Rectangular Segments Research Articles

Nonlinear finite element analysis of mine roadway arch support systems

A total Lagrangian, material-nonlinear finite element analysis of a steel arch model, developed to investigate the strength and behavior of mine roadway arch support systems from H-shaped steel sections, is presented. The beam-column (cubic-linear) element having six degrees-of-freedom is used in the simulation and the H-section is idealised by three rectangular segments. A 21 point numerical integration scheme is suggested to calculate the tangent stiffness matrix of the element. The material behavior is assumed to be trilinear and accounts for strain hardening and elastic unloading effects. The algorithm for nonlinear stress analysis safeguards against possible deviation from the stress-strain path of the material. The analysis is carried out by means of the Newton-Raphson method with a new, semi-empirical scheme devised to automate the loading to the peak point. To verify the model, predictions of arch strength are compared with experimental results from the present authors' previous work conducted by physical modelling. These were found to be in very good agreement.

Eddy current transients and forces in cryostat walls of superconducting solenoids

In a quenching superconducting magnet the decaying field induces currents in the metallic walls of its cryostat. The associated Lorentz forces stress the walls and cryogenic suspensions-an important issue with respect to magnet safety. Two methods for eddy current and force calculations in thin walls in the low dB/dt limit are presented for solenoidal magnets in concentric cylindrical walls. Elimination of circumferential induced currents by multiple azimuthal intersection into a number of insulated rectangular segments destroys rotational symmetry and results in a truly three-dimensional transient eddy current problem. For narrow segments a simple second-order differential equation for the eddy-current density is derived. A reference case is compared to results obtained with the commercial FEM-code CARMEN. For a large 4 T magnet, the currents, forces, and resulting mechanical displacements are given as an example. >

Flow of a laminar liquid film down a vertical surface

A theory of laminar film flow-down of an arbitrary width is presented taking into account the conditions occurring at the film edges. Using solutions of the minimum energy equations the film shape is described. The shape consists of a central rectangular segment and two side segments with a curved surface. Conditions are determined under which the film of minimum thickness is formed. Dependences determining linear wetting density (specific wetting rate) and mean liquid velocity in the minimum film of a given width as well as simplified relations for infinitely wide film are presented. Numerical calculations in the range 10 −3 to 4 ×10 4 mm −5 of the parameter characterizing the liquid and for contact angle ranging from 5° to 90° have been performed. Results of calculations are presented on graphs. For films much wider than the minimum rivulet the results of simplified calculations (infinite width) differ insignificantly from exact calculations.

Vibrational spectra of monolayer islands on single crystal faces. Island size and shape effects on infrared frequencies, intensities and bandwidths

A method for theoretical analysis spectra of rectangular segments (islands) of two-dimensional ordered overlayers of adsorbed species has been proposed. The simple formulae for frequencies, absorption coefficients and bandwidths as functions of island size and shape have been deduced. If frequencies and bandwidths of appropriate bands in infrared spectra of chemisorbed monolayers are measured simultaneously, the size and shape of the islands can be estimated.

Enamel crystal shape: history of an idea.

The purpose of this paper is to review evidence which casts doubt on the interpretation universally applied to hexagonal images seen in sectioned enamel. The evidence is based on two possible models to explain the hexagonal profiles seen in mammalian enamel with transmission electron microscopy. The "hexagonal ribbon" model proposes that hexagonal profiles are true cross-sections of elongated hexagonal ribbons. The "rectangular ribbon" model proposes that hexagonal profiles are caused by three-dimensional segments that are parallelepipeds contained in the Epon section. Since shadow projections of such rectangular segments give angles that are inconsistent with the hexagonal unit cell, a model based on ribbons with rhomboidal cut ends and angles of 60 and 120° is proposed. The "rhomboidal ribbon" model projects shadows with angles that are predicted by the unit cell. It is suggested that segments of such crystallites in section project as opaque hexagons on the imaging plane in routine transmission electron microscopy. Morphological observations on crystallites in sections - together with predictions from the hexagonal, rectangular, and rhomboidal ribbon models - indicate that crystallites in rat incisor enamel are flat ribbons with rhomboidal cross-sectional shape. Hexagonal images in electron micrographs of thin-sectioned enamel can result from rhomboidal-ended, parallelepiped-shaped segments of these crystallites projected and viewed as two-dimensional shadows.

Analysis of crystallite shape in rat incisor enamel.

The hydroxyapatite crystallites of mammalian enamel appear as hexagons when seen in cross-sections examined with the transmission electron microscope. Using goniometric transmission electron microscopy, stereo-pair electron micrographs and freeze-fracture replicas, two models have been proposed to explain the hexagonal crystallite profile. The "hexagonal ribbon" model proposes that hexagonal profiles are true cross-sections of elongated hexagonal ribbons. The "rectangular ribbon"model proposes that crystallite profiles are three-dimensional rectangular segments (parallelepipeds), which are contained in the Epon sections and project as opaque hexagons in routine transmission electron micrographs. Morphological observations together with predictions from models indicate that the crystallites in rat incisor enamel are flat ribbons with rectangular cross-sectional profiles. The hexagonal images seen in electron micrographs of thin sections of enamel result from viewing parallelepiped-shaped segments of these crystallites as two-dimensional shadows.

Faster Computation of Z-Matrices for Rectangular Segments in Planar Microstrip Circuits (Short Paper)

Currently available formulation of Z-matrices for rectangular segments in planar microstrip circuits involves numerical summation of the doubly infinite series in the corresponding Green's function. These computations can be accelerated considerably by using the formulation proposed here which is based on an analytical treatment of one of the summations involved.

The prominent nasal tip.

The authors associate the projection of the nasal tip to hypertrophy of the alar cartilages and, more specifically, of their medial branches. The heavy, blobby, or bulbous nose is caused by an increase of the columellar-alar angle of the alar cartilages, and bears no relationship to the cephalometric nasal index. Moreover, the bulbous nose usually has excess fatty tissue present in the tip of the nose. The projecting tip may be corrected by excising a rectangular or quadrangular segment from the medial branches of the alar cartilages, or by resecting the cupula of the alar cartilages, including a small or large segment of its medial branch, in order to obtain the desired effect, namely, to lower the tip and decrease the columellar-alar angle. The nasal index remains unchanged. If in addition, the tip of the nose is bulbous, the fatty tissue should be removed at the same time.

水深・幅ともに変化する二層水域での表面長波と界面長波

Equations for surface waves and interfacial waves and their relations in a basin with depth iscontinuities were given by Lamb, Le mehaute, Takano, and Rattray. If the length of the bay is much larger than the width, and the curvature of the bay aixs is small, it is possible to consider that the surface long waves, i.e. the tidal waves and the interfacial long waves generated in these basins can be treated as a one dimensional problem. The bay can be divided into many rectangular segments as shown in Fig. 1, and each of the divided segments corresponds to any of the model segments as shown in Fig. 2. The basic equations for the surface and the interfacial long waves in the model canals are given on the basis of Lamb and Takano's theory. The numerical computations for the surface long waves and the interfacial waves generated in a two layer basin with variation in depth and width. can be carried out by using the basic equations in the model canals.

San Fernando 地震の断層モデル

Simple dislocation fault models of the San Fernando, California, earthquake of 1971 as deduced from leveling data have been presented with emphasis on an abrupt change in dip angle of fault plane at a shallow depth, and geologic and geomorphic implications of the models have been discussed.Model-1 is a basic fault model ignoring the effects of sporadically distributed surface breaks. This model consists of two rectangular fault segments: the deeper (F1) and the shallower (F2). The geometry of F1 was fixed with the constraints that it should fit the focal mechanism and that the hypocenter should lie on F1. The geometry of F2 and the offsets on F1 and F2 were determined by trial and error. In Model-2, a subsidiary fault segment (F3) that represents the surface breaks was added in order to make displacement pattern near the surface breaks better fit.The results obtained are as follows:(1) The dip angle of F1 and F2 are 52° and 13° respectively. The dip of F2 is very low angle, so that the fault plane bends abruptly at a depth of about 2.5km.(2) The offsets on F1 and F2 are 1.5m and 5.5m respectively. The offset on F1 is notably smaller, so that no noticeable uplift appears in the San Gabriel Mountains which has been uplifted due to thrust faulting during late Cenozoic time as suggested by geological evidence. If we assume uniform offset on entire depths of fault plane, it becomes easier to avoid this contradiction. Therefore it seems likely that the deeper part of the fault had slipped seismically or possibly aseismically prior to the earthquake of 1971.(3) The geometry of fault models, together with some geological evidence, permits us to describe a probable history of structural evolution in the San Fernando Valley-San Gabriel Mountains border region: The Santa Susana fault, which is the projection of F1, had been active and thick basin deposit had been deposited on the down-thrown side of the fault until early Pleistocene time. In middle Pleistocene time, F2 was formed in, or on the base of, the basin deposit, and the Santa Susana fault became inactive. Consequently the location of surface faulting shifted several km south of the Santa Susana fault, and the up-thrown side of F2 has been uplifted and intensely deformed scince middle Pleistocene time.(4) Although the mechanism is unknown, the bending of fault plane can be explained in terms of an effect of “accretion” by the analogy of that in subduction zones. Such a bending model of fault plane may be applicable to some thrust fault systems in Japan which have very similar geologic and geomorphic settings to the San Fernando Valley-San Gabriel Mountains border region.

Design data for rectangular segment of cylindrical shell with normal loading

Rectangular segments of a cylindrical shell having simply supported edges and subjected to normal surface loading have been analysed. Stress resultants and deflections are presented in non-dimensional form for a range of shell parameters.

Computer determination of the shear center of open and closed sections

A computer program is developed for the determination of properties of open and closed section thin-walled areas of rectangular segments. A brief recapitulation of properties of plane areas including the determination of the shear center of open and multi-cellular closed sections is presented.

An ultrastructural analysis of the photoreceptors of the squid and their synaptic connections. I. Photoreceptive and non-synaptic regions of the retina.

AbstractAs part of a larger ultrastructural study on the photoreceptors of the squid,Loligo pealei, this paper reports findings on non‐synaptic regions. The cross‐sectional profiles of individual distal segments coincided in horizontal sections as far as 75 μ apart, but progressively less with greater separations. Areas of cross‐section showed a unimodal distribution skewed towards 6 μ2, the smallest areas. The distribution of ratios of villous to smooth border was unimodal and skewed with 1.0 being the most numerous and minimal ratio. This ratio tended to increase linearly with area. Cells of small cross‐section were completely surrounded by villous border of other cells and about 60° of the perimeter of any cell had microvilli on both sides of the border. Cells participated in odd or even numbers of rhabdomes, up to eight. Pentalaminar membrane junctions between microvilli of the same or neighboring cells were observed. Cytoplasmic microtubules were concentrated near villous borders. In light adaptation some ommin granules entered the photoreceptor tips, and the rhabdomes which formerly began near the surface, now began somewhat below this level. A terminal bar zone existed proximal to the rhabdomes. Here glial cytoplasm separated photoreceptors and both cells contained ommin granules. Photoreceptor somas lacked glial separation and were highly interplicated. Mitochondria were longitudinally arranged along the somal membrane. The planes of the lamellate membrane bodies, seen in the somal cytoplasm of the cells, did not exhibit a rectilinear pattern such as that displayed by the basically rectangular distal segment cross‐sections and microvillar orientations.

A Test for Transplantability of Animal Hearts

Current studies in transplantation of canine and human hearts have made it advisable to develop a method for detecting postmortem changes in hearts quickly and accurately. We use reversibility of the thermal responses of the viscoelastic properties of cardiac muscle to determine whether or not an excised heart is in a steady state. The test samples are taken from the tip of the atrial appendage and a report of cardiac muscle status may be made within 15 minutes, or before chemical signs of rigor mortis appear in the sampled organ. Methods Used in Designing the Test.— Rectangular segments of ventricles, atria, and atrial appendages were excised from in situ hearts of 17 dogs, 23 cats, and 13 rabbits anesthetized with 30 mg/kg of body weight of sodium pentobarbital. With this technique, a slit in the segment is slipped over two hooks to support it horizontally in a bath of known

A test for transplantability of animal hearts

Current studies in transplantation of canine and human hearts have made it advisable to develop a method for detecting postmortem changes in hearts quickly and accurately. We use reversibility of the thermal responses of the viscoelastic properties of cardiac muscle to determine whether or not an excised heart is in a steady state. The test samples are taken from the tip of the atrial appendage and a report of cardiac muscle status may be made within 15 minutes, or before chemical signs of rigor mortis appear in the sampled organ. <h3>Methods Used in Designing the Test.—</h3> Rectangular segments of ventricles, atria, and atrial appendages were excised from in situ hearts of 17 dogs, 23 cats, and 13 rabbits anesthetized with 30 mg/kg of body weight of sodium pentobarbital. With this technique, a slit in the segment is slipped over two hooks to support it horizontally in a bath of known

Kinetic Studies of Platelet Aggregation Induced by Adenosine Diphosphate and Its Inhibition by Chelating Agents, Guanidino Compounds, and Adenosine

SummaryThe kinetics, activation, pH dependence and inhibition of platelet aggregation induced by ADP were studied by recording the OD of stirred PRP from blood anticoagulated with acid-citrate-dextrose solution. There was a lag period between the addition of ADP and the initiation of aggregation. Addition of ADP in the absence of stirring or ionized calcium did not cause aggregation. When aggregation was subsequently initiated by stirring or the addition of CaCl2 there was no lag period. The steepest slope of the OD curve was used as the reaction velocity (V). It was affected by the concentration of calcium ions and was maximum at pH 8.0. When the ADP concentration was varied in the presence of different concentrations of ionized calcium, the overall kinetics revealed a series of rectangular hyperbola segments which did not pass through the origin. These observations led to the conclusion that the overall reaction can be depicted as a chain reaction: ADP interacts reversibly with platelets; when calcium is present these platelets become “sticky” and, when stirred, they aggregate. Kinetic studies of inhibition indicated that adenosine is a competitive inhibitor of ADP. The guanidino compounds tested were noncompetitive with respect to ADP but their inhibitory activity was counteracted by calcium.

Effect of Gravel on Unconsolidated Sands

The important factors in any study of the screening of sand with a gravelenvelope, as applied to use in oil wells, are:gravel size upon sand migrationsand size and shapegravel size and shaperatio of gravel size tosand sizeflow velocityviscosity of the fluid. Perhaps the first extensive investigation of the function of gravel inscreening sand was performed by Coberly and Wagner,' from which the followingconclusion was drawn: "The diameter of the largest grains in a singleclassified sand suitable for gravel packing is approximately 13 times the grainsize at the ten-percentile analysis of the formation sample." This appliesto sands classified by Tyler screens and is for gravel grains of the maximumsize that could be used to form a stable bridge. Field practice has shown thatthe screening effect of a given gravel for a given sand apparently varies withthe flow velocity. 2 Also, it has been assumed by some operators that thethickness of the walls of the gravel envelope surrounding the well has littleeffect upon the screening process. It is thought by others that a narrowenvelope of gravel might form an ineffective screen. Thus the purposes of thiswork are:To investigate the effect of gravel-sand size ratio upon screening actionunder the condition of varying flow velocities.To investigate the effect upon screening action of varying the thickness ofthe gravel screen.To investigate sand migration in the gravel screen and the effect of flowvelocity and gravel size upon sand migration. Description of Apparatus In an attempt to reproduce field conditions for the purposes of thisinvestigation, a flow tube was constructed, according to the manner of Uren, torepresent a radial drainage segment of an oil sand. To arrive at the dimensions of the flow tube, a radial drainage segment ofrectangular cross section was assumed to define an area of 2 sq. in. on theface of a well 6 in. in diameter. From this the dimensions of the segment werecalculated out to a distance of 5 ft. from the face of the well. By computingcross-sectional areas at a number of sections along the rectangular segment andtransforming these areas into the circular form, a drainage cone was obtainedhaving everywhere the same cross-sectional area as the drainage element ofrectangular cross section. To construct the apparatus, two sections of pipe of 7 5/8 in. inside diameter, one 13 in. and the other 4 ft. long, were joined by a bolted flange. A mandrelhaving the dimensions of the drainage cone was centered in the pipe and a neatcement mixture was cast around it. A protective gasket was placed between thetwo sections of pipe so that the cement body could be separated at that point.When the mandrel was withdrawn a drainage cone was obtained A round slotted screen, which could be screwed up against the end of thedrainage cone, held the gravel in place. T.P. 1195