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<p>We study the stress-strain state of an inhomogeneous orthotropic circular closed cylindrical shell subjected to initial axial loading and local heating by convective heat exchange. The material properties of the shell exhibit exponential variations across the thickness. In our investigation, we use a mathematical model of the shear theory of Timoshenko-type inhomogeneous shells. The two-dimensional heat-conduction equation is deduced under the condition of linear dependence of temperature on the thickness coordinate. By using the Laplace integral transform with respect to time and the finite Fourier transform with respect to spatial coordinates, we construct analytic solutions of the nonstationary problem of thermoelasticity for a finite hinged circular cylindrical shell. We perform the numerical analysis of the influence of the initial plane stressed state, the inhomogeneity parameter, and other thermophysical parameters on the displacements and stresses formed in the shell.</p>

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Analytic Solution to the Bending Problem for an Inhomogeneous Orthotropic Cylindrical Shell Under Local Heating and Axial Loading

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • R. M. Kushnir,
  • U. V. Zhydyk

摘要

We study the stress-strain state of an inhomogeneous orthotropic circular closed cylindrical shell subjected to initial axial loading and local heating by convective heat exchange. The material properties of the shell exhibit exponential variations across the thickness. In our investigation, we use a mathematical model of the shear theory of Timoshenko-type inhomogeneous shells. The two-dimensional heat-conduction equation is deduced under the condition of linear dependence of temperature on the thickness coordinate. By using the Laplace integral transform with respect to time and the finite Fourier transform with respect to spatial coordinates, we construct analytic solutions of the nonstationary problem of thermoelasticity for a finite hinged circular cylindrical shell. We perform the numerical analysis of the influence of the initial plane stressed state, the inhomogeneity parameter, and other thermophysical parameters on the displacements and stresses formed in the shell.