Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session X55: Shell Buckling IFocus

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Sponsoring Units: GSNP GSOFT Chair: Shmuel Rubinstein, Harvard University Room: BCEC 254B 
Friday, March 8, 2019 8:00AM  8:36AM 
X55.00001: Nondestructive prediction of the buckling load of soda cans and space rockets Invited Speaker: Emmanuel Virot What is the critical load required to crush a soda can or a space rocket shell? Surprisingly, there is no good way to estimate it, because of the high defectsensitivity of the buckling instability. Here we measure the response of (imperfect) soda cans to lateral poking and identify a generic stability landscape, which fully characterizes the stability of real imperfect shells in the case where one single defect dominates. We show that the landscape of stability is independent of the loading protocol and the poker geometry. 
Friday, March 8, 2019 8:36AM  8:48AM 
X55.00002: How localized imperfections modify the buckling threshold of cylindrical shells Emilio Lozano, Shmuel Rubinstein, Tobias Schneider Shells buckle and collapse at load levels below the thresholds predicted by linear stability analysis. The reduction of the loadcarrying capacity has been linked to extreme sensitivity to geometric imperfections. Historically, spatially extended periodic imperfections have been analyzed using linear and weakly nonlinear theory. Recent fully nonlinear approaches suggest however the importance of spatially localized imperfections. We thus characterize experimentally and numerically the effect of spatially localized imperfections in an axially loaded cylindrical shell. For different types of imperfections, the buckling thresholds as a function of its size shows similar behaviour. This suggests a universal failure mechanism due to local buckling. 
Friday, March 8, 2019 8:48AM  9:00AM 
X55.00003: Localized edge state equilibria control when a soda can buckles Emilio Lozano, Florian Reetz, Emmanuel Virot, Shmuel Rubinstein, Tobias Schneider Thinwalled cylindrical shells such as rocket walls (or soda cans) offer exceptional strengthtoweight ratios yet predicting at which load the structure becomes unstable and fails remains an unsolved problem. Shells buckle and collapse at loading conditions much below those predicted by linear stability theory. We thus propose a fully nonlinear approach and show that fully nonlinear equilibrium states located on the boundary of the unbuckled state's basin of attraction define critical perturbation amplitudes and guide the nonlinear initiation of catastrophic buckling. For a clamped thin cylindrical shell under axial compression a fully localized single dimple deformation is identified as the edge stateâ€”the attractor for the dynamics restricted to the stability boundary. Under variation of the axial load, the single dimple undergoes homoclinic snaking in the azimuthal direction, creating states with multiple dimples arranged around the central circumference. Once the circumference is completely filled with a ring of dimples, snaking in the axial direction leads to further growth of the dimple pattern. The bifurcation structure of the equilibria closely resembles that observed in the SwiftHohenberg equation with quadraticcubic nonlinearity. 
Friday, March 8, 2019 9:00AM  9:12AM 
X55.00004: Interacting defects affect the buckling of imperfect spherical shells Dong Yan, Matteo Pezzulla, Pedro Reis The presence, distribution, and interaction of defects dictate the buckling strength of shell structures. Even if the sensitivity of shell buckling to imperfections has long been recognized, to date, the successful prediction of critical loads is restricted to cases with a single defect, of known geometry. However, in reality, shells typically contain a distribution of defects and their interaction has not been well studied. In this talk, we will focus on spherical shells with multiple defects and study the role of defect interactions in dictating the buckling pressure. In the experiments, we fabricate polymeric shells containing two precisely engineered geometric defects through a customizable coating technique. We vary the relative size and location of these two defects and quantify the relationship between buckling pressure and defect distribution. The experimental results are then contrasted against finite element modeling (FEM) simulations. Upon validation of the numerics, we use FEM to perform a broader and more systematic exploration of the parameter space. Our results provide a better understanding of defect interactions, which we hope will put us on a step to better predict the buckling pressure of practical shell structures. 
Friday, March 8, 2019 9:12AM  9:24AM 
X55.00005: On Establishing Buckling Knockdowns for ImperfectionSensitive Shell Structures Symeon Gerasimidis, Emmanuel Virot, John Hutchinson, Shmuel Rubinstein This presentation contributes to recent efforts aiming to revise longstanding knockdown factors for elastic shell buckling, which are widely regarded as overly conservative for wellconstructed shells. The presented work focuses on cylindrical shells under axial compression with emphasis on the role of local geometric dimple imperfections and the use of lateral force probes as surrogate imperfections. Two buckling thresholds are identified (local and global buckling) and related for the two kinds of imperfections. Four sets of relevant boundary conditions are accounted revealing a strong dependence of the global buckling load on overall endrotation constraint when local buckling precedes global buckling. A reasonably complete picture emerges, which should be useful for informing decisions on establishing knockdown factors. 
Friday, March 8, 2019 9:24AM  9:36AM 
X55.00006: Quasistatic experimental pathfollowing Robin M Neville, Rainer Groh, Alberto Pirrera, Mark Schenk Our work aims to exploit structural nonlinearity in engineering, with a particular focus on aerospace applications, to develop wellbehaved nonlinear structures [1]. 
Friday, March 8, 2019 9:36AM  9:48AM 
X55.00007: On the role of localised postbuckling equilibria in axially compressed cylinders Rainer Groh, Alberto Pirrera We revisit buckling of axially compressed cylinders by considering fully localised postbuckling states in the form of one or multiple dimples. Using a combination of nonlinear quasistatic finite element methods and numerical continuation algorithms, we trace the evolution of odd and even dimples into one ring of circumferential diamond waves. The growth of the postbuckling pattern with varying compression is driven by a homoclinic snaking sequence, with even and odd dimple solutions intertwined. The initially stable and axially localised ring of circumferential diamonds destabilises at a pitchfork bifurcation to produce a second circumferential snaking sequence that results in the Yoshimura pattern. Localised dimple solutions represent saddle points in the energy landscape providing an exponentially decreasing energy barrier between the stable prebuckling and restabilised postbuckling wells. The significance of the Maxwell load as a measure for quantifying the onset of mountainpass solutions and the reduced resilience of the prebuckling state is assessed. Finally, conservative buckling loads for design are inferred by tracing critical boundaries of the snaking set. 
Friday, March 8, 2019 9:48AM  10:00AM 
X55.00008: Powering the Renaissance: Methods to Reveal the Energy Landscapes in Thin Shell Buckling Jack Panter, Junbo Chen, Teng Zhang, Halim Kusumaatmaja The extreme nonlinearity of thin shell buckling introduces significant challenges to studying even the simplest geometries. Here, we develop a new approach by coupling efficient and powerful energy landscape methods to a conceptually simple discretized elastic mesh model. This highly versatile approach can probe the buckling energy landscape of any thin shell, or composite of thin shells, without the need for a priori assumptions about deformation morphologies or symmetries. 
Friday, March 8, 2019 10:00AM  10:12AM 
X55.00009: Buckling of thermalized cylindrical shells Andrej Kosmrlj, David R. Nelson We explore how thermal fluctuations affect the buckling of thin cylindrical shells. It is known that for flat solid sheets thermal fluctuations effectively increase the bending rigidity and reduce the bulk and shear moduli. As a consequence, thermal fluctuations increase the critical buckling load. In cylindrical shells, thermal fluctuations also increase the bending rigidity and reduce the inplane elastic constants. However, the additional coupling between the shell curvature, the inplane stretching modes and the outofplane undulations leads to novel phenomena. In shells thermal fluctuations effectively generate compressive load. As a consequence, the critical axial buckling load for cylindrical shells is reduced due to thermal fluctuations, which is similar to the reduced buckling pressure for spherical shells, but different from the enhanced buckling load for flat sheets. Similar to spherical shells, we find that for cylindrical shells with a sufficiently large radius the thermally generated compression can be large enough that shells become unstable even in the absence of external load. Furthermore, we find that the critical radius also depends on the aspect ratio (length/perimeter) of cylindrical shells. 
Friday, March 8, 2019 10:12AM  10:24AM 
X55.00010: Imperfectioninsensitive thin wavy cylindrical shells under bending: Effect of local radius of curvature on buckling and imperfectionsensitivity. Kshitij Yadav, Symeon Gerasimidis The imperfectionsensitivity of thin cylindrical shells has long been an obstacle for their optimal applications. To nullify this behavior, a conservative knockdown factor method is utilized for the design of thin cylindrical shells. Alternatively, stiffeners are also used to increase their capacity and to reduce the imperfectionsensitivity. We explore wavy crosssectional thin cylindrical shells under bending to investigate the impact of imperfections on their load carrying capacity. We found that thin wavy cylindrical shells are insensitive to imperfections under bending in contrast to thin circular cylinders. This insensitivity is achieved by reducing the local radius of curvature and consequently, the effective radius of the cylindrical shell is reduced. This way cylindrical shells become less sensitive to imperfections and increase their load carrying capacity. 
Friday, March 8, 2019 10:24AM  10:36AM 
X55.00011: Outofplane buckling of architected sheets with nonperiodic cut patterns Connor McMahan, Paolo Celli, Basile Audoly, Chiara Daraio We investigate the outofplane shape morphing capability of elastic sheets with architected cut patterns. These cuts result in arrays of tiles connected by flexible hinges. We demonstrate that a nonperiodic cut pattern can cause a sheet to buckle into threedimensional shapes, such as domes or patterns of wrinkles, when pulled at specific boundary points. This phenomenon stems from the geometric incompatibilities between regions that are designed to undergo different amounts of strain. Global buckling modes observed in experiments are rationalized by an inplane kinematic analysis, and are reproduced in simulations of homogenized shell models implemented in the opensource finiteelement platform FEniCS. Our work illustrates a scalable route towards the fabrication of threedimensional objects with nonzero Gaussian curvature from initiallyflat sheets. 
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