Transverse Curvature Research Articles

Limitations of curvature-induced rigidity: How a curved strip buckles under gravity

The preference of thin flat sheets to bend rather than stretch, combined with results from geometry, mean that changes in a thin sheet's Gaussian curvature are prohibitively expensive. As a result, an imposed curvature in one principal direction inhibits bending in the other: the so-called curvature-induced rigidity. Here, we study the buckling behaviour of a rectangular strip of finite thickness held horizontally in a gravitational field, but with a transverse curvature imposed at one end. The finite thickness of the sheet limits the efficacy of curvature-induced rigidity in two ways: i) finite bending stiffness acts to “uncurve” the sheet, even if this costs some stretching energy, and ii) for sufficiently long strips, finite weight deforms the strip downwards, releasing some of its gravitational potential energy. We find the critical imposed curvature required to prevent buckling (or, equivalently, to rigidify the strip), determining the dependence on geometrical and constitutive parameters, as well as describing the buckled shape of the strip well beyond the threshold for buckling. In doing so, we quantify the intuitive understanding of curvature-induced rigidity that we gain from curving the crust of a slice of pizza to prevent it from drooping downwards as we eat.

The local intrinsic curvature of wavefronts allows to detect optical vortices.

We describe a method for effectively distinguishing the radiation endowed with optical angular momentum, also known as optical vortex, from ordinary light. We show that by detecting the inversion of the transverse intrinsic curvature sign (ITICS) an optical vortex can be locally recognized. The method is effective under conditions of huge importance for the exploitation of optical vortices, such as the far field of the source and access to a small fraction of the wavefront only. The validity of the method has been verified with table-top experiments with visible light, and the results show that a measurement performed over a transverse distance smaller than 4% of the beam diameter distinguishes a vortex from a Gaussian beam with a significance of 93.4%. New perspectives are considered for the characterization of vortices, with potential impact on the detection of extra-terrestrial radiation as well as on broadcast communication techniques.

Parameters influence of windshield curvature on pedestrian head injuries based on reverse engineering

With the development of the automobile industry, the problems of traffic accidents have attracted more and more attention, and many countries are also attaching importance to pedestrian protection. In the collision process of vehicle and pedestrian, the head of pedestrian is very easy to collide with the engine cover and windshield of the car, which causes fatal damage. In this paper, the curvature of four kinds of automobile front windshields is studied by reverse engineering and simulation experiments. By using reverse engineering software to dispose the scanned point cloud data, a smooth surface is derived, and finite element software is used to establish the model of the pedestrian head impactor hitting the windscreen of the car, and finally the simulation processing is carried out. Simulation results show that Head Injury Criteria is positively correlated with the transverse curvature of the front windshield and negatively correlated with the longitudinal curvature.

A general model to predict torsion and curvature increments of tensile armors in unbonded flexible pipes

An analytical model is proposed to investigate the local torsion and bending behavior of tensile armors in unbonded flexible pipes. The general expressions of torsion and curvature increments, including the effects of axial strain and twisting rotation of tendon cross-section, are firstly derived based on the generalized Frenet–Serret equations. Then the expressions corresponding to the strained helix assumption are obtained, which are further simplified by ignoring the twisting rotation. Afterwards, explicit expressions are given for axisymmetric case and tendon stick and slip states when bending is included. The developed model is finally verified with a finite element simulation. The results show that the model prediction of normal curvature increment is in good agreement with the numerical solution while the changes in torsion and transverse curvature cannot be obtained accurately through simple analytical formulas. Several earlier models are also discussed briefly and are demonstrated to be special cases of the present general model.

Introducing and Prospective Efficacy Comparison of an Innovative and Affordable Technique for the Treatment of Distal Radius Fractures

BackgroundThere are different treatments as well as controversies surrounding the adequate treatment for Distal Radius Fractures (DRF). In the absence of enough evidence[HYPHEN]base data regarding clinical effectiveness of available treatments, cost should be considered as an essential factor in selecting the surgical technique for DRF treatment. The goal of this study is introducing an improved and modified pin[HYPHEN]and[HYPHEN]plaster (MP&P) technique as an affordable alternative for treatment of DRF. This study also assesses and compares the outcomes of DRF treatment by using the introduced method versus external fixation (EF) technique. MethodsIn this clinical cohort study, 98 patients presenting with closed DRF Types III or IV, randomly were classified into two modified P&P (50 patients) and EF (48 patients) groups and assessed for functional, clinical, radiographic and overall outcome at the time, 2, 10 and 22 months after surgery. They were also followed[HYPHEN]up for up to 3 years to determine the rate of complications. ResultsEighty one percent of EF and 86% of MP&P group were female. The average ages in the EF and MP&P groups were 44.9 ± 12.4 and 46.1 ± 5.4, respectively. Around 70% of the patients in each group had a Type III fracture, and 30% had Type IV. The rate of complications was higher among EF group patients (seven major and seven minor complications) compared to the MP&P (only 4 minor complications), however the difference between two groups regarding the complications and treatment outcome were insignificant, except in extension ROM and the quick[HYPHEN]dash score (only in two and four months follow up visits) and also returning to work (only in two month follow up visit). ConclusionThis study introduces a modified P&P technique that protects the transverse palmar curvature, prevents the collapse of the distal radius, and simplifies casting, thereby obviating a full arm cast and mitigating elbow stiffness in patient outcomes. This modified technique could be considered as a more cost[HYPHEN]conscious alternative to external fixation for patients with distal radius fractures.

Bioinspired Variable Stiffness Dielectric Elastomer Actuators with Large and Tunable Load Capacity.

This article proposes a bioinspired variable stiffness dielectric elastomer actuator (VSDEA) that is inspired by the leaf habit of monocots. The VSDEA is a fully flexible strip with a curved cross section and a tip dielectric elastomer minimum energy structure (DEMES). An arc fixture is used to clamp the strip that imitates the connection mode between the leaf and the cylindrical stem of the monocot. When applying voltage on the tip DEMES, the transverse curvature of the strip is changed, and then, the bending stiffness of the VSDEA can be tuned. Effects of applied voltage and important design parameters on the bending behavior of the VSDEA are experimentally studied in detail. The results show that the bending stiffness of the VSDEA approximately decreases linearly with the increase of applied voltage, which is very advantageous for stiffness control. The load capacity of the VSDEA is enhanced due to the bioinspired clamping mechanism and can be tuned by the applied voltage. It can also be found from the tested VSDEA prototypes that, when the applied voltage ranges from 0 V to 5.6 kV, the maximum relative stiffness and critical load changes reach about 71.8% and 75.6%, respectively. The maximum stiffness and critical load are, respectively, 157.8 N/m and 889.9 mN, which are two orders greater in magnitude than general DEMESs; as a result, this VSDEA can bear a payload 139 times its weight. It demonstrates that the bioinspired VSDEA can be useful for soft robots, vibration control, and morphing applications.

The Lanczos Equation on Light-Like Hypersurfaces in a Cosmologically Viable Class of Kinetic Gravity Braiding Theories

We discuss junction conditions across null hypersurfaces in a class of scalar–tensor gravity theories (i) with second-order dynamics, (ii) obeying the recent constraints imposed by gravitational wave propagation, and (iii) allowing for a cosmologically viable evolution. These requirements select kinetic gravity braiding models with linear kinetic term dependence and scalar field-dependent coupling to curvature. We explore a pseudo-orthonormal tetrad and its allowed gauge fixing with one null vector standing as the normal and the other being transversal to the hypersurface. We derive a generalization of the Lanczos equation in a 2 + 1 decomposed form, relating the energy density, current, and isotropic pressure of a distributional source to the jumps in the transverse curvature and transverse derivative of the scalar. Additionally, we discuss a scalar junction condition and its implications for the distributional source.

Properties of Twofold Tape Loops: The Influence of the Subtended Angle

Tape springs are thin-walled structures with zero longitudinal and constant transverse curvature. Folding them twice and connecting both ends creates a tape loop which acts as a linear guide. At this time, there is insufficient understanding of the influence of the tape spring's cross section on its behavior. This study investigates the influence of the subtended angle on the tape spring's behavior, especially the energy distribution and the fold radius. First, some key aspects in the design of a twofold tape loop are discussed. By performing a curvature analysis of this folded geometry, the different regions within a tape spring are identified. This information is used to identify the influence of the subtended angle on the geometry and energy state of the tape loop. The fold radius and fold angle are determined by analyzing the geometry of the fold region. The analysis showed that the energy within the transition regions cannot be neglected. The energy within these regions and the length of the transition regions both increase with the subtended angle. It is also shown that the fold radius is not constant when the subtended angle is small. The subtended angle should be above 100 deg to ensure a constant radius.

Hybrid inversion method and sensitivity analysis of inherent deformations of welded joints

In order to efficiently predict the welding deformation of large and complex welded structures based on the inherent deformation method, it is necessary to obtain the inherent deformations of each weld seam beforehand. In this paper, a new method was proposed to inverse inherent deformations by combining inherent deformation method and complex method. The validity of the proposed hybrid inversion method was proved by the comparison with the results of thermal-elastic-plastic (TEP) model the effectiveness of which had been demonstrated by the welding deformation and residual stress obtained from the butt-welded experiment. And the independence of the method on initial value is verified by inversion results using different initial complex shapes. Finally, the sensitivity analysis of inherent deformations was also carried out, and the analysis result shows that longitudinal shrinkage, transverse shrinkage and transverse curvature have a more significant effect on calculation accuracy than longitudinal curvature for the present welded plates.

Research on continuous roll forming for manufacturing 3D curved surface parts with variable transverse curvatures

A flexible and precise forming technology for die-less, small-lot manufacture of 3D curved surface sheet metal parts is urgently required. Continuous roll forming (CRF) is a novel technique for generation of 3D curved surface rolls bending by two flexible rolls. In CRF process, the two flexible rolls are positioned vertically to form curved configurations and non-uniform roll gap. Then 3D curved surface parts with different transverse and longitudinal curvatures can be obtained by adjusting the configurations of the flexible rolls and the distribution of the roll gap. In this study, the CRF process was used to manufacture 3D curved surface part with variable transverse curvature instead of constant transverse curvature. The forming mechanism of CRF was proposed, the method to design configurations of the upper and lower flexible rolls was presented, and its validity was verified by simulation and experiment.

Shake table test on transverse steel damper seismic system for long span cable-stayed bridges

In current transverse seismic design of long span cable-stayed bridges, the conventional transverse fixed system (TFS) is usually adopted. This strategy inevitably increases seismic demands of substructures and towers, leading to high seismic-induced damage risks to the bridges. To address this issue, the authors recently developed a novel Transverse Steel Damper (TSD) and correspondingly proposed an innovative TSD seismic system (TSDSS), in which the TSDs were placed at deck-tower and/or deck-bent connections. To further verify the reliability and seismic isolation efficiency of TSDSS for long span cable-stayed bridges under near- and far-fault ground motions, a series of experiments on a 1/35-scale model of a kilometer-span cable-stayed bridge were conducted on a four-shake-table testing system. Experimental results indicate that (1) compared with the conventional TFS, the TSDSS can reduce transverse displacement and curvature demands along bent/tower columns, meanwhile limiting displacements at deck-bent/tower connections to an acceptable level in engineering practice. (2) The sensitivity of TSDSS to ground motions is obviously lower than that of the conventional TFS. The isolation efficiency of TSDSS is robust regardless under near- or far-fault ground motions; (3) Increasing the yield strength of TSDs can decrease the relative displacements at deck-bent/tower connections. In general, the TSDSS is experimentally validated to be a capable and reliable strategy for the seismic design of long span cable-stayed bridges. Additionally, the shake-table test is simulated using a finite element model, which provides good agreements with the test results.

Helical bistable composite slit tubes

Bistability in doubly curved and twisted (helical) composite slit tubes is investigated for the first time. This work establishes a natural extension in this area which has been focused on straight and until more recently, doubly curved (toroidal) tubes with positive Gaussian curvature. The model developed introduces longitudinal and transverse curvature, and twist into strips of laminated composite material. The composite is engineered to be bistable and the second stable state determined via strain energy minimisation using the Rayleigh-Ritz method. The strain energy is formulated as a function of curvature strains, longitudinal stretching and a variable middle ply fibre angle of the laminate. The second stable state forms a compact and untwisted cylindrical coil with the latter engineered by tailoring the middle ply fibre angle. A new manufacturing process capable of producing helically curved tubes using glass-fibre/polypropylene-matrix composite is presented to verify the hypothesis of this work. An untwisted coil enables the efficient stowage and deployment of new forms of bistable composite tube which adhere to similar form factors as straight and toroidal ones. By embedding electrical conductors, helical bistable composites enable new lightweight, compact and multifunctional structures for communication and sensing applications.

TVC effects on flow separation on slender cylinders

Occurrence of flow separation within the boundary-layer is primarily attributed to the growth of adverse pres-sure gradient within the boundary-layer. Such a separating boundary-layer can, however, be made to stay attached to the bounding surface due to various remedies where the surface transverse curvature (TVC) is one of them while the body contour is another. Assistive role of the surface transverse curvature is utilized in delaying the boundary-layer separation in a retarded flow past the slender bodies by assuming different body configurations. Axially-symmetric bodies of revolution of different shapes having a varying cross section in x, following the power-law form, have been considered in this study. It is shown that the point of separation is strongly dependent upon the surface curvature parameter k and the body-shape index n, which in fact control the flow separation. This fact ensures that an increase in the surface curvature parameter k and the body-shape index n leads to an increase in the wall shear stress which consequently delays the flow separation. Significant delay in flow separation is observed on cylinders having sufficiently large transverse curvature. Percent increase in the separation length corresponding to various values of the curvature parameter and the body-shape index has been calculated and reported in the form of Tables.

Numerical solutions of free convection flow of nanofluids along a radiating sinusoidal wavy surface

In this article, our interest is to investigate the free convection boundary-layer flow of a nanofluid past a sinusoidal semi-infinite vertical surface in the non-absorbing medium. The contribution of surface radiative heat flux is employed in the boundary conditions with the help of Stefan-Boltzmann law. Governing equations are transformed into a non-conserved dimensionless system and integrated numerically by means of an implicit finite difference scheme. The accuracy of numerical method is assessed by a comparison of the present results with the earlier published work and it is found that there exists a favorable agreement between the two. Our problem is subject to the influence of a set of parameters, which appear due to the presence of surface radiation, nanoparticles, and transverse curvature of vertical wall. It is noticed that radiative length parameter λ and surface radiation parameter R contribute in a reduction of local skin friction coefficient and local Nusselt number.

Global stability analysis of axisymmetric boundary layer over a circular cylinder

This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inflow boundary. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier–Stokes (LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi’s iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes is negative, and hence, the flow is temporally stable. The spatial structure of the eigenmodes shows that the disturbance amplitudes grow in size and magnitude while they are moving towards downstream. The global modes of axisymmetric boundary layer are more stable than that of 2D flat-plate boundary layer at low Reynolds number. However, at higher Reynolds number they approach 2D flat-plate boundary layer. Thus, the damping effect of transverse curvature is significant at low Reynolds number. The wave-like nature of the disturbance amplitudes is found in the streamwise direction for the least stable eigenmodes.

Investigation of human hair using ToF-SIMS: From structural analysis to the identification of cosmetic residues

Analysis of human hair using time-of-flight secondary ion mass spectrometry (ToF-SIMS) is particularly challenging because of the high transverse curvature of the hair fiber and the presence of the cuticle scales on its surface, which hampers mass spectrometric imaging. Delayed extraction of the secondary ions combined with a simple planar sectioning of the hair has been used to limit the image artifacts encountered with hair samples, giving access to the desired level of information. In this study, the entire structure of human hair was characterized using ToF-SIMS with longitudinal sectioning. Thus, the authors have examined the inner structure of the hair fiber and obtained chemical information from various regions of the hair. Atomic force microscopy (AFM) was also used to characterize the variation in surface properties that are dependent on the presence of different cosmetic residues on the hair surface. By subjecting a hair with an unknown cosmetic residue to AFM observation combined with principal component analysis of a ToF-SIMS image, the authors were able to identify the type of cosmetic present and to correlate its spectrometric signature with that of the original hair styling product. These results demonstrate the potential of their methodology for the investigation of human hair specimens and for the development of hair styling products in the cosmetic industry.

Natural Convection and Separation Points of a Non-Newtonian Fluid Along a Rotating Round-Nosed Body

The purpose of the present study is to present a numerical solution for the natural-convection flow of Ostwald/de Waele-type power-law non-Newtonian fluid along the surface of a rotating axisymmetric round-nosed body. For computational purpose, a rotating hemisphere is used as the case study to examine the effects of transverse curvature on heat transfer mechanism. The numerical scheme is applied after converting the dimensionless system of equations into primitive variable formulations. Implicit finite difference method is used to integrate the equations numerically. The numerical simulations performed are valid for shear-thickening fluids with a wide range of Prandtl numbers [i.e., ]. A detailed discussion is provided to understand the effects of buoyant forces and power-law exponent on the rate of heat transfer and skin-friction coefficient. A comparison of the present numerical results for different values of the buoyancy ratio parameter with other published data is shown in graphical form. The flow separation occurs when a portion of the boundary layer closest to the wall or leading edge reverses in flow direction. It is observed from our results that an increase in the power-law index and Prandtl number leads to an increase in the friction factor, as well as the rate of heat transfer.

Highly-resolved LES of turbulent convective flow along a PWR rod bundle

A detailed numerical analysis of the turbulent convective flow along the heated rods of an idealized Pressurized Water Reactor (PWR) sub-channel is investigated using the CFD code TransAT. The flow is pretty much similar to circular pipe flow. Turbulent effects are predicted using highly-resolved Large-Eddy Simulation (LES) with a grid resolution of up to 6 million cells, resolving the viscous-affected layer. The sub-grid scale (SGS) viscosity produced by the model is indeed found to be of marginal effect for the grid and Reynolds number employed. Only first-order turbulence statistics are presented here. The results are discussed in detail, in particular key features specific to rod bundles, including low-Re effects in the narrow gap zone and the strong secondary flow motion, which is shown to exceed the turbulence counterpart (through the shear stress) near the wall. The secondary-flow motion induced by the mean flow is shown to be responsible for a large portion of the wall-to-flow heat transfer. The comparison of the LES results with existing DNS of pipe flow shows a very good agreement as to first-order statistics; higher-order statistics (including energy budgets) of the fluctuating fields have not been explored. A data basis has been generated for turbulence model comparison. Like in turbulent pipe flow, a physical explanation for the observed differences can be routed in the transverse curvature effects of the bundle geometry.

Curved Bistable Composite Slit Tubes with Positive Gaussian Curvature

An investigation into the bistability of positively curved laminated composite slit tubes is presented, establishing a natural extension in this area that has previously been focused on straight tubes. Curved slit tubes are modeled as the surface segments of a torus. The design space is explored through a parametric study to investigate the effect on the second stable state, representing a small coil. This includes the effects of longitudinal curvature, cross-section subtending angles, nonuniform transverse curvature, and spatially varying laminate properties. The second equilibrium state is determined through strain energy minimization using the Rayleigh–Ritz method. To verify the model, samples are manufactured from glass-fiber braid and polypropylene resin. This investigation finds 1) the initial curvature along the length of the tube has little effect on coil radius, however, the coil has a distinct barrel shape; 2) highly enclosed and 3) highly curved cross-sections result in higher edge strains of the second equilibrium, enabling identification of practical bistable tubes; and 4) conversely, the greater the initial curvature along the length of the tube, the lower the second equilibrium strain.

Numerical investigations of CMC nozzle structures: constitutive modelling and finite element technology

AbstractThis work deals with the development of numerical tools predicting the lifetime of nozzle structures made of ceramic matrix composites (CMC). These materials are favorable for thermostructural components due to their excellent specific mechanical properties, high thermal conductivity and thermoshock resistance. The anisotropic constitutive behaviour of the CMC is reflected by a continuum model which is micro‐mechanically motivated. The model is based on structural tensors representing different fibre orientations. Furthermore, the thin structure of the nozzle requires an appropriate finite element technology in order to overcome locking phenomena. For this reason, a solid‐shell formulation with reduced integration is utilized, for which the implementation of the fibre orientation is crucial. The enhanced assumed strain (EAS) concept is used to avoid volumetric locking as well as Poisson thickness locking. The transverse shear and curvature thickness locking are cured by the assumed natural strain (ANS) concept. Using reduced integration together with hourglass stabilization leads to high computational efficiency. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)