Stability and stress analysis of ellipsoidal pipe reducers

Abstract

The present research work deals with the stability and stress analysis of ellipsoidal pipe reducers. Stability of the shells have been determined from the solution of nonlinear governing equations of axisymmetric deformations of shells of revolution, which ensures the state of minimum potential energy of the shell. The multisegment method of integration is used for obtaining the solutions of the governing nonlinear differential equations. Numerical solutions are obtained by a using a modified version of the computer program developed earlier for solving these governing equations by the multisegment method of integration. The interpretation of instability of the ellipsoidal reducers is based on Thompson's theorems. Critical pressures for the ellipsoidal reducers are calculated over useful ranges of the minor to major axes ratio, the thickness ratio and the diameter ratio. Critical pressures and the stress distributions are presented graphically and their dependence on different parameters are discussed. The critical pressure is plotted against diameter ratio of the pipe reducer, keeping other parameters constant. It has been found that the critical pressure varies almost linearly with the diameter ratio. It is found that long ellipsoidal reducers are prone to local instability near the larger end, but this critical zone occurs near either one of the two ends as the reducer becomes shorter. The results of stability and stress analysis of ellipsoidal pipe reducers are compared here with the results of conical, parabolic and toroidal reducers investigated by other researchers. Finally, the effect of change in boundary condition in stability and stress distribution is observed by allowing the smaller end of the ellipsoidal reducers flexibility in axial direction.