Principles of Structural Stability

Ziegler, Hans

doi:10.1007/978-3-0348-5912-7

Cited by 353 publications

(223 citation statements)

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“…Starting with structures and advancing to continuous media within the frameworks of linear and later nonlinear elasticity as well as inelasticity, the theory of stability in solids and structures has evolved and resulted in many seminal contributions, see, e.g., Refs. [8][9][10][11][12][13][14][15][16][17][18][19] for a nonexhaustive list of classics in the field.…”

Section: Introductionmentioning

confidence: 99%

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Kochmann

Bertoldi

2017

Applied Mechanics Reviews

196

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Instabilities in solids and structures are ubiquitous across all length and time scales, and engineering design principles have commonly aimed at preventing instability. However, over the past two decades, engineering mechanics has undergone a paradigm shift, away from avoiding instability and toward taking advantage thereof. At the core of all instabilities-both at the microstructural scale in materials and at the macroscopic, structural level-lies a nonconvex potential energy landscape which is responsible, e.g., for phase transitions and domain switching, localization, pattern formation, or structural buckling and snapping. Deliberately driving a system close to, into, and beyond the unstable regime has been exploited to create new materials systems with superior, interesting, or extreme physical properties. Here, we review the state-of-the-art in utilizing mechanical instabilities in solids and structures at the microstructural level in order to control macroscopic (meta)material performance. After a brief theoretical review, we discuss examples of utilizing material instabilities (from phase transitions and ferroelectric switching to extreme composites) as well as examples of exploiting structural instabilities in acoustic and mechanical metamaterials.

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Section: Introductionmentioning

confidence: 99%

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Kochmann

Bertoldi

2017

Applied Mechanics Reviews

196

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“…For centuries, engineers have experimented and calculated complex structures, such as frames, plates and cylinders, manifesting instabilities and bifurcations of various forms (Timoshenko & Gere 1961), so that certain instabilities have been found involving tensile loads. For instance, there are examples classified by Ziegler (1977) as 'buckling by tension' where a tensile loading is applied to a system in which a compressed member is always present, so that they do not represent true bifurcations under tensile loads. Other examples given by Gajewski & Palej (1974) are all related to the complex live (as opposed to 'dead') loading system; for instance, loading through a vessel filled with a liquid, so that Zyczkowski (1991) points out that 'With Eulerian behaviour of loading (materially fixed point of application, direction fixed in space), the bar cannot lose stability at all [· · · ].'…”

Section: Introductionmentioning

confidence: 99%

Structures buckling under tensile dead load

et al. 2011

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Some 250 years after the systematic experiments by Musschenbroek and their rationalization by Euler, for the first time we show that it is possible to design structures (i.e. mechanical systems whose elements are governed by the equation of the elastica) exhibiting bifurcation and instability ('buckling') under tensile load of constant direction and point of application ('dead'). We show both theoretically and experimentally that the behaviour is possible in elementary structures with a single degree of freedom and in more complex mechanical systems, as related to the presence of a structural junction, called 'slider', allowing only relative transversal displacement between the connected elements. In continuous systems where the slider connects two elastic thin rods, bifurcation occurs both in tension and in compression, and is governed by the equation of the elastica, employed here for tensile loading, so that the deformed rods take the form of the capillary curve in a liquid, which is in fact governed by the equation of the elastica under tension. Since axial load in structural elements deeply influences dynamics, our results may provide application to innovative actuators for mechanical wave control; moreover, they open a new perspective in the understanding of failure within structural elements.

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“…Below resonance (X=x 2 < 1), stiffness c 1 must satisfy c 1 =c 2 > ðX=x 2 Þ 2 , meaning that rotation below resonance destabilizes a range of positive c 1 that increases with X. Above resonance (X=x 2 > 1), stiffness c 1 must lie within the range (9). The resulting landscape of stable and unstable regimes (in light and dark gray, respectively) is shown in Fig.…”

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confidence: 99%

An infinitely-stiff elastic system via a tuned negative-stiffness component stabilized by rotation-produced gyroscopic forces

Kochmann

Drugan

2016

Applied Physics Letters

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An elastic system containing a negative-stiffness element tuned to produce positive-infinite system stiffness, although statically unstable as is any such elastic system if unconstrained, is proved to be stabilized by rotation-produced gyroscopic forces at sufficiently high rotation rates. This is accomplished in possibly the simplest model of a composite structure (or solid) containing a negative-stiffness component that exhibits all these features, facilitating a conceptually and mathematically transparent, completely closed-form analysis.

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Principles of Structural Stability

Cited by 353 publications

References 0 publications

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Structures buckling under tensile dead load

An infinitely-stiff elastic system via a tuned negative-stiffness component stabilized by rotation-produced gyroscopic forces

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