Nudging Axially Compressed Cylindrical Panels Toward Imperfection Insensitivity

Abstract

Curved shell structures are known for their excellent load-carrying capability and are commonly used in thin-walled constructions. Although theoretically able to withstand greater buckling loads than flat structures, shell structures are notoriously sensitive to imperfections owing to their postbuckling behavior often being governed by subcritical bifurcations. Thus, shell structures often buckle at significantly lower loads than those predicted numerically and the ensuing dynamic snap to another equilibrium can lead to permanent damage. Furthermore, the strong sensitivity to initial imperfections, as well as their stochastic nature, limits the predictive capability of current stability analyses. Our objective here is to convert the subcritical nature of the buckling event to a supercritical one, thereby improving the reliability of numerical predictions and mitigating the possibility of catastrophic failure. We explore the elastically nonlinear postbuckling response of axially compressed cylindrical panels using numerical continuation techniques. These analyses show that axially compressed panels exhibit a highly nonlinear and complex postbuckling behavior with many entangled postbuckled equilibrium curves. We unveil isolated regions of stable equilibria in otherwise unstable postbuckled regimes, which often possess greater load-carrying capacity. By modifying the initial geometry of the panel in a targeted—rather than stochastic—and imperceptible manner, the postbuckling behavior of these shells can be tailored without a significant increase in mass. These findings provide new insight into the buckling and postbuckling behavior of shell structures and opportunities for modifying and controlling their postbuckling response for enhanced efficiency and functionality.

Building blocks that govern spontaneous and programmed pattern formation in pre-compressed bilayers

“…However, exerting sufficient processing control over pre-compressed thin-film bilayers that may assume multiple stable shapes upon end shortening, or even exhibit spatially chaotic behaviour, can be difficult and expensive. Nonetheless, in addition to having enabled the acquisition of new understanding over their behaviour, the ability to trace a bilayer's full equilibrium manifold opens another opportunity: modal nudging [41,42]. Modal nudging is a recently developed design philosophy that uses the deformation modes associated with stable post-critical equilibria to alter the undeformed baseline geometry of a structure, thereby favouring the seeded postbuckling response over potential alternatives.…”

Spatial chaos as a governing factor for imperfection sensitivity in shell buckling

“…The reduction in stochasticity due to a dominant imperfection accounts for the accurately predicted buckling loads of shells with precisely engineered imperfections [20] and the ability to control their postbuckling response [21]. The dominant imperfection creates a localized prebuckling stress field that biases the shell to follow a specific equilibrium trajectory toward buckling.…”

Robust improvement of the asymmetric post-buckling behavior of a composite panel by perturbing fiber paths

“…Varying parameters can also improve performance or generate different behavior. Buckling loads can be improved by tailoring the thickness [13], applying seeded geometric changes to geometry [14,15,16], or tailoring the fiber path. Composite structures with engineered fiber paths are also known as variable stiffness composites and enable more careful tailoring of stiffnesses and tailor the buckling and out of plane behavior of structures [17,18,19,20].…”