Elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius

An analytical procedure for evaluation of elastic stresses and strains in rotating conical disks, either solid or annular, subjected to thermal load, and having a fictitious density variation along the radius is presented. The procedure is based on two independent integrals of the hypergeometric differential equation describing the displacement field; this procedure is just as general as the one found in technical literature, but less intricate and more reliable. General unpublished relations of stress state and displacement field in conical disk subjected, under elastic conditions, to thermal gradient, and featuring a density variation along the radius are defined. Particular consideration is given to some industrial example of turbine rotors carrying hub and rim with buckets on periphery or radial blades on lateral surfaces. The analytical results obtained by using the new general relations perfectly match those obtained by FEA.