Effects of constraint curvature on structural instability: tensile buckling and multiple bifurcations

Bifurcation of an elastic structure crucially depends on the curvature of the constraints against which the ends of the structure are prescribed to move, an effect which deserves more attention than it has received so far. In fact, we show theoretically and we provide definitive experimental verification that an appropriate curvature of the constraint over which the end of a structure has to slide strongly affects buckling loads and can induce: (i.) tensile buckling; (ii.) decreasing- (softening), increasing- (hardening), or constant-load (null stiffness) postcritical behaviour; (iii.) multiple bifurcations, determining for instance two bifurcation loads (one tensile and one compressive) in a single-degree-of-freedom elastic system. We show how to design a constraint profile to obtain a desired postcritical behaviour and we provide the solution for the elastica constrained to slide along a circle on one end, representing the first example of an inflexional elastica developed from a buckling in tension. These results have important practical implications in the design of compliant mechanisms and may find applications in devices operating in quasi-static or dynamic conditions.

Computational analysis of liquid crystalline elastomer membranes: Changing Gaussian curvature without stretch energy

Liquid crystalline elastomers (LCEs) can undergo extremely large reversible shape changes when exposed to external stimuli, such as mechanical deformations, heating or illumination. The deformation of LCEs result from a combination of directional reorientation of the nematic director and entropic elasticity. In this paper, we study the energetics of initially flat, thin LCE membranes by stress driven reorientation of the nematic director. The energy functional used in the variational formulation includes contributions depending on the deformation gradient and the second gradient of the deformation. The deformation gradient models the in-plane stretching of the membrane. The second gradient regularises the non-convex membrane energy functional so that infinitely fine in-plane microstructures and infinitely fine out-of-plane membrane wrinkling are penalised. For a specific example, our computational results show that a non-developable surface can be generated from an initially flat sheet at cost of only energy terms resulting from the second gradients. That is, Gaussian curvature can be generated in LCE membranes without the cost of stretch energy in contrast to conventional materials. © 2013 Elsevier Ltd. All rights reserved.

Comparison of moment-curvature models for fiber-reinforced polymer plate-end debonding studies using global energy balance approach

This paper compares a number of different moment-curvature models for cracked concrete sections that contain both steel and external fiber-reinforced polymer (FRP) reinforcement. The question of whether to use a whole-section analysis or one that considers the FRP separately is discussed. Five existing and three new models are compared with test data for moment-curvature or load deflection behavior, and five models are compared with test results for plate-end debonding using a global energy balance approach (GEBA). A proposal is made for the use of one of the simplified models. The availability of a simplified model opens the way to the production of design aids so that the GEBA can be made available to practicing engineers through design guides and parametric studies. Copyright © 2014, American Concrete Institute.

Local strain rate and curvature dependences of scalar dissipation rate transport in turbulent premixed flames: A direct numerical simulation analysis

The statistical behaviours of the instantaneous scalar dissipation rate Nc of reaction progress variable c in turbulent premixed flames have been analysed based on three-dimensional direct numerical simulation data of freely propagating statistically planar flame and V-flame configurations with different turbulent Reynolds number Ret. The statistical behaviours of N c and different terms of its transport equation for planar and V-flames are found to be qualitatively similar. The mean contribution of the density-variation term T1 is positive, whereas the molecular dissipation term (-D2) acts as a leading order sink. The mean contribution of the strain rate term T2 is predominantly negative for the cases considered here. The mean reaction rate contribution T3 is positive (negative) towards the unburned (burned) gas side of the flame, whereas the mean contribution of the diffusivity gradient term (D) assumes negative (positive) values towards the unburned (burned) gas side. The local statistical behaviours of Nc, T1, T2, T 3, (-D2), and f(D) have been analysed in terms of their marginal probability density functions (pdfs) and their joint pdfs with local tangential strain rate aT and curvature km. Detailed physical explanations have been provided for the observed behaviour. © 2014 Y. Gao et al.

Characterisation of carbon nano-onions using Raman spectroscopy

Characteristics of the Raman spectrum from carbon onions have been identified in terms of the position of the G peak and appearance of the transverse optic phonon peaks. Five new peaks were observed in the low wavenumber region, at about 1100, 861, 700, 450 and 250 cm(-1). The origins of these peaks are discussed in terms of the phonon density of states (PDOS) and phonon dispersion curves of graphite. The curvature of the graphene planes is invoked to explain the relaxation of the Raman selection rules and the appearance of the new peaks. The Raman spectrum of carbon onions is compared with that of highly oriented pyrolytic graphite (HOPG). The strain of graphene planes due to curvature has been estimated analytically and is used to account for the downward shift of the G peak. (C) 2003 Elsevier Science B.V. All rights reserved.

Turbulence modeling for flows around convex features giving rapid eddy distortion

Reynolds averaged Navier-Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, ReW ≤ 2.5 × 103. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov's νt-92; Secundov et al.'s two equation νt-L; Wolfshtein's k-l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k-ε models including those with wall distance based damping functions; Menter SST, k-ω and Spalding's LVEL model. The use of differential equation distance functions (Poisson and Hamilton-Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with ReW ≈ 2.5 × 103 the mixing length and k-l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov νt-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from ReW = 2500 to 250 surprisingly strengthens the cylinder's disruptive influence. Importantly, results for ReW ≪ 250 are virtually identical to those for ReW = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder-Sharma k-ε, Menter SST and k-ω show, in accordance with physical reality, the cylinder's influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model's erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k-l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%. © 2007 Elsevier Inc. All rights reserved.

Sound transmission in strongly-curved slowly-varying cylindrical and annular lined ducts with flow

In this paper we consider the propagation of acoustic waves along a curved hollow or annular duct with lined walls. The curvature of the duct centreline and the wall radii vary slowly along the duct, allowing application of an asymptotic multiple scales analysis. This generalises Rienstra's analysis of a straight duct of varying cross-sectional radius. The result of the analysis is that the modal wavenumbers and mode shapes are determined locally as modes of a torus with the same local curvature, while the amplitude of the modes evolves as the mode propagates along the duct. The duct modes are found numerically at each axial location using a pseudo-spectral method. Unlike the case of a straight duct, there is a fundamental asymmetry between upstream and downstream propagating modes, with some mode shapes tending to be concentrated on either the inside or outside of the bend depending on the direction of propagation. The interaction between the presence of wall lining and curvature is investigated in particular; for instance, in a representative case it is found that the curvature causes the first few acoustic modes to be more heavily damped by the duct boundary than would be expected for a straight duct. Analytical progress can be made in the limit of very high mode order, in which case well-known 'whispering gallery' modes, localised close to the wall, can be identified.

Microgripper using a diamond like carbon/metal bilayer

A novel normally closed microcage has been fabricated and characterized. This device was made from a highly compressively stressed diamond like carbon (DLC) and electroplated Ni bimorph structure. The large stress in the DLC causes the bimorph layer to curve once it is released from the substrate. The radius of curvature is in the range of 18 - 50μm, and can be controlled by varying the DLC and the Ni thicknesses. The devices can be operated in a pulsed mode current with low operation temperature, and can be opened by ∼60μm laterally with a power consumption of only ∼16mW. © 2004 IEEE.

Transparent electrode with a nanostructured coating.

Using single-walled nanotubes as an example, we fabricated transparent conductive coatings and demonstrated a new technique of centrifuge coating as a potential low-waste, solution-based batch process for the fabrication of nanostructured coatings. A theoretical model is developed to account for the sheet resistance exhibited by layered random-network coatings such as nanofilaments and graphene. The model equation is analytical and compact, and allows the correlation of very different scaling regimes reported in the literature to the underlying coating microstructure. Finally, we also show a refined experimental setup to systematically measure the curvature-dependent sheet resistance.

Deployable membranes designed from folding tree leaves.

A simple model of deploying tree leaves is assembled in different arrangements to produce polygonal foldable membranes for use as deployable structures. One family of folding patterns exhibits a small strain mechanism, which is investigated. Variations on the basic arrangements can be used to fold membranes with a discretized curvature.

Impedance control reduces instability that arises from motor noise.

There is ample evidence that humans are able to control the endpoint impedance of their arms in response to active destabilizing force fields. However, such fields are uncommon in daily life. Here, we examine whether the CNS selectively controls the endpoint impedance of the arm in the absence of active force fields but in the presence of instability arising from task geometry and signal-dependent noise (SDN) in the neuromuscular system. Subjects were required to generate forces, in two orthogonal directions, onto four differently curved rigid objects simulated by a robotic manipulandum. The endpoint stiffness of the limb was estimated for each object curvature. With increasing curvature, the endpoint stiffness increased mainly parallel to the object surface and to a lesser extent in the orthogonal direction. Therefore, the orientation of the stiffness ellipses did not orient to the direction of instability. Simulations showed that the observed stiffness geometries and their pattern of change with instability are the result of a tradeoff between maximizing the mechanical stability and minimizing the destabilizing effects of SDN. Therefore, it would have been suboptimal to align the stiffness ellipse in the direction of instability. The time course of the changes in stiffness geometry suggests that modulation takes place both within and across trials. Our results show that an increase in stiffness relative to the increase in noise can be sufficient to reduce kinematic variability, thereby allowing stiffness control to improve stability in natural tasks.

Hydrodynamic entrapment of bacteria swimming near a solid surface.

The near-surface motility of bacteria is important in the initial formation of biofilms and in many biomedical applications. The swimming motion of Escherichia coli near a solid surface is investigated both numerically and experimentally. A boundary element method is used to predict the hydrodynamic entrapment of E. coli bacteria, their trajectories, and the minimum separation of the cell from the surface. The numerical results show the existence of a stable swimming distance from the boundary that depends only on the shape of the cell body and the flagellum. The experimental validation of the numerical approach allows one to use the numerical method as a predictive tool to estimate with reasonable accuracy the near-wall motility of swimming bacteria of known geometry. The analysis of the numerical database demonstrated the existence of a correlation between the radius of curvature of the near-wall circular trajectory and the separation gap. Such correlation allows an indirect estimation of either of the two quantities by a direct measure of the other without prior knowledge of the cell geometry. This result may prove extremely important in those biomedical and technical applications in which the near-wall behavior of bacteria is of fundamental importance.