Pressurized Member with Elliptic Median Line: Effect of Radial Thickness Function

Abstract

Radial thickness function is represented by the first two terms of an even Fourier series and the unknown coefficient in the function is determined from the constraint: ‘maximum amplitude of stress in the member must be restricted to the minimum value possible’.

Using this technique, it is shown that for two members having a ratio of principal axes equal to 2.0, being of equal weight and subjected to the same maximum stress level, the member with varying radial thickness will withstand an applied pressure which is just over forty per cent higher than that carried by the traditional constant-thickness member. Alternatively, for equality in pressure loading and maximum stress level, the ratio of weights for the two members is 0.844, in favour of the variable-thickness member.