Abstract
An approach to the evaluation of nonstationary temperature fields and the thermoelastic state of multilayer hollow long thermally sensitive cylinders based on the use of the Kirchhoff substitution, generalized functions, and Green’s functions of the corresponding problems for a hollow cylinder with piecewise constant physicomechanical characteristics is illustrated. The problem of heat conduction is reduced to the solution of a Fredholm-Volterra nonlinear integral equation of the second kind for the Kirchhoff variable. In the problem of thermoelasticity, the coefficients of the equation (continuous inside each layer) are approximated by piecewise constant functions. The boundary conditions at the ends of the cylinder are satisfied in the integral form. Numerical analysis is performed for the case of a three-layer cylinder.
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