Flat Square Research Articles

Monitor screens use flat square tubes

Monitor screens use flat square tubes

The elastic stability of square perforated plates

A direct matrix method of analysis for the buckling loads on structures, which had already been proven on various structural forms, is applied to the examination of the stability of flat square plates with central square perforations. The results for a variety of boundary conditions are presented for a range of hole to plate size from 0 to 0.8. The method generally shows trends which are different to those predicted by other numerical methods, particularly over the range of the larger hole sizes. Possible reasons for these differences are suggested, but further work to obtain definitive results is clearly needed by all investigators.

Vibrations of corner point supported shallow shells of rectangular planform

AbstractThe first known solution of the title problem is presented. The Ritz method is used, with algebraic polynomials forming the set of trial functions. The condition that all three components of displacement be zero at the four corners is straightforwardly enforced. Numerical studies show that the convergence is relatively slow, requiring more terms than for shells which are completely free. The class of problems studied includes independent, constant curvature in each of the directions parallel to the edges, yielding vibration modes which fall into one of four symmetry classes, with symmetry or antisymmetry of the displacements existing with respect to each of the two symmetry axes of the problem. Detailed results are given for the frequencies and mode shapes of the first two modes of each symmetry class for shells having square planform and circular cylindrical, spherical and hyperbolic paraboloidal curvatures. Accuracy of the results is partially established by comparison with other previously published, accurate results for the corner supported flat square plate.

Multiphase behavior of large interacting molecules on a flat square lattice in the Percus-Yevick approximation

Multiphase behavior of large interacting molecules on a flat square lattice in the Percus-Yevick approximation

Two children with de novo del(9p)

We describe two patients with characteristic manifestations of the del(9p) syndrome. Among the prominent manifestation are moderate mental retardation, trigonocephaly, flat nasal bridge, anteverted nostrils, long philtrum, square and hyperconvex nails, and apparently long digits. The metacarpophalangeal pattern profiles of the patients showed that the clinical impression of long fingers may be due to relative shortness of the metacarpals rather than to elongation of the phalanges.

Electromagnetic scattering by surfaces of arbitrary shape

The electric field integral equation (EFIE) is used with the moment method to develop a simple and efficient numerical procedure for treating problems of scattering by arbitrarily shaped objects. For numerical purposes, the objects are modeled using planar triangular surfaces patches. Because the EFIE formulation is used, the procedure is applicable to both open and closed surfaces. Crucial to the numerical formulation is the development of a set of special subdomain-type basis functions which are defined on pairs of adjacent triangular patches and yield a current representation free of line or point charges at subdomain boundaries. The method is applied to the scattering problems of a plane wave illuminated flat square plate, bent square plate, circular disk, and sphere. Excellent correspondence between the surface current computed via the present method and that obtained via earlier approaches or exact formulations is demonstrated in each case.

Ab initio SCF and CEPA investigations of stable lithium clusters

Various approaches of two Li 2 molecules are investigated in a search for stable Li 4 cluster configurations and favourable pathways forming them. The lowest energy minimum is found for a singlet state in a rhombic structure with its short diagonal close to the equilibrium internuclear distance of free Li 2. The stability of this arrangement is traced to the binding potential of the p—π functions of its central Li 2 substructure. This suggests a flat square bipyramidal configuration for Li 6 which is indeed found to represent a local minimum. Binding energies for 2Li 2 → Li 4 and Li 2 + Li 4 → Li 6 are calculated as 15 kcal/mole and 24 kcal/mole, respectively. Formation of both clusters is possible without surpassing energy barriers. Harmonic vibrational frequencies are given for Li 4 and ionization potentials are calculated for Li 4 and Li 6.

Design curves for flat square spiral inductors : K. Green. Electron. Compon. 11 February (1972), p. 121

Design curves for flat square spiral inductors : K. Green. Electron. Compon. 11 February (1972), p. 121

Design curves for flat square spiral inductors : K. Green. R.A.E. Farnborough, Hants. March (1971), pp. 50. BR-25037, RAE-TR-71037

AISI type 304, type 430 and 21-6-9 stainless steels were tensile tested in contact with liquid copper and several liquid braze metals. Less extensive tests were performed on type 316, JBK-75 (an austenitic precipitation-hardened stainless steel similar to A-286) and HP 9-4-20 in the presence of liquid copper, braze alloys, aluminum and gold. The austenitic stainless steels (and HP 9-4-20) were severely embrittled copper and braze alloys with a high copper content and were nearly unaffected by a silver-base braze. Braze alloys with lower copper embrittlement. The highly embrittled samples failed integranularly. The severity of embrittlement by several liquid brazes was uncorrelated with their relative depths of penetration into the unstressed steel. No embrittlement of ferritic type 430 by any of the liquid metals was observed. Under welding conditions, 21-6-9 was found to be much more susceptible than type 304 to heat-affected-zone cracking when the surface was copper contaminated.

Elastic stresses and deflections of flat square plates under uniformly distributed normal pressure: A critical review

Published data on the maximum principal elastic stresses and deflections for thin, initially flat, square, isotropic plates under uniform normal pressure, supplemented by data provided by university and industrial sources, are correlated to produce design curves for four conditions of edge restraint. The trends disclosed by the correlation are discussed and the sources from which the data were obtained are briefly reviewed.

Model for Correlated Molecular Rotation

We report studies of models designed to emphasize the thermodynamic consequences of coupled molecular rotation in condensed phases. The coupling arises from hard molecular cores of nonspherical shape, here represented by flat coplanar squares in a one-dimensional array. Various forms are considered for the orientation-independent part of the interaction, from none to harmonic to delta function (or lattice model); the first and third are shown to represent the high- and low-temperature limits of the second, treated classically. The lattice model gives rise to a particular sort of first-order phase transition, the significance of which is clarified by the temperature dependence of the properties of the harmonic model.

The Post-Buckling Behaviour of Simply-Supported Square Plates

SummaryThe post-buckling behaviour of flat square plates loaded along two opposite straight edges is analysed using the von Kármán equations, trigonometric series and Galerkin’s method. The unloaded edges are considered to be either free to distort in the plane of the plate or maintained straight but allowed to move bodily; all edges are simply-supported in the out-of-plane direction. The non-linear algebraic equations are solved approximately using a McLaurin’s series expansion technique which facilitates the development of explicit expressions for ultimate load, end shortening and stiffness. The effects of initial geometric imperfections are also studied and it is shown that the results for ultimate load prediction and end shortening are in good agreement with test results.

矩形断面の柱の抗力に関する一実験

An experimental study is carried out on the aerodynamic drag of rectangular cylinders, where the REYNOLDS number ranges up to 6×104. It is revealed that the drag coefficient, CD, varies con-siderably with the d/h ratio of rectangles, and that the maximum value of CD is as high as 2.6 for d/h of 2/3 compared with CD of about 2.0 for the cases of flat plate and square cylinder (Fig.1). The STROUHAL number of the shedding vortices, on the contrary, remains approximately constant for d/h up to 1.0, decreases slowly for larger values of d/h, and then increases abruptly at d/h ratio of about 2.8 (Fig.2), where the flow reattaches on the lateral surfaces of the cylinder.

The Elephant and the Aryans

The association of man and elephant dates back to remote antiquity. The bones of the animal unearthed at Mohenjodaro, the realistic figurines, and the representations on the seals of the Indus sites point to the beginnings of this fateful friendship; the docility, intelligence, and easy obedience of the elephant must have quickly led to its domestication, once it was known and captured. That the prosperous civilization of the Indus used the elephant for riding and other purposes, appears almost certain; “the representations on the seals show the two breeds recognized today in India, the Kamooria Dhundia with its flat back, square head, and stout legs, and the inferior Meergha, less heavily built and with a sloping back.” The proto-Australoids were perhaps the first people to domesticate and train the elephant; the wordsgajaandmātaṅgahave been traced to the pre-Aryan peoples of India speaking Austric languages.

Observations on single crystals of an isotactic polyolefin: Morphology and chain packing in poly-4-methyl-pentene-1

Abstract Single crystals of isotactic poly-4-methyl pentene-1 were prepared from solution. The crystals were mostly flat squares with more or leas regular shapes. They consisted of thin square layers forming spiral terraces centred on screw dislocations. The molecules were found to be perpendicular to these layers. The same polymer could also be obtained in the form of thin fibrils with the molecules perpendicular to the fibril direction. Both these habits require chain folding, further implications of which are discussed. The unit cell was determined and was found to be tetragonal with a= b= 18.66 A and c = 13.80 A containing four obains. The pecking of these chains closely approximates a two-dimensional rock-salt type arrangement with one chain surrounded by four nearest neighbours. It is shown that the helical chains can be in gear with this type of pecking engaging most perfectly if half and half are of opposite winding direction.

The Application of Limit Analysis to Punch-Indentation Problems

Abstract Limit analysis is applied to obtain upper and lower bounds for the punch pressure in the indentation of the plane surface of an elastic-perfectly plastic material by a flat rigid punch. The two-dimensional flat punch and the three-dimensional flat square and rectangular punch problems are considered. The analysis assumes Tresca’s yield criterion of constant maximum shearing stress k, during plastic deformation. It is shown that the pressure required to produce indentation in the two-dimensional problem lies between 5k and (2 + π)k. The lower bound obtained for any rectangular punch is again 5k while the upper bound for a smooth punch lies between 5.71k for a square and (2 + π)k for a very long rectangle. A value of 5.36k is found for a ratio of length to breadth of 3. The limit pressure for a uniformly loaded area, as distinguished from an area loaded by a punch, is bracketed by 5k and (2 + π)k when the area is convex.

The stump-stitch technique for vaginal hysterectomy

The damage which is caused by the action of crushing clamps, and the danger of placing the ligatures in the line of the separating cut, in dissecting a bridge of tissue, are briefly mentioned. The stump-stitch technique is recommended for achieving perfect hemostasis of the parametrium and the adnexa in vaginal hysterectomy. The stitch must be applied through the entire thickness of the stump and as close to the ligature as possible. The importance of making flat square knots is stressed. A new technique of tying square knots with the ligatures of the parametrium is presented. New features are: (1) The elimination of unligated areas in dissecting a bridge of tissue by stitches through the previous stump, (2) the use of the stump-stitch technique in vaginal hysterectomy, (3) the performance of only partial dissection of ligated tissue as a means of facilitating the exposure of the previous ligature, (4) the regular placing of the stump stitch close to the ligature, (5) the technique of tying a flat square knot in the sagittal plane, and (6) the technique of the passing maneuver.

A characteristic type of instability in the large deflexions of elastic plates. I. Curved rectangular plates bent about one axis II. Flat square plates bent about all edges

Part I. From a general equation governing the bending of thin elastic plates into certain types of surfaces of revolution are derived expressions for the behaviour of rectangular plates with initial curvatures, subjected to pure bending about one axis. It is found that such plates exhibit the type of instability characteristic of thin-walled structures which depend for their stiffness on curvature. Curves are drawn showing the deformation suffered by such plates, and an expression for the critical bending moment at which instability occurs is obtained. Experimental results show satisfactory agreement.Part II. The analysis of part I is extended to deal with the case of flat square or rectangular plates loaded by distributed bending moments applied to all four edges. Curves are drawn to describe their behaviour, and they are found to exhibit the characteristic instability displayed by thin-walled curved structures. Experimental verification is satisfactory.

First Lessons in Practical Botany

THIS is an excellent little book. Its diligent study by teachers as well as pupils would give descriptive botany the real educational value which is so often claimed for it, and at bottom it no doubt possesses, if only the old type of manuals could be exterminated. What a weight would be removed from examiners' minds if examinees would really take to heart Mr. Bettany's impressive admonition (which should be hung in every examination room where plants are set for description):—“Do not suppose or imagine facts of structure which you cannot verify.” It is really refreshing to come upon a manual, the object of which is to drill students in a healthy scientific method, and not merely to teach them how to impose on examiners with a show of sham and often preposterous knowledge, which has but a temporary hold on the memory and none on the understanding. The only genuine criticism of a manual like this would proceed from one who had actually tested its use. Improvements will gradually suggest themselves; a few friendly suggestions might be even ventured upon offhand. On p. 63, for example, the following definition is open to objection:—“Trichome, a generic term for all organs developed by emergence from single cells of the epidermis.” The chapter on Floral Diagrams is good. But it never seems to have been suggested that a genuine interest might be given to lessons in botany by making the pupils arrange the actual parts of the flower so as to form the diagram. All that is wanted is a flat square of cork covered with paper, on which four concentric circles are traced. It would be best to have three such squares for each pupil, with three, four, or five radiating lines drawn intersecting the circles, according as flowers with a ternary, quaternary, or quinary symmetry are to be examined. As each successive whorl of floral organs is removed, its parts should be pinned out in their proper relative positions by the pupil. The cyclical symmetry of the flower is clearly brought out in this way, even where it is apparently disguised. Some details in working the method would need a little elaboration, as, for example, the treatment of gamopetalous flowers; but this may be left to the ingenuity of teachers like Mr. Bettany.