Rod elements are widely used in numerous technological applications. Temporal variations in the temperature field lead to the development of a time-dependent stress field within rod structures, affecting their strength and reliability during use. Determining the thermally-induced stress state of rod structures, taking into account their mechanical properties such as elasticity, is a critical scientific and engineering challenge. The use of mathematical modeling techniques allows the analysis of thermodynamic processes within the structure and its components, aiding in the determination of their dynamic and strength characteristics during the design stage.

This paper focuses on the Cauchy problem for the dynamics of a thermoelastic rod with arbitrary initial conditions and subjected to both thermal and mechanical influences. Using Green's tensor in the context of thermoelasticity equations, an analytical solution is derived, enabling the determination of deformations, stresses, and temperatures at any point along the rod and at any given time, based on known initial conditions and acting force and heat sources.

Numerical calculations of temperature and displacement are presented for scenarios involving pulsed concentrated thermal and force sources. Furthermore, solutions to the Cauchy problem are obtained for cases with distributed regular force and heat sources along the rod. The developed program provides a tool for studying thermodynamic processes in rods with various physical and mechanical properties under the influence of both distributed and concentrated pulsed thermal and force sources, described by singular generalized functions.

AINAKEYEVA N.Zh.

Researcher, Institute of Mechanics and Engeenering named after academician U.A. Dzholdasbekov, Almaty, Kazakhstan.

E-mail: nursaule_math@mail.ru; http://orcid.org/0000-0003-4643-6072

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