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.
