Modeling the Thermomechanical Characteristics of a Heat-Insulated Rod with a Variable Cross-Section

In this study, the thermomechanical behavior of a variable cross-section rod with fixed ends is studied using an analytical method. A rod with a radius that varies quadratically with length is considered, and it is thermally insulated on its side surface. Heat flow is applied to the left end of the rod, and heat exchange with the environment occurs at the right end. Based on the obtained temperature distribution, the thermal strains, stresses, displacements, and total elongation are determined. The results highlight the influence of boundary thermal conditions on the thermomechanical response of the rod, which is of interest for the design and analysis of structural elements operating under conditions of uneven thermal stress.