Quasistatic temperature stresses in a multilayer thermally sensitive cylinder

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 Greens 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.Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 4, pp. 7–16, July–August, 2004.     

Temperature Stresses and Displacements in a Multilayer Plate with Nonlinear Conditions of Heat Exchange

We propose a method for the determination of the stress-strain state formed in a multilayer plate under the conditions of radiation and convection heating with regard for the temperature and time dependences of the coefficients of heat exchange. The problem of heat conduction is reduced to the solution of a system of Volterra-type nonlinear integral equations of the second kind for the values of temperature on the outer surfaces of the plate. The integral equations are deduced with the help of the Green function of the nonstationary problem of heat conduction for the multilayer plate with constant coefficients of heat exchange and solved by using linear splines. The problem of thermoelasticity is solved in stresses. The boundary conditions on the cylindrical surface are satisfied in the integral form. The results of the corresponding numerical calculations are presented.