Engineering Transactions, 7, 2, pp. 193-233, 1959

Stan Naprężenia i Przemieszczenia w Grubej Płycie Kołowej Wywołany Działaniem Nieustalonego Pola Temperatury

W. Derski
Instytut Podstawowych Problemów Techniki PAN

The object of this paper is to determine the state of stress and displacement in a thick circular plate with thickness 2h and diameter 26, due to a non-steady-state axially symmetric temperature field. The temperature is a known function of the time and the coordinates. Three cases are considered. In the first case, the temperature field is symmetric in relation to the plane z 0. In the second case, the temperature field is determined by antisymmetric boundary conditions in nelation to the plane z = 0. In the third, the temperature acts on the surface z = h only.
We require that all the boundary conditions in the planes z = ± h be satisfied in an accurate manner, and the mechanical conditions on the surface r = b in an integral manner.

To determine the stress and displacement components the familiar method of potential of thermoelastic displacement is used. In order to satisfy the boundary conditions, Love's function is introduced. Besides the above, the limit cases for b -> ∞ are considered, and also the passage to the limit for the case of sudden heating. In the particular case of steady-state, it is found that the results are  in agreement with those of Ref. [6].

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


J. N. Goodier, On the Integration of the Thermo-Elastic Equations, Phil. Mag., Vol. 23, 157 (1937).

M. T. Huber, Teoria sprężystości, t. 2, PWN, Warszawa 1955.

A. E. Love, A Treatise on the Mathematical Theory of Elasticity, Londyn 1927.

A. Nádái, Elastische Platten, Berlin 1925.

W. Nowacki, The State of Stress in c Thick Circular Plate Due to a Temperature Field, Bull. Acad. Polon. Sci., Cl. IV, 4, 1957.

W. Nowacki, Stan naprężenia w grubej płycie kotłowej, wywołany działaniem pola temperatury, Arch. Inzyn. Ladow., 1 (1958).

E. Melan, H. Parkus, Wärmespannungen, Wieden 1953.

E. Melan, Spannungen infolge nicht stationärer Temperaturfelder, Öster. Ing.-Arch., 2-3, 9 (1955).

C. J. Tranter, Integral Transforms in Mathematical Physics, Londyn.

A. Timpe, Achsensymetrische Deformation von Umdrehungskörpern, ZAMM, Vol., 1924.