Analysis of Transverse Shear Strains in Pre-Twisted Thick Beams using Variational Asymptotic Method

The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam reference curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

Three-Dimensional Propagation of the Transmitted Shock Wave in a Square Cross-Sectional Chamber

An investigation into the three-dimensional propagation of the transmitted shock wave in a square cross-section chamber was described in this paper, and the work was carried out numerically by solving the Euler equations with a dispersion-controlled scheme. Computational images were constructed from the density distribution of the transmitted shock wave discharging from the open end of the square shock tube and compared directly with holographic interferograms available for CFD validation. Two cases of the transmitted shock wave propagating at different Mach numbers in the same geometry were simulated. A special shock reflection system near the corner of the square cross-section chamber was observed, consisting of four shock waves: the transmitted shock wave, two reflection shock waves and a Mach stem. A contact surface may appear in the four-shock system when the transmitted shock wave becomes stronger. Both the secondary shock wave and the primary vortex loop are three-dimensional in the present case due to the non-uniform flow expansion behind the transmitted shock.

Cross-sectional structure of tetrahedral amorphous carbon thin films

A cross-sectional transmission electron microscope study of the low density layers at the surface and at the substrate-film interface of tetrahedral amorphous carbon (ta-C) films grown on (001) silicon substrates is presented. Spatially resolved electron energy loss spectroscopy is used to determine the bonding and composition of a tetrahedral amorphous carbon film with nanometre spatial resolution. For a ta-C film grown with a substrate bias of -300 V, an interfacial region approximately 5 nm wide is present in which the carbon is sp2 bonded and is mixed with silicon and oxygen from the substrate. An sp2 bonded layer observed at the surface of the film is 1.3 ± 0.3 nm thick and contains no detectable impurities. It is argued that the sp2 bonded surface layer is intrinsic to the growth process, but that the sp2 bonding in the interfacial layer at the substrate may be related to the presence of oxygen from the substrate.

Factors associated with chronic pain in patients with bipolar depression: a cross-sectional study

Background: While pain is frequently associated with unipolar depression, few studies have investigated the link between pain and bipolar depression. In the present study we estimated the prevalence and characteristics of pain among patients with bipolar depression treated by psychiatrists in their regular clinical practice. The study was designed to identify factors associated with the manifestation of pain in these patients.- Methods:Patients diagnosed with bipolar disorder (n=121) were selected to participate in a cross-sectional study in which DSM-IV-TR criteria were employed to identify depressive episodes. The patients were asked to describe any pain experienced during the study, and in the 6 weeks beforehand, by means of a Visual Analogical Scale (VAS).- Results: Over half of the bipolar depressed patients (51.2%, 95% CI: 41.9%–60.6%), and 2/3 of the female experienced concomitant pain. The pain was of moderate to severe intensity and prolonged duration, and it occurred at multiple sites, significantly limiting the patient’s everyday activities. The most important factors associated with the presence of pain were older age, sleep disorders and delayed diagnosis of bipolar disorder.- Conclusions: Chronic pain is common in bipolar depressed patients, and it is related to sleep disorders and delayed diagnosis of their disorder. More attention should be paid to study the presence of pain in bipolar depressed patients, in order to achieve more accurate diagnoses and to provide better treatment options.

Topology of toroidal helical fields in non-circular cross-sectional tokamaks

The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade (HT-7U) when the equilibrium field with a monotonic q-profile is perturbed by a helical magnetic field. We find that a single mode (m, n) helical perturbation can cause the formation of islands on rational surfaces with q = m/n and q = (m +/- 1, +/- 2, +/- 3,...)/n due to the toroidicity and plasma shape (i.e. elongation and triangularity), while there are many undestroyed magnetic surfaces called Kolmogorov-Arnold-Moser (KAM) barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field B-r(r) and the toroidal magnetic field amplitude B(phi)0 is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.