Pressurized non-circular member—effect of mean-line form

Abstract

Using an energy analysis, it is shown that for each aspect ratio and for a particular family of curves representing the mean-line form, there will be one particular form which ensures that the maximum bending moment acting on the member takes a minimum value.

The traditional elliptic mean-line form currently used for some heat exchanger tubes, sluice-value bodies, and some aircraft monocoque stiffening frames, could be improved by using the optimum form which has heat transfer and fluid-flow characteristics similar to those associated with the elliptic profile (sometimes an essential feature of the design).

It is shown that when the aspect ratio is equal to two and the elliptic shape is replaced by an optimum form determined by the method described above, the uniform applied pressure can be increased by fifteen and one-half per cent before the maximum stress in the two members becomes equal.

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References

Holland

‘Pressurized member with elliptic median line: Effect of radial thickness function’, J. mech. Engng Sci., 1976, 18, 245–253.

Holland

‘Experiment on a pressurized elliptic cylinder’, Int. J. mech. Engng Education, 1976, 4, 257–263.

Mayer-Mita

‘Die berechnung dünnwandiger ovaler (im besonderen elliptisher) Röhren gegen gleichförmigen normaldruck’ (‘The calculation of thin-walled oval (particularly elliptical) tubes under uniform normal pressure), Z. Ver. dt. Ing., 1914, 58, 649–654.