Thermal Stresses of Rotating Hyperbolic Disks as Particular Case of Non-linearly Variable Thickness Disks

A theoretical method for the evaluation of elastic stresses and strains in rotating hyperbolic disks without singularity, also subjected to thermal load, is introduced. The differential equation governing the radial displacement field of the hyperbolic disk without singularity has been deduced from the governing equation of non-linearly variable thickness disks given by the power of a linear function of the radius. A general temperature distribution along the radius expressed by a polynomial relation is considered. To overcome convergence problems of the solution, with hypergeometric functions, analytic continuations of these series have been introduced that allow the extension the theoretical thermoelastic analysis to all cases of technical interest. Then, for the first time the authors are aware, closed-form solutions of the governing equation of hyperbolic disks without singularity are presented.