**14**, 4, pp. 531-557, 1966

### Dwuwymiarowe Zagadnienie Teorii Naprężeni Cieplnych

In addition, following the argument of Muschelishvili, the stresses and the displacements are expressed for the circle and the elastic semi-plane in terms of the temperature and an additional analytic function defined outside the region considered. A method is proposed for using the above relations in the case of a concentrated source of heat.

The last section of the paper is concerned with the determination of the thermal stress in a circular panel acted on by a connected source of heat of constant intensity W. The temperature T0 at the edge of the panel is also constant. The planes bounding the panel are thermally insulated.

Part of the periphery of the panel is free, the remaining part being fixed. A closed-form solution is obtained. By passing to the limit we obtain from it the solutions for panels with free and fixed edge. Diagrams of σrr and σrψ are given for a portion of the fixed edge.

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#### References

B. E. GATEWOOD, Thermal Stresses, New York 1957.

I. N. GOODIER and P. G. HODGE, Elasticity and Plasticity, New York 1958.

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И. H. Векуа, H. И. Мусхелишвили, Методы теории аналитических функций в теории упругости, Тр. Всес. съезда по теор. и прикл. механ. I960. М. Л. АН СССР.