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Volume 6
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Article

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

by
Anarbay Kudaykulov
†,
Azat Tashev
,
Bagdat Teltayev
* and
Aizhan Muta
*
U. Joldasbekov Institute of Mechanics and Engineering, Almaty 050010, Kazakhstan
*
Authors to whom correspondence should be addressed.
†
Deceased author.
Thermo 2026, 6(1), 2; https://doi.org/10.3390/thermo6010002 (registering DOI)
Submission received: 30 November 2025 / Revised: 17 December 2025 / Accepted: 24 December 2025 / Published: 26 December 2025
Versions Notes

Abstract

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.
Keywords: variable cross-section rod; thermal insulation; heat exchange; analytical solution; finite element method; elongation; strain; stress variable cross-section rod; thermal insulation; heat exchange; analytical solution; finite element method; elongation; strain; stress

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MDPI and ACS Style

Kudaykulov, A.; Tashev, A.; Teltayev, B.; Muta, A. Modeling the Thermomechanical Characteristics of a Heat-Insulated Rod with a Variable Cross-Section. Thermo 2026, 6, 2. https://doi.org/10.3390/thermo6010002

AMA Style

Kudaykulov A, Tashev A, Teltayev B, Muta A. Modeling the Thermomechanical Characteristics of a Heat-Insulated Rod with a Variable Cross-Section. Thermo. 2026; 6(1):2. https://doi.org/10.3390/thermo6010002

Chicago/Turabian Style

Kudaykulov, Anarbay, Azat Tashev, Bagdat Teltayev, and Aizhan Muta. 2026. "Modeling the Thermomechanical Characteristics of a Heat-Insulated Rod with a Variable Cross-Section" Thermo 6, no. 1: 2. https://doi.org/10.3390/thermo6010002

APA Style

Kudaykulov, A., Tashev, A., Teltayev, B., & Muta, A. (2026). Modeling the Thermomechanical Characteristics of a Heat-Insulated Rod with a Variable Cross-Section. Thermo, 6(1), 2. https://doi.org/10.3390/thermo6010002

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