The Analysis of Radial Flow Impellers by the Matrix Finite Element Method

Abstract

The stress analysis of an axisymmetrical body under the influence of a field of centrifugal body force is of considerable importance to the design of rotating machinery. The classical problem of the rotating disc of uniform thickness was considered by Maxwell as long ago as 1850. For this, the simplifying assumption that the stresses are functions of the distance from the centre only, with no change across the thickness, was made. Since then, the same basic analysis has been extended to discs of conical and hyperbolical cross-section profile, with or without a central hole, references to which may be found in a number of text books. The analysis of a disc with an elliptical cross-section was published by Chree in 1895. The solution for a disc of constant thickness has been refined to allow stress variation across the thickness. Although these solutions, in common with many analytical solutions in the theory of elasticity, do not satisfy all the boundary conditions exactly, they serve as very good approximations in practice.