Engineering Transactions,

**6**, 2, pp. 255-263, 1958### Stan Naprężenia w Cienkiej Tarczy Kołowej, Wywołany Działaniem Nieustalonego Pola Temperatury

The object of this paper is to determine the thermal stresses in a thin circular plate. These stresses are provoked by an axially symmetric non-steady temperature field due to a sudden action of a heat source distributed along the edge. The heat exchange with the ambient medium takes place on both surfaces ±δ(δ -plate thickness).

The action of the heat source is such that, with the time tending to infinity, the temperature tends to a steady-state distribution. The stresses are determined in the most general case. The assumption that the time tends to infinity, t ->∞, makes it possible by passing to the limit, to obtain stresses for the steady-state temperature field. Thus, the results obtained coincide with those given in the monograph by E. Mellan and H. Parkus, [5].

In addition there are obtained the stresses for an infinite solid circular cylinder, thermal conditions being independent of the longitudinal co-ordinate. The state of stress is determined by passing to the limit for zero, with a coefficient determining the heat exchange on the surfaces. The temperature field is found using the Laplace transformation. For the determination of the stress components, the potential of thermo-elastic displacement is used.

The action of the heat source is such that, with the time tending to infinity, the temperature tends to a steady-state distribution. The stresses are determined in the most general case. The assumption that the time tends to infinity, t ->∞, makes it possible by passing to the limit, to obtain stresses for the steady-state temperature field. Thus, the results obtained coincide with those given in the monograph by E. Mellan and H. Parkus, [5].

In addition there are obtained the stresses for an infinite solid circular cylinder, thermal conditions being independent of the longitudinal co-ordinate. The state of stress is determined by passing to the limit for zero, with a coefficient determining the heat exchange on the surfaces. The temperature field is found using the Laplace transformation. For the determination of the stress components, the potential of thermo-elastic displacement is used.

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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

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A. Gray, T. M. Mac Robert, A Treatise on Bessel Functions, Londyn 1952.

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E. Melan, H. Parkus, C. Wärmespannungen, Wiedeń 1953.

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