Buckling instability on a rotating plane

The concept of Maximum Drawing Ratio (MDR), supplementary to the well-known Limit Drawing Ratio (LDR), is defined, examined, and illustrated by experiments. In essence the MDR is reached when the two basic failure modes, namely: rupture (due to tensile instability) and wrinkling (due to buckling instability) are delayed till they occur simultaneously. Thus the process is beneficially utilized for higher drawing ratio by postponing earlier interception of either one of the above failures alone. The ability to suppress (up to a certain extent) the appearance of these failure modes depends heavily on the fluid-pressure path which controls the hydroforming process. The effect of the material properties, like the strain hardening exponent, the normal anisotropy of the blank, etc., as well as the geometrical properties (i.e., the thickness of the blank, the radius of curvature at the lip, etc.) on the MDR, are considered here in some detail. The nature of the solutions by which MDR is reached is discussed.

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Elastic-instability–enabled locomotion

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2013801118 ◽

2021 ◽

Vol 118 (8) ◽

pp. e2013801118

Author(s):

Amit Nagarkar ◽

Won-Kyu Lee ◽

Daniel J. Preston ◽

Markus P. Nemitz ◽

Nan-Nan Deng ◽

...

Keyword(s):

Symmetry Breaking ◽

Scaling Laws ◽

Multiple Scales ◽

Symmetric Cone ◽

Simple Approach ◽

Inertial Forces ◽

Elastic Instability ◽

Anisotropic Friction ◽

Buckling Instability ◽

Elastic Instabilities

Locomotion of an organism interacting with an environment is the consequence of a symmetry-breaking action in space-time. Here we show a minimal instantiation of this principle using a thin circular sheet, actuated symmetrically by a pneumatic source, using pressure to change shape nonlinearly via a spontaneous buckling instability. This leads to a polarized, bilaterally symmetric cone that can walk on land and swim in water. In either mode of locomotion, the emergence of shape asymmetry in the sheet leads to an asymmetric interaction with the environment that generates movement––via anisotropic friction on land, and via directed inertial forces in water. Scaling laws for the speed of the sheet of the actuator as a function of its size, shape, and the frequency of actuation are consistent with our observations. The presence of easily controllable reversible modes of buckling deformation further allows for a change in the direction of locomotion in open arenas and the ability to squeeze through confined environments––both of which we demonstrate using simple experiments. Our simple approach of harnessing elastic instabilities in soft structures to drive locomotion enables the design of novel shape-changing robots and other bioinspired machines at multiple scales.

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Dynamics of Tubular Cantilevers Conveying Fluid

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1970_012_017_02 ◽

1970 ◽

Vol 12 (2) ◽

pp. 85-103 ◽

Cited By ~ 113

Author(s):

M. P. Paidoussis

Keyword(s):

Quantitative Agreement ◽

Dynamical Behaviour ◽

Oscillatory Instability ◽

Complex Frequency ◽

Buckling Instability ◽

Gravity Forces ◽

Stability Maps ◽

Conditions Of Stability ◽

Conveying Fluid ◽

Flow Velocities

In Part 1 a general theory is presented to account for the small, free, lateral motions of a vertical, uniform, tubular cantilever conveying fluid, with the free end being either below the clamped one (‘hanging’ cantilever) or above it (‘standing’ cantilever). Gravity forces are not considered to be negligible. It is shown that, when the velocity of the fluid exceeds a certain value, the cantilever in all cases becomes subject to oscillatory instability. In the case of hanging cantilevers buckling instability does not occur. Standing cantilevers, on the other hand, may buckle under their own weight; it is shown that in some cases flow (within a certain range of flow velocities) may render stable a system which would buckle in the absence of flow. Extensive complex frequency calculations were conducted to illuminate the dynamical behaviour of the system with increasing flow. The conditions of stability have also been extensively calculated and stability maps constructed. It is shown that dissipative forces may have either a stabilizing or a destabilizing effect on the system, partly depending on the magnitude of these forces themselves. The experiments described in Part 2 were designed to illustrate the dynamical behaviour of vertical tubular cantilevers conveying fluid. The experiments were conducted with rubber tubes conveying either water or air. The tubes were either hanging down or standing upright. It was observed that for sufficiently high flow velocities both hanging and standing cantilevers become subject to oscillatory instability. It was also observed that standing cantilevers which would buckle under their own weight in the absence of flow, in some cases are rendered stable by flow within a certain range of flow velocities. Qualitative and quantitative agreement between theory and experiment was satisfactorily good.

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Buckling instability and adhesion of carbon layers

Thin Solid Films ◽

10.1016/0040-6090(84)90365-1 ◽

1984 ◽

Vol 120 (2) ◽

pp. 109-121 ◽

Cited By ~ 151

Author(s):

G. Gille ◽

B. Rau

Keyword(s):

Buckling Instability

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Synthesizing Precompressed Beams As Bistable Compliant Mechanisms

Volume 4A: Dynamics, Vibration, and Control ◽

10.1115/imece2017-70336 ◽

2017 ◽

Author(s):

Mohammed Abdullah Maaz Siddiqui ◽

Hong Zhou

Keyword(s):

Rigid Body ◽

Axial Compression ◽

Stable Equilibrium ◽

Compliant Mechanisms ◽

Input Power ◽

Elastic Deformations ◽

Buckling Instability ◽

Beam Thickness ◽

Fixed End ◽

Input Torque

Bistable mechanisms provide two stable positions. Input power is not needed to maintain any of the two stable positions. To switch from one stable position to another, input power is required. Bistable mechanisms have many applications including valves, closures, switches and various other devices. Unlike conventional rigid-body bistable mechanisms that rely on relative motions of kinematic joints, bistable compliant mechanisms take advantage of elastic deformations of flexible members to achieve two stable positions. There are two symmetric buckled shapes in a precompressed beam that has one fixed end and one pinned end. The two buckled shapes match the two stable equilibrium positions of bistable compliant mechanisms. The precompressed beam can be rotationally actuated at the pinned end to snap from one buckled shape to another. Synthesizing precompressed beams as bistable mechanisms is challenging because of buckling instability and integrated force and deflection characteristics. In this paper, the buckled shape is derived for a precompressed beam with fixed and pinned ends. The input torque at the pinned end is analyzed for a precompressed beam to snap between its two symmetric buckled shapes. Precompressed beams are synthesized as bistable compliant mechanisms through axial compression and beam thickness in this paper.

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Stretching Hookean ribbons part I: relative edge extension underlies transverse compression and buckling instability

The European Physical Journal E ◽

10.1140/epje/s10189-021-00092-z ◽

2021 ◽

Vol 44 (7) ◽

Author(s):

Meng Xin ◽

Benny Davidovitch

Keyword(s):

Transverse Compression ◽

Buckling Instability ◽

Edge Extension

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Non-parametric density reconstruction of the Galactic bulge area using red clump stars in the VVV survey

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa2834 ◽

2020 ◽

Vol 499 (2) ◽

pp. 1937-1947

Author(s):

Dylan Paterson ◽

Brendan Coleman ◽

Chris Gordon

Keyword(s):

Parametric Method ◽

Major Axis ◽

Galactic Bulge ◽

Buckling Instability ◽

Giant Stars ◽

Red Clump ◽

Red Giant ◽

High Resolution Reconstruction ◽

Spiral Arm ◽

Non Parametric

ABSTRACT Studies of the red clump giant population in the inner Milky Way suggest the Galactic bulge/bar has a boxy/peanut/X-shaped structure as predicted by its formation via a disc buckling instability. We used a non-parametric method of estimating the Galactic bulge morphology that is based on maximum entropy regularization. This enabled us to extract the 3D distribution of the red giant stars in the bulge from deep photometric catalogues of the VISTA Variables in the Via Lactea survey. Our high-resolution reconstruction confirms the well-known boxy/peanut/X-shaped structure of the bulge. We also find spiral arm structures that extend to around 3 kpc in front of and behind the bulge and are on different sides of the bulge major axis. We show that the detection of these structures is robust to the uncertainties in the luminosity function.

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