Plane Boundary Value Problems of Thermoelasticity and Their Generalized Solutions

Abstract

Nonstationary boundary value problems of uncoupled thermoelasticity are considered. A method of boundary integral equations in the initial space-time has been developed for solving boundary value problems of thermoelasticity by plane deformation by use general functions method (GFM). The generalized solutions of boundary value problems are constructed in the space of generalized vector functions. Fundamental Green tensor, stress tensor and their antiderivatives over time are used for construction their regular integral representations. By use analogue of Gauss formula for fundamental stress the singular boundary integral equations are constructed to determine the unknown boundary functions. The resulting formulas have important engineering application. They make possible to determine the thermal stressed state of the medium by the boundary values of stresses, displacements, temperature and heat flux, without solving singular boundary integral equations. Because for real engineering problems these physical characteristics can be experimentally measured at the boundary. Moreover, the formulas allow to calculate the influence of each of these characteristics of the process on its stressstrain state. The last one is very important in designing structures made of thermoelastic materials.