Buckling of an imperfect spherical shell subjected to external pressure

Abstract

This paper presents numerical results focusing on the buckling behaviour of externally pressurised imperfect spherical shells. The numerical model followed the recommendations of the European Standard EN1993-1-6. A good agreement between the model FE and the experimental results with an average difference of less than 7% was found. The perfect steel spherical shell is then subjected to several imperfection approaches, such as (a) eigenmode imperfection and (b) single load indentation (SLI) imperfection. The eigenmode shape imperfection proves to be the worst imperfection for the externally pressurised spherical shells, yet the SLI is an attractive technique to simulate the realistic imperfection (i.e., dent/dimple). Based on the recommendation of the European Standard EN1993-1-6 for imperfection tolerance, the SLI imperfection was used for the realistic-case imperfection approach for different spherical shell configurations. A lower-bound closed-form empirical formula for a spherical shell under external pressure was proposed for the spherical shell with the single load indentation (SLI). The results show that for a shell shape parameter λ ≥ 10, the EBC provides a much higher knockdown factor compared to the guidelines of NASA SP -8032, Wagner, and lower-bound closed-form empirical formula (the differences are in the range of 48%–56%).