Stability and stress analysis of toroidal pipe-reducers

Abstract

The present research work deals with the stability and stress analysis of toroidal pipe reducers. Stability of the shells have been determined from the solution of nonlinear governing equations of axisymmetric deformations of shells of revolution. The multisegment method of integration is used for obtaining the solutions of the governing nonlinear differential equations. Numerical solutions are obtained by using a modified version of the computer program, developed by Uddin [98] for solving these governing equations by the multi segment method of integration. The interpretation of instability of the toroidal reducers is based on Thompson's theorems I and II [95]. Critical pressures for the toroidal reducers are calculated over useful ranges of the curvature 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 toroidal 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 toroidal pipe reducers are compared here with the results of conical reducers obtained by Ali [6] and parabolic reducers obtained by Rahman [66]. Comparison between a toroidal reducer and a conical reducer with identical parameters shows that the former one develops uniform stresses of lower magnitude. Consequently, they are found to be much more stable than their counter-parts under uniform external pressure. Further, toroidal reducer are found to sustain higher critical pressure than parabolic reducers except for higher diameter ratio.