Shell-buckling revisited: “Everybody loves a buckling problem!”

Abstract

From viral capsids and fuel tanks, to architectural domes, slender shells are ubiquitous in natural and engineered structures. The mechanics of shells is tightly intertwined with the underlying geometry and the onset for instability is a classic problem in structural mechanics. Since the golden era of shell buckling in the 1960’s, a plethora iof theoretical and computational studies have addressed this canonical problem, but there is a striking lack of precision experiments to corroborate the multitude of predictions. We have recently revisited this old field by introducing a framework of precision model experiments to thoroughly quantify both the buckling onset, as well as the postbuckling regime of pressurized spherical shells. Central to this effort, we have devised a robust, versatile, and precise fabrication mechanism to rapid prototype thin shells of nearly constant thickness that contain precisely designed geometric imperfections. By systematically varying the amplitude of these defects, we study the effect that these imperfections have on the buckling strength of our spherical shells. Small deviations from the spherical geometry result in large reductions in the buckling pressure and our experimental results agree well with some existing theories. We then perform a broader exploration for other classes of defects, for which theoretical predictions are yet to be developed. Our ultimate goal is to develop a predictive foundation for the mechanisms that affect the knockdown factors of spherical shells towards a rational design framework that goes beyond the prevailing empirical status quo.