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 uniffed 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.