Fabrication and buckling of thin spherical shells containing precise geometric imperfections

Abstract

We revisit the classic problem of buckling of thin spherical shells under uniform pressure and explore the effect that geometric imperfections can have on their buckling behavior. Since the 1960s, numerous theoretical and computational studies have addressed the imperfection sensitivity of buckling of thin elastic shells. However, there is a lack of precise experiments to corroborate these predictions, especially for spherical shells, which is the central topic of this thesis. First, we develop a novel fabrication technique to produce thin hemispherical elastic shells by the coating of spherical molds with a polymer solution. Upon curing the thin liquid film yields the elastic structure of nearly constant thickness. We experimentally investigate the drainage dynamics, the final thickness, and its uniformity. Our results are directly compared with theoretical and numerical analyses. Secondly, we study the buckling of spherical shells that contain a precisely engineered geometric imperfection. Our shell fabrication technique allows us to introduce a single dimple-like defect with controllable geometric properties. We systematically vary the amplitude and width of the defect, and then we present a quantitative relationship between the critical buckling pressure and the defect geometry. Our results can be predicted by both the finite element method and numerical simulations of a reduced shell theory model. Finally, we fabricate hemispherical bilayer shells containing a defect. To do so, we coat two different polymer solutions, layer by layer, onto the hemispherical molds containing a defect. We find that the bilayer shell can self-repair or self-aggravate the geometric imperfections due to residual swelling. Hence, the critical buckling pressure can be increased or decreased over time depending on the order of coating of each polymer layer. The fabrication technique and experimental results presented in this thesis open exciting new avenues in the study of the buckling of spherical shells, and we hope that it will instigate a resurgence of interest in this classic but important field of mechanics.