Modeling Thermomechanical Effects in Rods with Variable Cross-Section and Local Heat Sources

Abstract

This study is a numerical study of the transient thermomechanical behavior of rods with variable cross-section exposed to partial thermal insulation, localized heat flows, and convective heat exchange. The main goal is to increase the accuracy and reliability of modeling related thermomechanical reactions in heterogeneous structural elements widely used in engineering applications. The main idea is based on the development of a mathematically consistent model based on the principle of conservation of energy, which allows simultaneous assessment of temperature fields and stress-strain state under inhomogeneous boundary conditions. The contribution of this work is to develop a computational algorithm capable of detecting spatial and temporal temperature changes and deformations with increased stability and efficiency. Numerical calculations show that the temperature along the rod varies non-linearly, reaching a maximum increase of about 18-25% near the zones of concentrated heat flow, while the thermal elongation differs by up to 12% compared with homogeneous models. The calculated stress values indicate an increase in peak thermal stresses by 20-30% in areas with a reduced cross-sectional area, which confirms the strong influence of geometric variability. Convergence analysis shows that reducing the sampling step by 50% increases the accuracy of the solution by about 8-10% while maintaining computational costs within acceptable limits (an increase of <15%). The results confirm that the proposed method provides stable solutions with an error of less than 5% compared to reference analytical solutions. The novelty of the research lies in the integration of variable geometry, mixed boundary conditions, and transient effects into a single numerical model that provides more realistic predictions than traditional simplified models. The results obtained can be effectively applied in the design and optimization of the main components operating under coupled thermomechanical loads.