One-Dimensional Transient Thermal Stress Problem for Nonhomogeneous Hollow Circular Cylinder and Its Optimization of Material Composition for Thermal Stress Relaxation

Abstract

In this study, the one-dimensional transient thermal stress problem of a non-homogeneous hollow circular cylinder with arbitrarily distributed and continuously varied material properties, such as functionally graded materials, is evaluated theoretically. Using the analytical procedure of a laminated hollow circular cylinder model, the analytical temperature solution for the cylinder is derived approximately. Furthermore, making use of Airy's stress function method, the thermal stress components are formulated under the mechanical condition of being traction-free. As a numerical example, a hollow circular cylinder composed of zirconium oxide(ZrO₂)and titanium alloy(Ti-6Al-4V)is considered. To optimize(i.e., minimize) the thermal stress distribution, numerical calculations are carried out, and the optimum material composition is determined taking into account the effect of the temperaturedependence of the material properties. Furthermore, taking into account the variation in the thickness of the cylinder, the temperature rise of the surrounding medium, and the relative heat transfer coefficients on the inner and outer surfaces, the optimum values of the material composition are obtained. Numerical data for the calculations are shown graphically.