Tensile bifurcations in a truncated hemispherical thin elastic shell

The work described in this paper is concerned with providing a rational asymptotic analysis of the wrinkling bifurcation experienced by a thin elastic hemispherical segment subjected to vertical tensile forces on its upper rim. This is achieved by considering the interplay between two boundary layers and matching the corresponding solutions associated with each separate region. Our key result is a four-term asymptotic formula for the critical load in terms of a small parameter proportional to the ratio between the thickness and the radius of the shell. Comparisons of this formula with direct numerical simulations provide further insight into the range of validity of the results derived herein.