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.
