DOI: https://doi.org/10.1007/BF01586793

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