Solution of generalized thermoelasticity problems using the R-function method

The present article examines non-classical models for heat conduction problems, incorporating equations and boundary conditions that include thermal inertia terms. These models enable the identification of thermal stresses resulting from thermal shocks induced by external environmental factors. We propose the R-function method as a comprehensive approach, broadly applicable to isotropic bodies with diverse geometric configurations. Structural solutions to the problems suggested by Academician V.L. Rvachov enable precise representation of body geometries and various types of boundary conditions. This is achieved using the left-hand sides of the geometric form equations, constructed through R-operations: R-disjunction, R-conjunction, and R-negation.