Determination of thermal stress and strain in plates by the direct method

Abstract

The article discusses the use of the finite difference method of one variable, the method of straight lines, to determine temperature stresses and strains in plates with a fixed, hinged supported or completely free contour. This method was developed by L.V. Kantorovich, the finite difference method for solving in one variable, i.e. solving the Laplace and Pousson equations. Later, this method was improved by V.A. Fadeev, L.P. Vinokurov and M.G. Slobodyansky, and in the middle of the last 20th century by P.M. Varvak. The Kirchhoff-Love hypothesis is used. It is assumed that the cross section of the plate that is flat and normal to the median plane does not distort and after deformation remains flat and normal to the median plane, the displacement of points located in the median plane of the plate is considered very small compared to the thickness. A nonstationary problem has been solved in which the temperature distribution over the thickness of the plate – h for the singularity is assumed to be nonlinear. Temperature deflections and stresses along the middle of rectangular plates with embedded, supported or completely free boundary conditions on the contour were obtained.