The paper presents a global formulation of the initial – boundary problem of coupled thermoelasticity. The principle of virtual work was used. The equation for virtual work in thermoelasticity has been formulated for various types of thermal boundary conditions as well as internal sources of heat. The problem of coupled thermoelasticity in a plane stress state, especially in a rigid disk, is considered in a further part of the paper. In the formulation of the virtual work principle, some changes of the boundary thermal conditions have been considered on a plane bordering the rigid disk, on the assumption that the temperature distribution is symmetrical with respect to the central surface of the rigid disk.
Приведен синтез линейных регуляторов для задач оптимального управления нестационарными колебаниями, возникающими в режимах пуска/торможения автомобильных кранов. Для обоснования достаточных условий оптимальности решения указанной задачи, сформулированных В.Ф. Кротовым, установлено и решено методом неопределённых коэффициентов уравнение Р. Беллмана.
In this work the connected thermoelastic contact problem for an elastic half-space to which some area heat radiant is brought is considered. Applying a method of integral transformations of Fourier to system of the differential equations of thermoelasticity and a heat conduction equation, the problem is reduced to system of two two-dimensional integral equations for definition of thermoelastic normal voltages and temperature distribution.