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

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].