Abstract
Boundary value problems of uncoupled thermoelasticity are considered on a star graph, which can be used to study various mesh structures under the action of forces and thermal heating (cooling). Based on the generalized function method, a unified technique has been developed for solving boundary value problems of uncoupled thermoelasticity, typical for engineering applications. Generalized solutions to nonstationary and stationary boundary value problems of uncoupled thermoelasticity on a stellar graph are constructed under various boundary conditions at the ends of the graph and generalized Kirchhoff conditions at its common node. Regular integral representations of solutions to boundary value problems are obtained in analytical form.The solutions obtained make it possible to simulate force and heat sources of various types, including using singular generalized functions. The method of generalized functions presented here makes it possible to solve a wide class of boundary value problems with local and connected boundary conditions at the ends of the edges of the graph and different transmission conditions at its node.