Stability and stress analysis of parabolic pipe-reducers

Abstract

For joining pipes of unequal diameters, truncated parabolic shells can be used as pipe reducers instead of the traditional conical frustums, as the doubly curved parabolic shell elements are superior to the conical shells in withstanding high pressure. The present investigation analyses the stability and stresses in the truncated parabolic shells to be used as pipe reducers and also compares the results with those of conical reducers obtained by Ali. The analysis is based on the nonlinear governing equations for 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 computer program, developed by Uddin,for solving the governing equations by the multisegment method of integration. The interpretation of instability of the parabolic reducers is based on Thompson's theorems r and II. Critical pressures for the parabolic reducers are calculated varying the thickness ratio and the diameter ratio. Critical pressures and the stress distributions are presented graphically and thei.r dependence on ,different parameters are discussed. It is found that long parabolic reducers are prone to local instability near the larger end of the reducer but this critical zone shifts towards the smaller end as the two ends of the reducer are brought closer. Comparison between a parabolic reducer and a conical reducer with identical parameters shows that the former one develops uniform stresses of lower magnitude. Consequently,' it" is found that they are much more stable than their counter parts under uniform external pressure.