Thermal stress analysis of layered cylindrical shells

The use of layered metal-ceramic composite panels as abradable tip seals in jet engines may lead to significant increases in engine efficiency. This paper describes the development of a thermal stress analysis capability based on classical shell theory for the analysis of panels with all four edges free. Various boundary conditions on the top and bottom surfaces of the plate are examined. The material properties can be isotropic, transversely isotropic, or orthotropic, and may be functions of temperature. All heat flow takes place in the radial direction, allowing a one-dimensiona l heat transfer analysis. Solutions for the case of top and bottom surfaces fully restrained, top and bottom surfaces free to move tangentially but not radially, and for the case of a flat plate completely unrestrained can be obtained in closed form directly from the force-strain relations. Examples of solutions for each of these types of boundary conditions are presented. The solution for a curved plate cooled with no external restraints cannot be obtained directly from the force-strain relations. For that case, a RayleighRitz analysis was used. Assumed displacement functions are chosen for u, v, and H% with unknown participation parameters. Using the force equilibrium equations, the unknown parameters in u and v can be expressed in terms of the parameters of w. The potential energy is then minimized with respect to the parameters of w to find the equilibrium state. The analysis capability was then used to explain the fractures and deformations resulting from fabrication and anticipated use. The analysis can also be used to develop alternate fabrication strategies to maximize the production yield.