Ponding instability of air-supported spherical membranes with initial imperfections

The stability of a spherical, air-supported membrane subjected to a concentrated load and an accumulating ponding fluid is the subject of the present paper which consists of two parts: in the first part a spherical elastic membrane with an initial imperfection at the apex is considered. The effect of the ponding fluid accumulating in the initial depression reduces the value of the critical load significantly. Simple formulae for the critical load are obtained. In the second part, the case of a non-symmetric load applied to the membrane is considered. Results indicate that the eccentricity causes a significant increase in the value of the critical load thereby making the axisymmetric loading the governing configuration.