Abstract
This paper presents a comprehensive study on periodic boundary value problems (BVPs) in thermoelastic star graphs, utilizing the method of generalized functions. The research focuses on the behavior of rod structures subjected to thermal heating and cooling, providing a unified approach to solving various boundary value problems relevant to practical applications. We derive integral representations of generalized solutions that facilitate the determination of displacements, deformations, stress, temperature, and heat fluxes across each element of the graph. The study also addresses the modeling of force and heat sources through both regular and singular generalized functions under diverse boundary conditions. By establishing continuity and Kirchhoff conditions at the common node of the graph, we formulate the governing equations for the amplitudes of displacement and temperature. The findings highlight the versatility of the proposed method, which can be extended to a wide range of network structures, distinguishing it from existing techniques. This work contributes to the understanding of thermoelastic behavior in complex systems, with implications for engineering applications in fields such as mechanical design, materials science, and structural analysis.