In the present paper, solutions of the equations of uncoupled thermoelastodynamics of ther- moelastic rods are constructed for power and thermal effects. Based on the Fourier transform, the Green tensor and generalized solutions of the thermoelasticity equations are constructed in the original...

In this study, heat conductivity boundary value problems on a star graph are considered, inspired by engineering applications, e.g., heat conduction phenomena in mesh-like structures. Based on the generalized function method, a unified technique for solving boundary value problems on such graphs is developed. Generalized solutions to transient and stationary boundary value problems are constructed for different conditions at the end edges, with the Kirchhoff conditions at the common node. Regular integral representations of solutions to boundary value problems are obtained using the properties and symmetry of the fundamental solution’s Fourier transform. The derived results allow the action of various heat sources to be simulated, including concentrated ones by using singular generalized functions. The generalized function method enables a wide variety of boundary value problems to be tackled, including those with local boundary conditions at the ends of the graph, and various transmission conditions at the common node. Based on the research, the authors propose an analytical solution method under the action of various heat sources to solve various boundary value problems on a star thermal graph.

We consider spatially one-dimensional boundary value problems of uncoupled thermoelasticity, which can be used to study various rod structures under thermal heating conditions. This model well describes thermodynamic processes at low strain rates. Here, a unified methodology has been developed for solving various boundary value problems typical of practical applications. The task is set to determine the thermo-stressed state of a thermoelastic rod under various boundary conditions at its ends, as well as the acting forces and heat sources along the entire length of the rod.Shock elastic waves arising in such structures under the action of shock loads are considered. Based on the method of generalized functions, generalized solutions of non-stationary and stationary direct and semi-inverse boundary value problems in the class of generalized vector functions of slow growth are constructed. Regular integral representations of generalized solutions are also given, which provide analytical solutions to the posed boundary value problems. The peculiarity of the constructed solutions makes them convenient for engineering applications because make it possible to study the influence of each boundary condition, as well as the acting power and heat sources separately, which is very important when assessing the strength properties of rod structures.

Rod structures are widely used in mechanical engineering as connecting and transmission links for structural elements of a wide variety of machines and mechanisms. During operation, they are subject-ed to variable mechanical and thermal influences, which create a complex stress-strain state in structur-al elements, depending on their temperature, and affecting their strength and reliability. Therefore, the determination of the thermally stressed state of rod structures, taking into account their mechanical properties (in particular, elasticity and thermal conductivity) is one of the topical scientific and tech-nical problems. Here, spatially one-dimensional unsteady boundary value problems (BVPs) of uncoupled ther-moelasticity are considered, which can be used to study various bar structures. This model describes well thermodynamic processes at low strain rates and here a unified technique is proposed for solving various BVPs typical of practical applications. Problems of determining the thermally stressed state of a thermoelastic rod using a model of uncoupled thermoelasticity are considered. Generalized solutions of non-stationary and stationary direct and semi-inverse BVPs under the action of power and heat sources of various types are con-structed on the basis of the method of generalized functions. Acting sources can also be specified by singular generalized functions, under different boundary conditions at the ends of the rod. Con-sidered are shock elastic waves that arise in such structures under the action of shock loads. Regu-lar integral representations of generalized solutions are obtained, which give an analytical solution to the stated BVPs.

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. According to generalized functions method the generalized solutions of boundary value problems are constructed and their regular integral representations are obtained. These solutions allow, using 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 forces and thermal loads. Resolving singular boundary integral equations are constructed to determine the unknown boundary functions.