Fiber Stabilization of Bent Cylinders, With an Application to Intervertebral Disks

1983 ◽  
Vol 105 (3) ◽  
pp. 294-295 ◽  
Author(s):  
K. E. Schreiner
Keyword(s):  
Cross Section ◽  
Pure Bending ◽  
Cross Sectional ◽  
Intervertebral Disks ◽  
Reinforcing Fibers ◽  
Sectional Plane ◽  
The Cross

Fibers cannot carry compression, and reinforcing fibers in a cylinder can only carry load if they are kept taut by the deformations of the cylinder. In the present study it is found that in pure bending, deformations that change the pitch, i.e., the angle between the fibers and the cross-sectional plane, towards 30 deg will slacken the fibers. With an initial pitch different than 30 deg, fibers in one half of the cross section will then be slackened by bending, and this half of the cylinder becomes unstable. Applied to the mechanics of the intervertebral disks, this may help explain mechanisms leading to nucleus prolaps.

scholarly journals A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory

2008 ◽  
Vol 15 (2) ◽  
pp. 179-192 ◽  
Author(s):  
Jiao Sujuan ◽  
Li Jun ◽  
Hua Hongxing ◽  
Shen Rongying
Keyword(s):  
Cross Section ◽  
Spectral Element ◽  
Higher Order ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Coupled Equations ◽  
Aspect Ratios ◽  
Sectional Plane ◽  
The Cross ◽  
Element Matrix

The spectral element matrix is derived for a straight and uniform beam element having an arbitrary cross-section. The general higher-order beam theory is used, which accurately accounts for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the cross-sectional plane. Two coupled equations of motion are derived by use of Hamilton's principle along with the full three-dimensional constitutive relations. The theoretical expressions of the spectral element matrix are formulated from the exact solutions of the coupled governing equations. The developed spectral element matrix is directly applied to calculate the exact natural frequencies and mode shapes of the illustrative examples. Numerical results of the thick isotropic beams with rectangular and elliptical cross-sections are presented for a wide variety of cross-section aspect ratios.

scholarly journals Effect of inertial lift on a spherical particle suspended in flow through a curved duct

2019 ◽  
Vol 875 ◽  
pp. 1-43 ◽  
Author(s):  
Brendan Harding ◽  
Yvonne M. Stokes ◽  
Andrea L. Bertozzi
Keyword(s):  
Reynolds Number ◽  
Spherical Particle ◽  
Cross Section ◽  
Bend Radius ◽  
Cross Sectional ◽  
Particle Reynolds Number ◽  
Curved Duct ◽  
Sectional Plane ◽  
Flow Through ◽  
The Cross

We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable equilibria within the cross-sectional plane towards which particles migrate. The Navier–Stokes equations determine the hydrodynamic forces acting on a particle. A leading-order model of the forces within the cross-sectional plane is obtained through the use of a rotating coordinate system and a perturbation expansion in the particle Reynolds number of the disturbance flow. We predict the behaviour of neutrally buoyant particles at low flow rates and examine the variation in focusing position with respect to particle size and bend radius, independent of the flow rate. In this regime, the lateral focusing position of particles approximately collapses with respect to a dimensionless parameter dependent on three length scales: specifically, the particle radius, duct height and duct bend radius. Additionally, a trapezoidal-shaped cross-section is considered in order to demonstrate how changes in the cross-section design influence the dynamics of particles.

On Saint-Venant’s Problem for an Inhomogeneous, Anisotropic Cylinder—Part II: Cross-Sectional Properties

2000 ◽  
Vol 68 (3) ◽  
pp. 382-391 ◽  
Author(s):  
J. B. Kosmatka ◽  
H. C. Lin ◽  
S. B. Dong
Keyword(s):  
Cross Section ◽  
Symmetry Plane ◽  
Material Symmetry ◽  
Shear Center ◽  
Cross Sectional ◽  
Mean Values ◽  
Anisotropic Cylinder ◽  
Sectional Plane ◽  
Weighted Integrals ◽  
The Cross

Cross-sectional properties of a prismatic inhomogeneous, anisotropic cylinder are determined from Saint-Venant solutions for extension-bending-torsion and flexure, whose method of construction was presented in a previous paper. The coupling of extensional, bending, and twisting deformations due to anisotropy and inhomogeneity leads to some very interesting features. Herein, it is shown that for an inhomogeneous, anisotropic cylinder whose cross-sectional plane is not a material symmetry plane, distinct modulus-weighted and compliance-weighted centroids and distinct principal bending axes are possible. A line of extension-bending centers is given on which an axial force causes extension and bending only but no twist. Two shear centers are given, one using the Griffith-Taylor definition that ignores cross-sectional warpages and the other by stipulating a zero mean rotation over the cross section. The center of twist is discussed, and this property depends on root end fixity conditions that are prescribed in terms of their mean values based on integrals over the cross section rather than by a pointwise specification. While these shear center and center of twist definitions have some rational bases, it is recognized that other definitions are possible, for example those based on modulus or compliance-weighted integrals. Two examples, an angle and a channel, both composed of a two-layer ±30 deg angle-ply composite material, illustrate the procedures for determining these cross-sectional properties.

scholarly journals The influence of secondary flow in a two-phase gas-solid system in straight channels with a non-circular cross-section

2016 ◽  
Vol 20 (suppl. 5) ◽  
pp. 1419-1434
Author(s):  
Sasa Milanovic ◽  
Milos Jovanovic ◽  
Boban Nikolic ◽  
Vladislav Blagojevic
Keyword(s):  
Turbulent Flow ◽  
Secondary Flow ◽  
Cross Section ◽  
Circular Cross Section ◽  
Channel Cross Section ◽  
Two Phase ◽  
Cross Sectional ◽  
Specific Flow ◽  
Sectional Plane ◽  
The Cross

The paper considers two-phase gas-solid turbulent flow of pneumatic transport in straight horizontal channels with a non-circular cross-section. During turbulent flow, a specific flow phenomenon, known as secondary flow, occurs in these channels in the cross-sectional plane. The existence of strong temperature gradients in the cross-sectional plane of the channel or the cases of curved channels result in the appearance of the secondary flow of the first kind. However, in straight channels with a non-circular cross-section, in the developed turbulent flow mode, a secondary flow, known as Prandtl?s secondary flow of the second kind, is induced. The paper presents a numerical simulation of a developed two-phase turbulent flow by using the PHOENICS 3.3.1 software package. Reynolds stress model was used to model the turbulence. The paper provides the data on the changes in turbulent stresses in the channel cross-section as well as the velocities of solid particles transported along the channel.

Automated Diagonal Slice and View Solution for 3D Device Structure Analysis

2018 ◽  
Author(s):  
Sang Hoon Lee ◽  
Jeff Blackwood ◽  
Stacey Stone ◽  
Michael Schmidt ◽  
Mark Williamson ◽  
...  
Keyword(s):  
Cross Section ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Image Data ◽  
Planar Surface ◽  
Device Structure ◽  
Cross Sectional ◽  
Device Structures ◽  
The Cross ◽  
Planar Analysis

Abstract The cross-sectional and planar analysis of current generation 3D device structures can be analyzed using a single Focused Ion Beam (FIB) mill. This is achieved using a diagonal milling technique that exposes a multilayer planar surface as well as the cross-section. this provides image data allowing for an efficient method to monitor the fabrication process and find device design errors. This process saves tremendous sample-to-data time, decreasing it from days to hours while still providing precise defect and structure data.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

The Cross Section of Expected Returns with MIDAS Betas

2011 ◽  
Vol 47 (1) ◽  
pp. 115-135 ◽  
Author(s):  
Mariano González ◽  
Juan Nave ◽  
Gonzalo Rubio
Keyword(s):  
Cross Section ◽  
Risk Premium ◽  
Market Risk ◽  
Ordinary Least Squares ◽  
Mixed Data ◽  
Expected Returns ◽  
Data Sampling ◽  
Cross Sectional ◽  
Market Risk Premium ◽  
The Cross

AbstractThis paper explores the cross-sectional variation of expected returns for a large cross section of industry and size/book-to-market portfolios. We employ mixed data sampling (MIDAS) to estimate a portfolio’s conditional beta with the market and with alternative risk factors and innovations to well-known macroeconomic variables. The market risk premium is positive and significant, and the result is robust to alternative asset pricing specifications and model misspecification. However, the traditional 2-pass ordinary least squares (OLS) cross-sectional regressions produce an estimate of the market risk premium that is negative, and significantly different from 0. Using alternative procedures, we compare both beta estimators. We conclude that beta estimates under MIDAS present lower mean absolute forecasting errors and generate better out-of-sample performance of the optimized portfolios relative to OLS betas.

An Analytical Method of Analyzing the Heat Conduction for the Unequal Cross-Section Straight Fin

2013 ◽  
Vol 365-366 ◽  
pp. 1211-1216
Author(s):  
Fan Zhang ◽  
Peng Yun Song
Keyword(s):  
Heat Conduction ◽  
Cross Section ◽  
Analytical Method ◽  
Thermal Analyses ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
Calculation Results ◽  
The Cross ◽  
Analytical Expressions

The cross-section area of straight fin is often considered to be equal in the thermal analyses of straight fin, but sometimes it is unequalin actual situation. Taking a straight fin with two unequal cross-sectional areas as an example,an analytical method of heat conduction for unequal section straight fin is presented. The analytical expressions of temperature field and heat dissipating capacity about the fin,which has a smaller cross-section area near the fin base and a larger one, is obtained respectively. The calculation results of the unequal cross-section are fully consistent with the equal area one, so the method is proved right. The results show that the larger the cross section areanear the base,the better is the heat transfer, and the temperature at the base with larger cross-section area is lower than that with smaller cross-section area when the amount of heat is fixed.

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