Stan Naprężęnia i Przemieszczenia w Grubych Płytach, Wywołany Działaniem Nieustalonego Pola Temperatury

The paper is composed of three parts. The first is devoted to a circular plate, the second - to a rectangular plate and the third contains a discussion of the results and a numerical example. The aim of the paper is the determination of the state of stress and displacement in a thick plate, due to the action of a non-steady-state temperature field. The thermal action is determined by means of a prescribed temperature distribution. Three cases are considered. and the character of considered. In the first the region the thermal action is symmetric in relation to the middle plane of the plate Z = 0. In the second - the temperature field is determined by 'boundary conditions asymmetric in relation to the plane z = 0. In the third case the region of thermal action lies in the plane z = h only. In each of these three cases are discussed physically possible thermal boundary conditions on the part of the boundary that does not constitute the region of thermal action. To determine the stress and displacement components the potential of thermoelastic displacement is used as usually. Mechanical boundary conditions are satisfied in an accurate manner on the surfaces Z w -Eh and in the integral manner on the lateral surfaces. In the case of rectangular plates even an approximate satisfaction of the boundary conditions on the lateral surfaces leads to an infinite system of differential equations.
The solutions obtained have the form of simple double and triple trigonometric series converging slowly for small values of time. To overcome this difficulty an asymptotic solutions are given valid for small values of time.