Polygonal Tubes Research Articles

A 3D dynamic stress model for the growth of hollow silicon polygons

The paper presents dynamic 3D finite element simulation of stress and deformation of growing thin-walled, polygonal tubes. As an example, the growth of octagonal silicon tubes by the edge-defined film-fed growth (EFG) method is chosen. In tubes with wall thickness in the order of several 100 μm the increasing strain energy during growth is periodically reduced by deflections of the walls at regular intervals. The influence of various temperature profiles on the deflection behavior is studied. The applicability of this model to the EFG growth of silicon octagons is discussed by means of experimental observations.

Virtual Tubelets—efficiently visualizing large amounts of particle trajectories

The depiction of particle trajectories is an effective means for the visualization of fluid flows. However, standard visualization techniques suffer from a variety of weaknesses, ranging from ambiguous depth perception for simple line drawings to a high geometrical complexity and decreased interactivity for polygonal tubes. This paper addresses these problems by introducing a novel approach to pathline visualization, which we call Virtual Tubelets. It employs billboarding techniques in combination with suitable textures in order to create the illusion of solid tubes, thus efficiently and unambiguously depicting large amounts of particle trajectories at interactive frame rates. By choosing an appropriate orientation for the billboards, certain issues concerning immersive displays with multiple projection screens are resolved, which allows for an unrestricted use in virtual environments as well. Using modern graphics hardware with programmable vertex and pixel pipelines results in an additional speed-up of the rendering process and a further improvement of image quality. This creates a nearly perfect illusion of tubular geometry, including plausible intersections and consistent illumination with the rest of the scene. The efficiency of our approach is proven by comparing rendering speed and visual quality of Virtual Tubelets to that of conventional, polygonal tube renderings.

Microwave‐Assisted Synthesis of Metallic Nanostructures in Solution

Microwave (MW) rapid heating has received considerable attention as a new promising method for the one-pot synthesis of metallic nanostructures in solutions. In this concept, advantageous application of this method has been demonstrated by using some typical examples for the preparation of Ag, Au, Pt, and AuPd nanostructures. Not only spherical nanoparticles, but also single crystalline polygonal plates, sheets, rods, wires, tubes, and dendrites were prepared within a few minutes under MW heating. Morphologies and sizes of nanostructures could be controlled by changing various experimental parameters, such as the concentration of metallic salt and surfactant polymer, the chain length of the surfactant polymer, the solvent, and the reaction temperature. In general, nanostructures with smaller sizes, narrower size distributions, and a higher degree of crystallization were obtained under MW heating than those in conventional oil-bath heating. The origin of these characteristic features under MW irradiation is discussed in terms of thermal and non-thermal effects under MW irradiation.

Stress intensity factors for cracked triangular cross‐section thin‐walled tubes

ABSTRACTFor one kind of finite‐boundary crack problems, the cracked equilateral triangular cross‐section tube, an analytical and very simple method to determine the stress intensity factors has been proposed based on a new concept of crack surface widening energy release rate and the principle of virtual work. Different from the classical crack extension energy release rate, the crack surface widening energy release rate can be defined by the G*‐integral theory and expressed by stress intensity factors. This energy release rate can also be defined easily by the elementary strength theory for slender structures and expressed by axial strains and loads. These two forms of crack surface widening energy release rate constitute the basis of a new analysis method for cracked tubes. From present discussions, a series of stress intensity factors are derived for cracked equilateral triangular cross‐section tubes. Actually, the present method can also be applied to cracked polygonal tubes.

A New Eurypterid (Chelicerata: Eurypterida) from the Upper Devonian Gogo Formation of Western Australia, With A Review of the Rhenopteridae

A new eurypterid, Rhenopterus waterstoni sp. nov., is described from the Gogo Formation (Frasnian, Upper Devonian) of Western Australia. This species is distinguished from related forms by the tuberculation of the anteriormost tergite and crenulated posterior margins of the carapace and opisthosomal segments. It is the only eurypterid specimen known from the Gogo Formation, the most complete eurypterid from Australia, and also the youngest representative of Rhenopterus in the fossil record. Structures retrieved from between the prosomal‐opisthosomal juncture comprise polygonal tubes 30–40 μm in diameter, which are interpreted as sarcomeral sheaths of muscular tissue. Rhenopterus is reviewed: R. latus Størmer, 1936 is synonymized with R. diensti Størmer, 1936 as it is here recognized as a female sexual dimorph; R. maccarthyi (Kjellesvig‐Waering, 1934) is an orthocone nautiloid.

Atomic-scale simulations of copper polyhedral nanorods

We have investigated the structure and properties of copper nanorods composed of acentral atomic strand and polygonal tubes, using a classical molecular dynamicssimulation with a well-fitted many-body potential function of the second-momentapproximation of the tight-binding scheme. The ultra-thin multi-shell nanorodspossessed a hexagonal surface lattice and had needle-like edges. The structure ofpentagonal multi-shell nanorods was that of a square surface lattice fordiameters of several nanometres. The properties were close to those of aface-centred-cubic lattice, as the sub-units were composed of both triangular- andquadrangular-pyramid shapes oriented along the ⟨100⟩direction. Our investigation showed the relationship between ultra-thin multi-shellnanorods and a tetrahedron, and revealed that pentagonal copper nanorods canbe classified by three types of needle-like nanorods: (i) icosahedral, (ii) decahedraland (iii) decagonal discus.

Torsion of tubes of arbitrary shape

The method of eigenfunction expansion and matching can be applied to arbitrary shaped, hollow tubes which are described by curved and straight pieces. The method is highly efficient and superior to finite differences. The oval tube and the rounded polygonal tube are studied in detail. Approximate formula for torsional rigidity from membrane analogy is valid only for thin tubes with thickness less than 0.2. Maximum shear stress occurs either at re-entrant inner corners or at the outer boundary on the minor axis.

Effect of contact angle on drainage and imbibition in regular polygonal tubes

Wettability and pore structure are primary factors in determining the capillary behavior of porous media. A key characteristic of the pore structure of real porous media is the angular corners of the pores. As a model of pore structure, angular tubes are much more realistic than the commonly used cylindrical tube model. However, their behavior is quite complicated because contact angle, corner angle, and the meniscus in the corners are all variables. The Mayer and Stowe-Princen (MS-P) theory of drainage, together with a detailed model of meniscus behavior in a corner during imbibition, enables the relationships between capillary pressure and saturation to be investigated as a function of contact angle and pore geometry. In this study, a general relationship between contact angle, corner angle, liquid saturation, and the curvature of a meniscus in the corner of an n-sided tube is derived. For any corner angle, there is a critical contact angle at which the meniscus becomes flat and the capillary pressure falls to zero. Drainage of polygonal tubes (having cross-sections such as equilateral triangles and squares) is analyzed as a function of contact angle using the MS-P theory. For imbibition, there are two filling mechanisms: the tube can be filled by a meniscus advancing along the tube or it can be filled by expanding the menisci from the tube corners. For both mechanisms, the contact angle is treated as having either zero or finite contact angle hysteresis. Systematic changes in drainage and imbibition capillary pressure curves with contact angle are obtained. The results are qualitatively consistent with several features of the behavior of natural porous media, including the effect of wettability on the displacement efficiency of crude oil by water.

Writing interrelated programs for the MK-56 calculator

Despite the limited number of commands available (up to 98), the MK-56 calculator can be used to perform complex calculations requiring a large number of commands. This is accomplished by writing several interrelated programs so that data obtained from one program is inserted into the next programs and so forth, until all of the necessary parameters are obtained. Here, no intermediate entries are necessary all o f the operations reduce to the completion of a single table. Described below is an example of writing interrelated programs to design the rolls for a multistand mill which is to produce rectangular tubes. To obtain such tubes, the initial circular tube is shaped in several four-high stands with individual drives. In the example we will use, the calculations will be limited to determination of the dimensions of the tube in each stand (Fig. I and Table 1). The initial data for the calculations is as follows: number of stands n, wall thickness S, radius of curvature of the finished shape r c, dimensions of the sides of the tube A and B, diameters of the rolls D ~' and D b. During the shaping of a circular tube into a rectangular tube, the perimeter of the tube is reduced. This reduction can be determined from the empirical formula (3). The radius of curvature of the tube in each stand is calculated from the condition of a uniform load distribution on all of the stands. Here, it is assumed that the work done in shaping the polygonal tube is directly proportional to the logarithm of the ratio of the mean radii (over the neutral layer) of curvature of the tube in two adjacent stands (Eqs. (7)-(9) in Table 1). In rolling a circular tube into a rectangular tube in plane rolls, deflection of the inside surfaces of the tube is unavoidable. To circumvent this problem, the working part of the roll body should be made concave. The critical radius of concavity (when there should theoretically be no convexity or sagging of the surfaces) can be determined from empirical formula (10)i To guarantee the absence of such deflection, this radius is decreased by a factor of 1.2 for the last stand. The radii for the other stands are determined from the condition of a constant ratio of the radii of the adjacent stands, beginning with the circular tube. The formulas were divided into three groups and were used as the basis for writing three interrelated programs. The arrows in Table 2, with the number of the program at the beginning, indicate which initial data is necessary for the given program. The numbers under the parameters indicate the program used to determine them. There is yet one more innovation. The calculator indicates the method to be^Ssed (PP or BT) to enter data. When the display reads "0," it is necessary to use the method BT. When the display reads "88", the method PP must be employed. Also, when the second method is used, it is not necessary to press the key PP after the last parameter. Thus, a single rule can be formulated: press S/P after the last parameter when entering the initial data.

Ultra-large-area silicon sheet growth for low cost photovoltaics

On the basis of the growth of hollow polygonal tubes of silicon by the edge-defined film-fed growth technique, it is speculated that ultra-large-area crystals can be produced. Area growth rates of 750 – 1500 cm 2 min −1 are postulated to be feasible using this technique, thus leading to very low manufacturing costs.

A new and unusual skeletal organism from the Lower Cambrian of Labrador

An unusual carbonate skeletal organism is found in abundance in the upper of two archaeocyathid-rich horizons in the Lower Cambrian Forteau Formation of southern Labrador. The commonly cryptic organism consists of splaying and branching irregularly polygonal tubes which are open. Tabulae and dissepiments are absent; the walls are thick (200–950 μm) in relation to the diameter of the tubes (150 μm to 5 mm). Only very rarely is wall microstructure preserved. It consists of elongate calcite crystals perpendicular to the wall margin in vertical section. The wall is covered by a thin (20–35 μm) outer layer. Pore-like structures with curved necks are very rarely found perforating the wall outer layer.The affinities of this organism are unknown, but it does have features which are both coral-like and sponge-like. It is here placed in the Incertae Sedis.

Initial Buckling of Channels in Compression

An exact analysis of the behavior of thin rectangular plates subjected to uniform shear and widthwise direct stresses, and a longitudinal compressive stress which is constant in the longitudinal direction, and small edge forces applied to the longitudinal edges which vary sinusoidally with the longitudinal coordinate, is outlined. Hence, the initial buckling stree (or frequency of vibration) and mode of any structure consisting of a series of such plates connected along their longitudinal edges can be found (e.g., open sections, polygonal tubes, various types of stiffened plates and corrugated core sandwich panels). Uniformly compressed symmetrical channels are specifically considered in this paper. The modes are shown to be either symmetrical or antisymmetrical, but interaction between local and overall deformation, of either the Euler or flexural-torsional type, is automatically included and is always present to a greater or lesser extent. Numerical results for the buckling stresses and modes of a family of channels are obtained and compared with recently published approximate results. Appreciable discrepancies are found.

Buckling Analysis of Plate Structures by the Strip Elements

This paper provides a new approach to the buckling analysis of plate structuers whose section are not varied along the longitudinal axis, for example, stiffened plates with one directional stiffeners, corrugated plates, polygonal tubes, sandwich plates with corrugated cores and so on.In this approach, the prebuckling stresses are assumed to be normal stresses in the longitudinal direction only, however the distribution pattern may be arbitrary.The foundamental concepts of this method are as follows. The plate elements which compose the section of the plate structures are divided into the narrow strip elements and then the stiffeness matrixes of these strip elements are derived by assuming the displacement functions and using the energy theorems. In the subsequent processes, the usual techniques of matrix method can be applied and then bucklig load is computed as the lowest eigen value. Several kinds of plate structures were analized by this method and experiments were also conducted. The coincedence was fairly good.

Local buckling of long polygonal tubes in combined compression and torsion

General criteria, based upon the concept of stability functions, are derived for the local buckling of a polygonal tube, with N identical walls, due to combined uniform longitudinal compression and torsion. Interaction curves are calculated for the cases of N = 3 and N = 4. The results for the triangular tube provide an explanation of the indeterminacy of the mode under pure compression.

Critical pressures and buckling modes of regular polygonal prismatic tubes

The critical pressures and buckling modes of regular polygonal prismatic tubes of 3, 4 and 5 sides under uniform external pressures are determined in this paper.

Stress Distribution of a thick Tube, subjecting to an Internal Pressure, which has a Cross Section of Regular Polygon and a Circular Hole in its Center

(This Paper was read before the Meeting of the Japan Society of Mechanical Engineers and Applied Mechanics held in Nagoya on the 26th. Nov. 1945) The solution for an internal pressure acting at a circular hole in the center of a regular polygonal tube can be obtained from the following complex function z=C∫ (1-tn)n^^2 dt, z=x+iy, t=ρ (cos θ+i sin θ) using the orthogonal curvilinear coordinate. The differential equation for Airy's stress function F in this case becomes [numerical formula] where h2=c-2 (1-2ρncosnθ+ρ2n) n^^2 The boundary conditions for this problem are σρ=0, τρθ=0 for ρ=1 σρ=-p, τρθ=0 for ρ=ρ0, where σρ, σθ, represent a normal stress acting a curve of ρ=const. and θ=const. on the x, y plane, and τρθ a tangential stress acting along the both curves. Then σρ, σθ, τρθ and F can be write in the following form : [numerical formula] where Ao, As, Bs, Co, Cs and Ds are constants and they are determined by the boundary conditions. The details are descibed in the original paper.