A parametric investigation into the membrane stresses of hydrostatically loaded circular and elliptic toroidal shells
This study explores the membrane stresses of hydrostatically loaded elliptical and circular toroidal tanks. Equations are derived, using the membrane theory of shells, to obtain equations which can accurately describe the meridional and hoop stress behaviour at locations sufficiently far away from any bending disturbance occurring within the shell. The derived expressions are validated using the finite element software ADINA, indicating excellent agreement between the analytical and numerical solutions. A parametric study is undertaken, whereby the membrane profiles for prolate, oblate and circular toroidal shells is investigated. Parameters which are varied are the opening and aspect ratio of toroidal shells. Stress resultant profiles are shown for numerous cases in order to aid designers on suitable ratios to minimise membrane stresses for use when designing hydrostatically loaded toroidal shells. Lastly, numerical examples are investigated, keeping the volume constant and comparing the surface area due to a variation of opening and aspect ratios. It was found that when investigating toroidal shells, considerations are required when choosing the aspect ratio and opening ratios. Based on the results obtained, compromises between prolate and circular cross-sections with relatively small opening ratios are recommended in order to minimise the cost and maximise the structural efficiency, based on the membrane stresses occurring within the shell.
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