Arbitrary Cross Section Research Articles

Model of deformation of a feather quill when rolling with a ribbed roller on the flat surface

Mathematical modeling is an effective and cost-effective alternative to a trial physical experiment in solving problems associated with the development of new technologies and equipment. The paper is devoted to modeling the deformation process of a feather quill when rolling by a ribbed roller on a flat surface to form thorough kneading on its concave side, providing additional bending. The technology is used to enhance the Executive ability (“Fill Power” measure) of feather stock of land birds, which are used for manufacturing down-feather products, as an alternative to increasingly scarce and expensive feahers of waterfowl. This is especially true for products with a short service life, intended for use in the rectifying natural disasters and the consequences of accidents.The developed mathematical model allows us to investigate the dependence of the resistance force of the roller on the design parameters of the working body: the knurling pitch; the angular size of the flute; the diameter of the riffle vertices.Stresses arising in the structure of the quill under the action of compressive load, when loading and removing the load in an arbitrary cross-section of a feather quill have different values and are described by the corresponding regression models. The solution of the system of regression equations together with the kinematic equations of motion of the working body allows to determine the strength of resistance and power requirement of the deformation of feather quill of land birds to improve the “Fill Power” of feather stock.The dependence of the total rolling resistance force for the working body and the chicken feather quill of the given parameters obtained on the model is given.

Rapid distortion theory on transversely sheared mean flows of arbitrary cross-section

This paper is concerned with rapid distortion theory on transversely sheared mean flows that (among other things) can be used to analyse the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It expands on a previous analysis of Goldsteinet al. (J. Fluid Mech., vol. 824, 2017, pp. 477–512) that uses a pair of conservation laws to derive upstream boundary conditions for planar mean flows and extends these findings to transversely sheared flows of arbitrary cross-section. The results, which turn out to be quite general, are applied to the specific case of a round jet interacting with the trailing edge of a flat plate and are used to calculate the radiated sound field, which is then compared with experimental data taken at the NASA Glenn Research Center.

Searching for shear forces flows in arbitrary cross-sections of thin-walled bars: numerical algorithm and software implementation

Development of a general computer program for the design and verification of thin-walled bar structural members remains an actual task. Despite the prevailing influence of normal stresses on the stress-strain state of thin-walled bars design and verification of thin-walled structural members should be performed taking into account not only normal stresses, but also shear stresses.Therefore, in the paper a thin-walled bar of an arbitrary cross-section which is undergone to the general load case is considered as investigated object. The main research question is development of mathematical support and knoware for numerical solution for the shear stresses problem with orientation on software implementation in a computer-aided design system for thin-walled bar structures.The problem of shear stresses outside longitudinal edges of an arbitrary cross-section (including open-closed multi-contour cross-sections) of a thin-walled bar subjected to the general load case has been considered in the paper. The formulated problem has been reduced to the searching problem for unknown shear forces flows that have the least value of the Castigliano’s functional. Besides, constraints-equalities of shear forces flows equilibrium formulated for cross-section branch points, as well as equilibrium equation formulated for the whole cross-section relating to longitudinal axes of the thin-walled bar have been taken into account.A detailed numerical algorithm intended to solve the formulated problem has been proposed by the paper. The algorithm is oriented on software implementation in systems of computer-aided design of thin-walled bar structures. Developed algorithm has been implemented in SCAD Office environment by the program TONUS. Numerical examples for calculation of thin-walled bars with open and open-closed multi-contour cross-sections have been considered in order to validate developed algorithm and verify calculation accuracy for sectorial cross-section geometrical properties and shear stresses caused by warping torque and shear forces. Validity of the calculation results obtained using developed software has been proven by considered examples.

Beam & Shell Models for Composite Straight or Curved Bridge Decks with Intermediate Diaphragms & Assessment of Design Specifications

In this research effort, the generalized warping and distortional problem of straight or horizontally curved composite beams of arbitrary cross section, loading and boundary conditions is presented. An inclined plane of curvature is considered. Additionally, the stiffness of diaphragmatic plates has been introduced in the formulation in order to compare with the case where rigid diaphragms are assumed. Isogeometric tools (NURBS) are employed in order to obtain the results for the 1D formulation and 3D shell models are developed in FEM commercial software for composite cross sections with diaphragms. The number of intermediate diaphragms according to bridges design specifications is compared to the analyzed diaphragmatic arrangements in order to assess the overall structural behavior of bridges decks. For this purpose, examples of curved beam models with open or closed cross sections and various arrangements of diaphragms have been studied.

Calculation of wave dispersion curves in multilayered composites using semi-analytical finite element method

The enormous potential of Guided waves have a significant use for non-destructive evaluation(NDE) and structural health monitoring(SHM). It is common to use different solution approaches to predict dispersion curves depending on the material type, isotropic, transversely isotropic, or orthotropic, of the medium in which the wave propagates, shape of the waveguide, etc. Inability to model waveguides of arbitrary cross-section by existing matrix methods has led to development of Semi-Analytical Finite Element(SAFE) Method. In this study, rapid and accurate prediction of the propagation characteristics for guided waves in a wide range of structures has been performed by implementation of SAFE method. Damped and undamped waveguides of different shapes can be modelled. Wave propagation characteristics in both isotropic and anisotropic composite structures can also be studied. To benchmark the solution, a case study using Transfer Matrix Method (TMM) for composite plate has been evaluated. It was found that the element discretizaton plays an important role in accurate prediction of modes in SAFE method, neglecting which leads to loss of higher order modes.

Correlations for Convection in Hydrodynamically Developing Laminar Duct Flow

Abstract A generalized correlation for combined entry convection in ducts of arbitrary cross section has been developed. The correlation is constructed for the average Nusselt number using knowledge of fully developed transport constants. The general correlation reproduces the first principle solutions for the well-established round and parallel plate duct geometries to within ±5% for both constant temperature and constant heat flux wall conditions when Pr ≥ 0.7. A survey of the literature demonstrates that the new generalized correlation performs as well or better than existing correlations, which are expressed for specific geometries and wall conditions. The new correlation is generally in good agreement with the first principle solutions of less common duct geometries so long as the duct has a convective surface equal to the wetted perimeter. The new correlation is not recommended for ducts having small aspect ratios that pinch the flow when convection is prescribed by the H2 constant heat flux wall condition.

Current density in a group of long parallel conductors

An original method is proposed for the calculation of current density in a finite number of long parallel solid conductors of arbitrary cross section. Some pairs of the conductors under examination can be connected to a voltage source; they are active. The other conductors are passive. The currents, voltages and magnetic fields are assumed to be quasi-stationary and the displacement current is neglected. The permeability of the conductor material is constant and equals the vacuum permeability. No method has so far been published that would allow an exact calculation of current density in all the cases that satisfy the above assumptions. The application of the method is demonstrated by solving an example with two active conductors, one of which is of circular and the other of rectangular cross section, while a third passive conductor is of rectangular cross section.

Modeling of corrosion-mechanical behavior of multi-element metal structures of transport works in real-world conditions

The article is part of the author’s dissertation research. Multi-element metal structures are widely used in the construction of transport structures (metal spans, trusses of railway bridges, overpasses, etc.). During operation, such structures are subjected to the joint effect of loads, temperatures, and corrosive media. In accordance with this, the task of predicting the behavior of such structures seems to be relevant. It consists in the development of effective models oriented to the calculation of the bearing capacity of structural elements subjected to corrosive wear. The article discusses the most common corrosion damage to metal multi-element structures of transport facilities, the classification of corrosion processes according to the nature of the surface destruction, the main types of metal elements and bridge structures. The main parameters characterizing the corrosive wear of metal structures were determined. Ways to account for the effect of aggressive environment on metal structures, i.e. well-known mathematical models and work, in which attention is paid to the problem of corrosion, wear modeling. The process of identifying corrosion wear models (determining unknown model coefficients) is described. The system of equations for determining the coefficients of a mathematical model of corrosive wear is given. The values of the coefficients of the models used to predict the behavior of structures, with a different choice of an intermediate point are given. A statically indefinable flat five-element truss of arbitrary cross section, part of the rods of which works in tension and part in compression is considered. For this design solves the problem of assessing durability. To solve this problem, use the corrected Euler method. The obtained numerical values of the durability of trusses of five rods, depending on the lengths of the rods.

A finite element solution of earthquake-induced hydrodynamic forces and wave forces on multiple circular cylinders

This paper investigates the interaction of water with multiple circular cylinders subjected to earthquake ground motion and incident linear waves respectively. Accurate and efficient finite element models are firstly presented to calculate the earthquake-induced hydrodynamic forces and wave forces on uniform vertical cylinders with arbitrary cross-section. An elliptical boundary surrounding all the cylinders is introduced so that the whole domain is partitioned into unbounded and bounded domains. The elliptical exact absorbing boundary condition for simulating unbounded domain is derived in the elliptical coordinate system. A coupled equation is obtained by adding the impedance matrix of unbounded domain to that of bounded domain. The proposed models are furtherly used to investigate the earthquake-induced hydrodynamic forces and wave forces on pile group with two, three and four piles, where the coefficients of pile group are given. The results indicate that interaction of water with multiple cylinders is significant when the relative distance between two adjacent piles is less than three. This phenomenon depends on the relative distance between piles, width-depth ratio, wave numbers, and the direction of earthquake or incident wave. In addition, the simplified formulas of the coefficients of pile group of added mass are proposed for engineering application.

Wave diffraction from multiple truncated cylinders of arbitrary cross sections

Many marine structures are supported by piles or caissons which, from a mathematical point of view, can be assimilated to an array of truncated cylinders of arbitrary cross sections. The focus of this paper is such an array subjected to harmonic waves of small steepness. We develop an analytic method based on linear potential flow theory to solve the diffraction problem and evaluate the excitation forces and moments acting on each cylinder. The water domain is divided into the interior regions below each cylinder and an exterior region extending to infinity in the horizontal plane. A series of eigen-functions are applied to express the velocity potential in each region. The Fourier series method combined with the eigen-function expansion matching method is used to satisfy the wetted surface body conditions and continuity conditions between adjacent regions. The analytic model is validated by comparing its results with numerical modelling results and published data. It is then applied to two truncated cylinders with caisson cross sections, and results are given for the excitation forces and moments on each cylinder for different values of incident wave direction and spacing between the cylinders, and for different configurations.

Large Eddy Simulations of Turbulent Flows at Supercritical Pressure in a Vertical Heated Pipe Using Unstructured Cartesian Grids with Local Refinement

This paper presents the results of numerical simulation of turbulent flow of CO2 at supercritical pressure (SCP) in a uniform heated vertical tube using the large eddy simulation (LES) with the Smagorinsky subgrid scale (SGS) model. Unstructured Cartesian grids with local anisotropic refinement were used for modeling hydrodynamics and heat transfer in a circular pipe. Such grids unlike structured grids in cylindrical coordinates allow one to construct more optimal meshes for the LES method. In addition, such meshes allow one to simulate flows in channels of arbitrary cross-section. To verify the proposed methodology the results of the direct numerical simulation were used. Numerical simulations have been performed using the “in-house” CFD code ANES.

Scattering and Shielding Analyses of Carbon Fiber Composites-Based Cylindrical Shells Using a Multifilament Doublet Current Method

We present in this paper, a multifilament doublet current method (MFDCM) combined with the tensorial impedance boundary condition (TIBC) to simulate and analyze scattering and shielding performances of carbon fiber composite (CFC) material-based cylindrical shells. The TIBC of a shell made up with the multilayered CFC material with an arbitrary fiber orientation in each layer is introduced and derived. The MFDCM is subsequently formulated by employing the TIBC to handle numerical calculations with the anisotropic lossy material, such as a multilayered CFC material, for the first time. Monostatic and bistatic echo widths are investigated with reference to different layer numbers, fiber orientations, and incident wave polarizations. These different scenarios are also taken into consideration in the shielding effectiveness (SE) prediction. Both TE and TM modes are excited within the cylindrical shell under arbitrary incident plane waves over a high frequency range. Results are in excellent agreement with published ones. The proposed method has its merits on simplicity and conciseness. Also it can be applied to handle shells of arbitrary smooth cross sections.

A MoM solution for TM scattering by dielectric cylinders above an infinite flat surface

A simple solution method is presented for transverse magnetic plane wave scattering by a dielectric cylinder of arbitrary cross-section in front of an infinite flat dielectric surface. The interface between two semi-infinite, dissimilar half-spaces is considered by a perturbed equivalent magnetic current. Coupled integral equations are obtained from a special form of surface equivalence principles and are solved numerically by the Method of Moments. The scattered tangential electric field at interface is displayed and far-zone fields are compared to the results available in the literature.

Harmonic Vibration and Resonance Effects in the Case of Longitudinal Shear of a Hollow Cylinder with Crack

We propose an efficient analytic-numerical method for the evaluation of dynamic stresses in a hollow cylindrical body of arbitrary cross section with a through crack under the conditions of antiplane deformation. This method enables us to separately solve the integral equations on the surface of the defect and satisfy the conditions of harmonic loading on the boundary of the body. We deduce the formulas for the dynamic stress intensity factors in the vicinity of the crack and study the influence of its geometric parameters and the frequency of vibration on the indicated factors, in particular, with the evaluation of resonance frequencies.

Finite Element Analysis of Stimulated Brillouin Scattering in Integrated Photonic Waveguides

We describe a finite element algorithm for modeling stimulated Brillouin scattering in optical waveguides of arbitrary cross-section. The method allows rapid calculation of optical and elastic dispersion relations, field profiles, and gain. Additionally, we provide an open and extensible set of standard problems and reference materials to facilitate the bench-marking of our solver against subsequent tools. Such a resource is needed to help settle discrepancies between existing formulations and implementations, and to facilitate comparison between results in the literature. The resulting standardized testing framework will allow the community to gain confidence in new algorithms and will provide a common tool for the comparison of experimental designs of opto-acoustic waveguides.

Fragmentation model of a rapidly expanding ring with arbitrary cross-section

In the paper (Goloveshkin and Myagkov 2014) we proposed a two-dimensional energy-based model of fragmentation of rapidly expanding cylinder under plane strain conditions. The model allowed one to estimate the average fragment length and the number of fragments produced by ductile fracture of the cylinder. In present note we show that the proposed approach can be used to estimate the number of fragments in a problem of fragmentation of a rapidly expanding ring with arbitrary cross-section.

Wave Scattering by a Cylindrical Metasurface Cavity of Arbitrary Cross Section: Theory and Applications

This paper presents a technique, combining the integral equations (IE) and the Generalized Sheet Transition Conditions (GSTCs) with bianisotropic susceptibility tensors, to compute electromagnetic wave scattering by cylindrical metasurfaces -- forming two-dimensional porous cavities -- of arbitrary cross sections. Moreover, it applies this technique to two problems -- cloaking with circular and rhombic shapes and illusion optics with an elliptic shape -- that both validate it, from comparison with specifications used in an exact synthesis of the metasurfaces, and reveal interesting capabilities of such metasurface structures. Particularly, active cylindrical metasurfaces can perfectly cloak and hence eliminate the extinction cross section of various cylindrical shapes, and simple purely passive versions of them, practically more accessible, still perform quite good cloaking and provide remakable extinction cross section reduction.

Computation of Viscous Flow between Two Arbitrarily Moving Cylinders of Arbitrary Cross Section

An algorithm is constructed for numerical study of the plane viscous flow (in the Stokes approximation) between two arbitrarily moving cylinders of arbitrary cross section. The mathematical model of the problem is described by the biharmonic equation, which is reduced, with the help of the Goursat representation, to a system of equations for two harmonic functions. The system is solved numerically by applying the boundary element method without saturation. As a result, the desired biharmonic stream function and the velocity field are determined. Test examples are used to compare the results with well-known exact solutions for circular cylinders.

Meso-macro numerical modeling of noncircular braided composite parts based on braiding process parameters

In the past few decades, the applications of composite structures reinforced with braided preforms have been growing increasingly in various industries due to their intrinsic properties. Therefore, their mechanical properties are worth studying experimentally, analytically and numerically. In this respect, the goal of the current study is to perform a finite element modelling on biaxially and triaxially braided composites with constant arbitrary cross-section. Thus, the braid angles formed by clockwisely and counter-clockwisely moving of carriers on noncircular parts, have been initially demonstrated to be unequal, unlike in circular parts. As a result, considering a parallelogram shape for the representative unit cell (RUC), the geometrical relationships for a RUC of 2D biaxially and triaxially braided composite are derived and implemented in VUMAT subroutine. Then, after determination of 3D effective stiffness matrix for each RUC, the finite element modelling is performed to predict bending behavior of final braided composite part. In these simulations, the stiffness variation all over the part is considered and mechanical behavior of composite parts is predicted based on the initial parameters of the braiding process. The obtained results from both experimental and simulations showed an acceptable agreement.

Wave radiation from multiple cylinders of arbitrary cross sections

A semi-analytic model based on linear potential theory is developed to solve wave radiation from an array of truncated cylinders with arbitrary cross sections, free to oscillate independently in water of finite depth. The radiated velocity potential in the interior region below each cylinder and the exterior region extending to infinity are expressed as a series of eigenfunctions in the local cylindrical coordinate system using the method of separation of variables. They are solved subsequently by imposing the continuity condition of the velocity and pressure at the wetted surfaces of the cylinders and the fluid interfaces between adjacent regions. In the process, the Fourier series expansion method is applied to the terms regarding the arbitrary cross sections. The model is successfully validated through a case study with two caissons – excellent agreement is obtained with a numerical model based on the boundary element method. The semi-analytic model is then applied to explore the influence of layout (angle and spacing between the two caissons) on the added-mass and radiation damping coefficients. It is found that the hydrodynamic interaction between the two caissons can increase or decrease the value of the coefficients depending on the wave frequency.