Оn the Use of the Modified Method of Lines in Nonthin Plate Thermoelasticity Problems

Abstract

This article considers the first stage of the algorithm of the modified method of lines for the boundary problem of thermoelasticity in a flat setting. The numerical-analytical method is based on the dimensionality reduction of the initial equations of thermoelasticity along one or two spatial coordinates (in this work, one at a time). For dimensionality reduction of the initial equations and boundary conditions, the projection method with the use of locally lumped functions associated with the selected system of straight lines as basic ones is used. Considering the nonorthogonality of the selected basic functions for constructing the reduced equations, tensor notation and the corresponding rules for tensor operations are used. This approach greatly simplifies the construction of design equations, and in the future, the use of modern numerical methods to solve them. The results of the study are compared with the known analytical solutions, as well as with the solutions obtained by other schemes of the finite element method in the PC "LIRA-CAD" and the PC "SCAD Office".
 The article is devoted to the modified method of lines in space problems of thermoelasticity. Recently, the theory of thermoelasticity has undergone significant development due to the important problems that arise in the design of various structures, including building. The elements of these structures operate in conditions of uneven non-stationary heating, which changes the physical and mechanical properties of materials and there are temperature gradients, which are accompanied by unequal thermal expansion of parts of the elements. In turn, the engineer faces the task of calculating such structures. In this article, the focus is on spatial structures.