Analytical method for solving the first boundary value problem of coupled thermoelasticity on a two-link graph and its applications

Boundary value problems of rod thermodynamics on a two-link graph are solved using a coupled thermoelasticity model. Using the method of generalized functions, an effective methodology for solving boundary value problems for a two-link thermoelastic graph with linear transmission conditions for stresses and heat fluxes is developed for equal displacements and temperatures at the common node of the two-link graph and for specified displacements and temperatures (first boundary-value problem) or specified stresses and heat fluxes (second boundary-value problem) at the graph ends. Analytical solutions to boundary value problems of coupled thermoelasticity on a two-link graph are obtained. These solutions can be used to study various mesh-like structures subject to mechanical stresses (impact) and thermal heating (cooling). The constructed equations of connections allow us to determine unknown boundary functions (displacements, stresses, temperatures, and heat fluxes) for a two-link graph. Regular integral representations of generalized solutions are obtained in Fourier transform space, yielding analytical solutions to the posed boundary value problems for stationary oscillations with a given frequency. An inverse Fourier transform is used to reconstruct the original solutions. This work can be recommended to design organizations for assessing the strength and reliability of beam structures under various force and thermal effects.