Stan Naprężenia w Cienkiej Tarczy Kołowej, Wywołany Działaniem Nieustalonego Pola Temperatury
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, .
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.
A. Gray, T. M. Mac Robert, A Treatise on Bessel Functions, Londyn 1952.
M. T. Huber, Teoria sprężystości, Pisma t. 4, PWN, Warszawa 1954.
K. Knopp, Szeregi nieskończone, PWN, Warszawa 1956.
E. Melan, Spannungen infolge nicht stationärer Temperaturfelder, Öster. Ing.-Arch., t. 9, 2-3 (1955).
E. Melan, H. Parkus, C. Wärmespannungen, Wiedeń 1953.
C.J. Tranter, Integral Transforms in Mathematical Physics, tłum. ros. IL. Moskwa 1956.