Defect-Defect Interactions in the Buckling of Imperfect Spherical Shells

We perform finite element simulations to study the impact of defect-defect interactions on the pressure-induced buckling of thin, elastic, spherical shells containing two dimpled imperfections. Throughout, we quantify the critical buckling pressure of these shells using their knockdown factor. We examine cases featuring either identical or different geometric defects and systematically explore the parameter space, including the angular separation between the defects, their widths and amplitudes, and the radius-to-thickness ratio of the shell. As the angular separation between the defects is increased, the buckling strength initially decreases, then increases before reaching a plateau. Our primary finding is that the onset of defect-defect interactions, as quantified by a characteristic length scale associated with the onset of the plateau, is set by the critical buckling wavelength reported in the classic shell-buckling literature. Beyond this threshold, within the plateau regime, the buckling behavior of the shell is dictated by the largest defect.