Аннотация
Abstract Problems of determining the thermostressed state of a thermoelastic rod using the coupled thermoelasticity model are considered. In this case, the heat conductivity equation includes divergence of the speed of material points of the medium; the elasticity equations include the temperature gradient. The generalized functions method is used to construct generalized solutions to nonstationary and stationary direct and semi-inverse boundary value problems under the action of power and thermal sources of various types, including those described by singular generalized functions under different boundary conditions at the ends of rod. Thermal shock waves arising in such structures under the action of impact loads and heat fluxes are considered, and the conditions at their fronts are obtained. The uniqueness of the solutions to the posed boundary value problems, including those with allowance for shock waves, has been proved. Regular integral representations of the generalized solutions are presented, which yield an analytical solution to the posed boundary value problems.