Thermal stresses in layered thick cylindrical shells of infinite length

A layered infinite closed thick cylindrical shell subjected to steady thermo-loads on surfaces, which is treated as two-dimensional plane strain problem, i.e., a layered ring with rectangular cross section of unit width, was investigated based on exact thermoelasticity theory. An analytical method for the temperature, stress, and displacement fields in the shell was presented. First, the general solutions of temperature, displacements, and stresses in a single-layer ring were deduced, which exactly satisfy the two-dimensional heat conduction equation and the two-dimensional elasticity equations in polar coordinates by use of the Fourier series expansion. On the basis of continuities of physical quantities on the interface of two adjacent layers, the relationships of temperature, heat flux, displacement, and stress between the outermost surface and innermost surface of the layered ring were recursively obtained by use of the transfer matrix method. Excellent convergence of the solutions was observed. Comparing the present results with those obtained from the finite element method indicates the correctness of the present method. The influences of temperature loads, ring thickness, layer number, and material properties on the distributions of temperature, displacements, and stresses in the layered rings were studied in detail.