Stability of spherical shells

Thesis



Recent application of using spheres as carriers of LNG on ships has highlighted a lack of guidance given to the inclusion of imperfections and to the operating con- ditions imposed as a result of the motion of the ship.

Spheres with a radius to thickness ratio of between 450 and 1700 were made by electrodeposition of copper on a wax former. Imperfections of three types were introduced:

• a) A local flat.
• b) A zone of reduced curvature.
• c) A bulge.

These shells were tested under partial vacuum and the deformation at selected points monitored by proximity gauges. Buckling pressures were found to range between ⅕ and one-fifteenth of the theoretical value for a perfect shell. The experimental results were analysed on the basis of Koiter's imperfection theory and by a numerical computer solution. The former showed good agreement with types a) and b) and no agreement with type c); the latter showed little agreement with the experimental results. The ASME design code was found to be adequate for all imperfection sizes considered, BS 5500 only partly.

Cast epoxy models with a radius to thickness ratio of 900, supported on an equatorial ring and partially filled with water, were subjected to vertical accelerations both normal and inclined to their equatorial rings. Buck- ling was detected by proximity gauges, and occurred as a result of tensile meridional and compressive circumferential stresses. The sphere was found to be imperfection insen- sitive and to be more susceptible to buckling at approximately ⅓ and ⅔ full for respectively the normal and inclined loading cases. Both a numerical com- puter solution and an analytical analysis were found to be in good agreement with the experimental results. Both the ASME and BS5500 design codes were however, found for this mode of failure to be too conservative for design purposes.

Authors: Murray, P

• Publication date: 1978
• DOI: 10.5287/ora-pp1qnedb9
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Subjects: Sphere; Shells (Engineering); Buckling (Mechanics); Strength of materials