Метод обобщенных функций в плоских краевых задачах несвязанной термоэластодинамики

Abstract

Non-stationary boundary value problems of uncoupled thermoelasticity are considered.             A method of boundary integral equations (BIME) in the initial space-time has been developed for solving non-stationary boundary value problems of thermoelasticity under plane deformation. On the basis of the method of generalized functions, generalized solutions of boundary value problems are constructed using the Green's function for the heat equation and the Green's tensor of the Lame equations under the action of non-stationary power and heat sources of various types. Integral representations of the solution of boundary value problems are obtained. These solutions allow, based on known boundary values and initial conditions (displacements, temperature, stresses and heat flux), to determine the thermally stressed state of the medium under the influence of various power and thermal loads. Resolving boundary integral equations are constructed to determine the unknown boundary functions.