Variety Of Cross-sectional Shapes Research Articles

Применение трехмерного сканирования для исследования составных пазовых орудий раннего голоцена Восточной Сибири (на примере орудий из комплексов стоянки Казачка-1)

The article demonstrates the potential applications of 3D scanning of composite slotted tools and the use of models as a basis for further scientific research. The scanning was carried out with high-precision equipment (Solutionix D700 scanner). The scanner provides high precision data acquisition of the geometry and surface of an artefact. As examples of archaeological artefacts we used composite slotted tools from the site of Kazachka-I. There were two bone tools from cultural layers 19 and 11. As a result of three-dimensional scanning application, a series of high-resolution scaled models was created. The series of cross-sections and metric measurements were made on the obtained models with the use of special software. Through analysis of cross-sectional shapes and comparison with experimental modelling data, conclusions on the basic process steps in slotted tools manufacture have been drawn. V-, U- and W-shaped cross-sections have been identified. Slots of bone tool from layer 19 has V- and U-shaped cross-sections. Slots of bone tool from layer 11 have U- and W-shaped cross-sections. The variety of cross-sectional shapes may indicate different techniques in the manufacture of the slots. The U-shaped cross-section may have been created by cutting the slot with a stone tool, the edge of which has been broken in the process. The W-shape may indicate that the direction of motion of the tool in this section was changed during operation. The V-shape was obtained by using a sharp tool throughout the slotting process. These conclusions are preliminary and need to be verified by a series of experiments and use-wear analysis.

A Rayleigh--Ritz method for Navier--Stokes flow through curved ducts

We present a Rayleigh–Ritz method for the approximation of fluid flow in a curved duct, including the secondary cross-flow, which is well known to develop for nonzero Dean numbers. Having a straightforward method to estimate the cross-flow for ducts with a variety of cross-sectional shapes is important for many applications. One particular example is in microfluidics where curved ducts with low aspect ratio are common, and there is an increasing interest in nonrectangular duct shapes for the purpose of size-based cell separation. We describe functionals which are minimized by the axial flow velocity and cross-flow stream function which solve an expansion of the Navier–Stokes model of the flow. A Rayleigh–Ritz method is then obtained by computing the coefficients of an appropriate polynomial basis, taking into account the duct shape, such that the corresponding functionals are stationary. Whilst the method itself is quite general, we describe an implementation for a particular family of duct shapes in which the top and bottom walls are described by a polynomial with respect to the lateral coordinate. Solutions for a rectangular duct and two nonstandard duct shapes are examined in detail. A comparison with solutions obtained using a finite-element method demonstrates the rate of convergence with respect to the size of the basis. An implementation for circular cross-sections is also described, and results are found to be consistent with previous studies. doi:10.1017/S1446181118000287

A RAYLEIGH–RITZ METHOD FOR NAVIER–STOKES FLOW THROUGH CURVED DUCTS

We present a Rayleigh–Ritz method for the approximation of fluid flow in a curved duct, including the secondary cross-flow, which is well known to develop for nonzero Dean numbers. Having a straightforward method to estimate the cross-flow for ducts with a variety of cross-sectional shapes is important for many applications. One particular example is in microfluidics where curved ducts with low aspect ratio are common, and there is an increasing interest in nonrectangular duct shapes for the purpose of size-based cell separation. We describe functionals which are minimized by the axial flow velocity and cross-flow stream function which solve an expansion of the Navier–Stokes model of the flow. A Rayleigh–Ritz method is then obtained by computing the coefficients of an appropriate polynomial basis, taking into account the duct shape, such that the corresponding functionals are stationary. Whilst the method itself is quite general, we describe an implementation for a particular family of duct shapes in which the top and bottom walls are described by a polynomial with respect to the lateral coordinate. Solutions for a rectangular duct and two nonstandard duct shapes are examined in detail. A comparison with solutions obtained using a finite-element method demonstrates the rate of convergence with respect to the size of the basis. An implementation for circular cross-sections is also described, and results are found to be consistent with previous studies.

Fluid flow in a spiral microfluidic duct

We consider the steady, pressure driven flow of a viscous fluid through a microfluidic device having the geometry of a planar spiral duct with a slowly varying curvature and height smaller than width. For this problem, it is convenient to express the Navier–Stokes equations in terms of a non-orthogonal coordinate system. Then, after applying appropriate scalings, the leading order equations admit a relatively simple solution in the central region of the duct cross section. First-order corrections with respect to the duct curvature and aspect ratio parameters are also obtained for this region. Additional correction terms are needed to ensure that no slip and no penetration conditions are satisfied on the side walls. Our solutions allow for a top wall shape that varies with respect to the radial coordinate which allows us to study the flow in a variety of cross-sectional shapes, including trapezoidal-shaped ducts that have been studied experimentally. At leading order, the flow is found to depend on the local height and slope of the top wall within the central region. The solutions are compared with numerical approximations of a classical Dean flow and are found to be in good agreement for a small duct aspect ratio and a slowly varying and small curvature. We conclude that the slowly varying curvature typical of spiral microfluidic devices has a negligible impact on the flow in the sense that locally the flow does not differ significantly from the classical Dean flow through a duct having the same curvature.

Direct Synthesis of Nanofibrous Nonwoven Carbon Components: Initial Observations, Capabilities, and Challenges

Widespread adoption of carbon nanomaterials has been hindered by inefficient production and utilization. A recently developed method has shown possibility to directly synthesize bulk nanostructured nonwoven materials from catalytically deposited carbon nanofibers (CNFs). The basic manufacturing scheme involves constraining carbon nanofiber growth to create three-dimensionally featured, macroscale products. Although previously demonstrated as a proof of concept, the possibilities and pitfalls of the method at a larger scale have not yet been explored. In this work, the basic foundation for using the constrained formation of fibrous nanostructures (CoFFiN) process is established by testing feasibility in larger volumes (as much as 2000% greater than initial experiments) and by noting the macroscale carbon growth characteristics. It has been found that a variety of factors contribute to determining the basic qualities of the macroscale fiber collection (nonwoven material), and there are tunable parameters at the catalytic and constraint levels. The results of this work have established that monolithic structures of nonwoven carbon nanofibers can be created with centimeter dimensions in a variety of cross-sectional shapes. The only limit to scale noted is the tendency for nanofibers to entangle with one another during growth and self-restrict outward expansion to the mold walls. This may be addressed by pregrowing carbon before placement or selective placement of the catalyst in the mold.

Ultimate behavior of steel beams under non-uniform bending

The ultimate behavior of steel beams deeply influences the overall performance of steel frames. The main response parameters are the rotation capacity and the flexural ultimate resistance. The former is the source of the local ductility supply needed to achieve a global dissipative behavior of structures under seismic actions, whereas the latter governs the flexural overstrength whose knowledge is needed for an appropriate application of hierarchy criteria in seismic design of structures. Therefore, a twofold classification of steel members according to their ductility and overstrength is the most appropriate approach for seismic design applications. Currently, modern international design codes are based on the classification of steel sections for both plastic and seismic designs of structures, providing misleading emphasis mainly on local buckling as the primary strain-weakening effect. Even though different methods are available in the technical literature for predicting the ultimate behavior of steel members under non-uniform bending, the problem still deserves further investigations, because of the high number of parameters affecting the ultimate response and the variety of cross-sectional shapes. Therefore, a new experimental program dealing with a wide range of cross section typologies (I and H sections, Square and Rectangular Hollow sections) under monotonic and cyclic loading has been carried out by testing specimens with different local slenderness ratios properly selected to integrate the data already available in the technical literature. The obtained results are herein presented and discussed.

Computation of major axis shear deformations in wide flange steel girders and columns

Shear deformations in the clear span region of wide flange girders and columns can often be responsible for a significant portion of the lateral flexibility of steel moment resisting frames. To include shear deformation in the analysis of such structures, the shear modulus of the material and the effective shear area of the various cross sections are required. The effective shear area is often defined in terms of a sectional form factor, κ , which is equal to the total cross sectional area divided by the effective shear area. Structural engineering literature provides several formulas for computing the form factor for a variety of cross sectional shapes, including wide flange beams. When applying these formulas to sections in the AISC section database, however, it was found that the results varied considerably, particularly for jumbo sections. The purpose of the work reported in this paper was to determine which of the existing formulas is most accurate when applied to all sections in the database. A special virtual work based finite element analysis procedure was developed for this purpose. The results of the analysis indicate that a simple empirical formula for determining the form factor may be applied with sufficient accuracy in most situations. Because the analysis of rectangular sections provides insight into the wide flange beam problem, a detailed discussion of the computation of the form factor for rectangular sections is also provided.

Visualization of sound reflection and diffraction using finite difference time domain method.

Visualization of sound field helps us to intuitively understand mechanisms of various acoustic phenomena and therefore the technique is much effective for both of educational and engineering purposes. This paper presents some examples of sound field visualization based on numerical analysis. In order to analyze such complicated acoustic phenomena as reflection, diffraction and interference, the finite difference time domain (FDTD) method based on the wave theory is applied to the calculation. In the FDTD algorithm, all of the sound field is computed in discrete time steps and therefore transient acoustic phenomena can be easily animated. As an application of the numerical technique to environmental noise control engineering, sound reflection and diffraction around noise barriers with a variety of cross sectional shapes and noise propagation from depressed/semi-underground road structures are introduced in this paper.

Electrospinning process and applications of electrospun fibers

Abstract An electric field is used to create a charged jet of polymer solution. As this jet travels in air, the solvent evaporates leaving behind a charged fiber that can be electrically deflected or collected on a metal screen. Fibers with a variety of cross sectional shapes and sizes were produced from different polymers. The diameter of these fibers was in the range of 0.05 to 5 microns. This paper describes the electrospinning process, the processing conditions, fiber morphology, and some possible uses of electrospun fibers.

Scattering by small thin dielectric particles

In the analysis of electromagnetic scattering by distributions of small dielectric particles an approximation to the scattered field can be obtained by representing the electrical interaction of the particles in terms of the dipole moments of the individual particles. The calculation of the moments necessitates the solution of certain static scattering problems, and this becomes numerically difficult when the particles are thin. An integral equation formulation of the static scattering problem specialized to the case of thin planar dielectric plates is presented, along with an efficient numerical routine. Dipole moments are obtained over a range of permittivities for plates with several thicknesses and a variety of cross-sectional shapes, and the shape dependence is discussed.

Sequential Quadratic Programming and Dynamic Optimal Design of Rotating Blades*, †

ABSTRACT By studying the Kuhn-Tucker conditions for a structural optimal design problem with multifrequency constraints, we show in this paper that the Optimality Criterion (OC) approach and Mathematical Programming (MP) can be unified. This unification leads to a new approach—Sequential Quadratic Programming (SQP)—which we combine with a technique of temporary relaxation of constraints and application of rational move-limits, based on deviations due to linearization of nonlinear constraints. The SQP algorithm is applied to solve the dynamic optimal design problem of rotating blades with prescribed multifrequency constraints on both flapping and chordwise vibration. A computer program based on the Finite Element Method and explicit design sensitivities is developed and a set of examples is tested. Numerical results for a variety of cross-sectional shapes are presented.

Paper 7. Unsteady Flow around a Slender Fish-Like Body

This paper attempts to extend some recent theoretical calculations on the unsteady flow generated by body movements of a slender ‘flat’ fish by further including the effect of finite body thickness in the consideration for various configurations of side and caudal fins as major appendages. Based on the slender-body approximation, the cross-flow is determined for different longitudinal body sections which are characterized by a variety of cross-sectional shapes and flow conditions (such as having smooth or fin-edged body contours, with or without vortex sheets alongside the body section). The effect of body thickness is found to arise primarily from its interaction with the vortex sheet already existing in the cross-flow. New results for the transverse hydro-dynamic force acting on the body are obtained, and their physical significances are discussed.