A new closed-form solution has been developed for the axisymmetric problem of thermoelasticity, specifically targeting a thick-walled hollow isotropic cantilevered cylinder. This solution is particularly pertinent in scenarios that involve unsteady axisymmetric thermal action applied to the external cylindrical surfaces of the cylinder, characterized by dynamic variations in temperature over both spatial variables and time. The thermal influence exerted on the cylinder's surface changes dynamically, reflecting the complexities of real-world conditions and operational environments. In this sophisticated model, the inner curvilinear surface of the cylinder is subject to convective heat exchange with the surrounding environment, which is maintained at a constant temperature. The inherent complexity involved in integrating the initial differential equations, especially due to the presence of a non-self-conjugate operator, necessitates the construction of a closed-form solution that can only be achieved within an uncoupled formulation. Initially, the study focuses on the heat conduction problem, deliberately excluding the effects of volumetric changes in the body on the temperature function to simplify the analysis. The solution to this problem is achieved through a systematic application of the Fourier cosine transform concerning the axial variable, combined with the generalized method of finite integral transforms (FIT) applied to the radial coordinate. Following this initial analysis, the research progresses to consider the thermoelasticity problem while incorporating a specific temperature field. In this advanced phase, the boundary conditions at the ends of the cylinder are transformed into mixed homogeneous design relations, which facilitate a more manageable approach to solving the transformed problem. This is accomplished through the sequential application of both sine and cosine Fourier transforms, alongside the FIT method, which enhances the robustness of the solution. The calculation algorithm developed through this comprehensive research enables the precise determination of the stress-strain state and temperature distribution within the cantilevered cylinder. This innovative approach has significant implications for the calculation and design of load-bearing structures, particularly circular columns that experience unsteady heating during operational conditions or emergency situations. Furthermore, the algorithm serves as a valuable tool for validating results in the development of numerical calculation methods, thereby contributing to advancements in the field of structural engineering and thermoelastic analysis. The findings from this study not only enhance theoretical understanding but also provide practical applications in engineering design, ensuring safety and reliability in structural performance under varying thermal conditions.
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