Modal nudging in nonlinear elasticity: Tailoring the elastic post-buckling behaviour of engineering structures

Cox, Bradley; Groh, Rainer; Avitabile, Daniele; Pirrera, Alberto

doi:10.1016/j.jmps.2018.03.025

Cited by 35 publications

(18 citation statements)

References 35 publications

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“…This improvement is over twice that of a uniformly thickened cylinder, 9%, with the same mass increase, the transition profile for which is shown as the dotted black line. This landscape biasing against the transition is the antithesis to modal nudging 49 , the recently formalised technique for slender structures in which minimal structural modifications are made in order to select a specific failure mode.…”

Section: Resultsmentioning

confidence: 99%

Harnessing energy landscape exploration to control the buckling of cylindrical shells

et al. 2019

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Even for relatively simple thin shell morphologies, many different buckled configurations can be stable simultaneously. Which state is observed in practice is highly sensitive to both environmental perturbations and shell imperfections. The complexity and unpredictability of postbuckling responses has therefore raised great challenges to emerging technologies exploiting buckling transitions. Here we show how the buckling landscapes can be explored through a comprehensive survey of the stable states and the transition mechanisms between them, which we demonstrate for cylindrical shells. This is achieved by combining a simple and versatile triangulated lattice model with efficient high-dimensional free-energy minimisation and transition path finding algorithms. We then introduce the method of landscape biasing to show how the landscapes can be exploited to exert control over the postbuckling response, and develop structures which are resistant to lateral perturbations. These methods now offer the potential for studying complex buckling phenomena on a range of elastic shells.

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Section: Resultsmentioning

confidence: 99%

Harnessing energy landscape exploration to control the buckling of cylindrical shells

et al. 2019

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“…The high-rate motion and multistability are appealing features of buckling phenomena which can usefully exploited at different scales for smart morphable or shape-adaptive structures, devices or metamaterials (inspired, for example, by origami or kirigami technique) [82]. This can be achieved by specific design strategies (e.g., the modal nurging) which lead the structure to a peculiar equilibrium path [83].…”

Section: Next-generation Challengesmentioning

confidence: 99%

Recent Developments in the Dynamic Stability of Elastic Structures

Mascolo

2019

Front. Appl. Math. Stat.

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Dynamic instability in the mechanics of elastic structures is a fascinating topic, with many issues still unsettled. Accordingly, there is a wealth of literature examining the problems from different perspectives (analytical, numerical, experimental etc.), and coverings a wide variety of topics (bifurcations, chaos, strange attractors, imperfection sensitivity, tailor-ability, parametric resonance, conservative or non-conservative systems, linear or non-linear systems, fluid-solid interaction, follower forces, etc.). This paper provides a survey of selected topics of current research interest. It aims to collate the key recent developments and international trends, as well as describe any possible future challenges. A paradigmatic example of Ziegler paradox on the destabilizing effect of small damping is also included.

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“…These attractive stable states are normally inaccessible as they are separated from the natural response of the structure by unstable equilibrium paths. Here, to connect and exploit these paths we apply a previously introduced design framework known as modal nudging [27]. Modal nudging uses the deformation modes associated to these stable post-buckled equilibria to alter the undeformed baseline geometry of the structure imperceptibly, thereby favouring the seeded post-buckling response over potential alternatives.…”

Section: Aims and Objectivesmentioning

confidence: 99%

“…A validation of preliminary results, which is undertaken using the commercial finite element analysis software ABAQUS, is also included. Section 3 provides a comprehensive discussion of the baseline response of both shell models and includes [27] a number of figures illustrating the complexity manifest in the full spectrum of equilibrium paths. In section 4, the modal nudging technique is employed to favourably alter the response of the cylindrical panels.…”

Section: Aims and Objectivesmentioning

confidence: 99%

“…Generally speaking, any stochastic imperfection reduces the capacity of imperfection-sensitive structures, although specific imperfection shapes, such as imperfections based on linear combinations of the first few critical eigenvectors, can also lead to a pronounced knock-down on load-carrying capacity. The perturbations applied in modal nudging [27] differ in that the small geometric changes are (i) deterministically imposed; and (ii) do not lead to reduced structural capacity, but to an entirely new structural response. In many cases, this new "nudged" structural response improves the load-carrying capacity, compliance, stability and efficiency of the structure.…”

Section: Modal Nudging Of the Baseline Structural Responsementioning

confidence: 99%

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Nudging Axially Compressed Cylindrical Panels Toward Imperfection Insensitivity

Cox

Groh

Pirrera

2019

Journal of Applied Mechanics

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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.

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Modal nudging in nonlinear elasticity: Tailoring the elastic post-buckling behaviour of engineering structures

Cited by 35 publications

References 35 publications

Harnessing energy landscape exploration to control the buckling of cylindrical shells

Harnessing energy landscape exploration to control the buckling of cylindrical shells

Recent Developments in the Dynamic Stability of Elastic Structures

Nudging Axially Compressed Cylindrical Panels Toward Imperfection Insensitivity

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