Analysis of stresses and displacements in two-layer inhomogeneous hollow cylinders using the complex potential method

Abstract This study presents an analytical solution for the thermoelastic state of a long, two-layer hollow cylinder composed of inhomogeneous materials under mixed boundary conditions. By accounting for distinct thermoelastic properties and internal heat generation within layered structures, this research addresses a significant gap in the existing literature. The thermal field is determined by expressing the temperature function as a power series. Leveraging the classical and effective Kolosov--Muskhelishvili complex potential method, the thermoelastic problem is transformed into the complex domain. This approach simplifies the analysis of displacements and stresses induced by thermal loading. To ensure high analytical precision, the particular solution for the resulting mixed boundary-value problem is sought in the form of a Laurent series of a complex variable. The surfaces of the layers are assumed to be either thermally insulated or maintained at zero temperature. Furthermore, it is demonstrated that the internal stress field is significantly influenced by the intensity of the internal heat source. The derived formulas provide crucial insights into the distribution of thermal stresses and displacements in non-homogeneous layered structures. Given that these results pertain to complex thermal loading conditions, they hold great significance for high-performance engineering applications. Mathematics Subject Classification: 374B10, 74K25, 30E25, 74E05, 74S25