Elliptical Cross Section Research Articles

Точные формулы напряженности магнитного поля внутри и вне однородного эллипсоидального магнетика во внешнем однородном в области магнетика поле

The direct problem of magnetostatics is considered - the calculation of the resulting magnetic field strength inside and outside a homogeneous magnet in the form of an arbitrary ellipsoid placed in the area of uniformity of the external magnetic field. The final formulas for calculating the field strength containing elementary functions or incomplete elliptic integrals are given. From them, the strength formulas for the "limiting" cases of a magnet of the specified shape are obtained – a plate of finite thickness, an infinite circular cylinder and a cylinder with an elliptical cross section, a ball. A comparison with a number of known formulas for these cases is made.

Numerical simulations of sintering coupled with heat transfer and application to 3D printing

During sintering two solids bond together and reduce the total surface to minimize their interfacial energy. It is an important phenomenon in many processes, including 3D printing, where the sintering of 3D printed layers conditions strongly the mechanical properties of 3D printed parts. Heat transfer can have a strong effect on the sintering dynamics. In amorphous materials, the viscous dissipation is increased at lower temperature, due to the higher viscosity, thus slowing down the sintering dynamics. Numerical simulations of sintering consider fluid inertia and result in a slower dynamics than the simplified analytical models often used in the literature. However, up to now, even the numerical simulations have neglected the strong viscosity gradients that can result from temperature gradients and have instead considered an uniform effective viscosity. We present a novel and generic approach to simulate the sintering coupled with heat transfer, able to consider layers with circular or elliptical cross sections and materials with a strong dependency of viscosity with temperature. We apply this approach to the sintering and cooling of two 3D printed food layers and quantify the strong viscosity gradients occurring within the sintering layers as a result of the heat transfer. The effect on the sintering and cooling dynamics of printing process parameters such as the layer size, external and nozzle temperatures and heat transfer coefficient has been investigated. Lowering the layer thickness enhances both the sintering and the cooling dynamics; whereas lower nozzle temperature slows down the sintering process due to the lower initial viscosity. The results presented in this study can help optimising 3D printing conditions or material formulation. The novel simulation approach presented can be applied to a wide range of other sintering processes where viscosity gradients cannot be neglected. • A novel approach is proposed to simulate the sintering coupled to heat transfer. • The sintering of 3d printed layers undergoing cooling was considered. • The sintering dynamics is slower than the analytical models due to the fluid inertia. • Strong viscosity gradients can exist as a result of the cooling. • Cooling after deposition slows down the sintering dynamics.

Study on the Liquid Centroid Positions of Elliptical Tank Trucks under Different Steering Conditions

There is a certain gas phase space in the filling of tank trucks, and the position of the liquid center of mass in the tank will change when the tank truck is being steered, which affects the driving stability of the vehicle. Taking the elliptical cross section of the tank truck body as the research object and based on the quasi-static mechanical model, the exact algorithm model of liquid centroid positions in different steering conditions of tank trucks have been deduced. Then, taking centrifugal acceleration, the liquid filling ratio, and the tank shape and dimension as independent variables and the centroid coordinates as the dependent variables, respectively, and applying MATLAB to describe the change of the liquid centroid position, the liquid centroid position in the elliptical tank truck is described when the elliptical tank truck is being steered. The factors affecting the steering stability of the tank truck are also analyzed. The conclusion provides a theoretical basis for further research into the running stability of tank trucks, the optimization of a tank’s shape and size, the modeling of lateral sloshing mechanics, and the software algorithm for the reconstruction of tank truck accidents.

Termite coprolites (Blattodea: Isoptera) from the Early Cretaceous of eastern Inner Mongolia, Northeast China

Well-preserved coprolites (fossil faecal pellets) were found from lignite seams of the Lower Cretaceous Huolinhe Formation at the Huolinhe Basin in eastern Inner Mongolia, Northeast China. These coprolites provide a combination of following features: oval to cylindrical shaped with six longitudinal ridges, hexagonal to elliptical cross-sections, and one blunt end and the other pointed end. According to these distinct features and their size range, the producers of these coprolites are attributed to termites. Termites were estimated to have originated in the earliest Cretaceous with an evolutionary radiation in the Early Cretaceous. The presence of wood debris in the coprolites indicate that the Early Cretaceous termites from the Huolinhe Basin had wood-feeding habits; and anatomical features displaying on the wood debris further suggest their feeding preference was coniferous wood. Besides, the results of a k-means clustering analysis performed for these coprolites indicate that three clusters with different proportion were present, suggesting the division of labor in termites’ sociality existed as early as the Early Cretaceous.

Study of gain and trajectories in elliptical electron beam considering a planar wiggler and self fields and ion-channel in free electron laser

In this study, the relativistic electron beam with an elliptical cross-section is introduced instead of the relativistic electron beam with a circular cross-section in free-electron laser (FEL). Influences of ion-channel guiding, axial magnetic field, Planar Wiggler Magnetic Field (PWMF) and self-fields on trajectories of the elliptical relativistic electron beam have also been investigated. At first, it was assumed that the PWMF is applied along the minor axis of the beam cross-section ellipse. In the second case, the PWMF was applied along the major axis of beam cross-section ellipse, the results of which were compared for the two cases. Effects of elliptical cross-section demotions and elliptical electron beam density on electron trajectory have been studied. The results were compared in the limit that the elliptical electron beam is converted to a circular electron beam, which has also been graphically presented. Moreover, a limit case in which the elliptical beam is converted into a sheet beam was studied. Furthermore, a formula was obtained for the small signal gain in a FEL with elliptical electron beam. The obtained gain for a FEL, together with a relativistic electron beam with an elliptical cross section was compared to the maximum gain for a FEL together with a relativistic electron beam with a circular cross section. It is shown that increasing the ratio of the semi-major to semi-minor axes of the beam cross-section causes the gain rate of the FEL to increases. We investigated a study of electron trajectories and dispersion equation in relativistic electron beam with elliptical cross section under the influence of electromagnetic wave wiggler and axial magnetic field considering ion-channel guiding and self fields in Appendix A.

Preformed Fragment Velocity Distribution of Elliptical Cross-section Projectile

In the field of warhead design, non-cylindrical warhead, especially elliptical cross-section warhead, has received considerable attention. In this study, the initial velocity and distribution characteristics of the preformed fragments of a columnar projectile with an elliptical cross-section were examined. To obtain the velocity distribution of the fragments in this kind of projectile, three elliptical cross-section projectiles with different geometric sizes were test based on the static detonation tests. Then, the numerical models of the elliptical cross-section projectile have been established and validated according to the experiment results. Besides, two kinds of initiation types were studied by the simulation model, and the results indicate that not only the geometric size but the initiation type do great influences on the fragment velocity distribution in the direction of the axis. An empirical model was proposed based on the fragment two-step acceleration progress, and it was in good accordance with numerical results.

Research on Buckling Properties of Toroidal Pressure Hull with Elliptical Cross-section

Research on Buckling Properties of Toroidal Pressure Hull with Elliptical Cross-section

Perfect Nonradiating Modes in Dielectric Nanofiber with Elliptical Cross-Section

Perfect Nonradiating Modes in Dielectric Nanofiber with Elliptical Cross-Section

Study on the nonlocal effects in dimers of circular and elliptical cross-sections

The nonlocal effects of dimers consisting of two cylinders are studied, whose cross-section is elliptical. Importantly, the results with dimers whose cross-section is circular are compared. For comparison, the curvature of the ellipse is set the same as the circle, and four different geometries are considered. The electric field enhancement at the gap center and the absorption spectrum of the dimers are calculated. For the second geometry, either the electric field enhancement at the gap center or the absorption spectrum is approximately calculated using the first geometry, the frequencies corresponding to the peaks are totally different. Similarly, for the fourth geometry, either the electric field enhancement at the gap center or the absorption spectrum is approximately calculated using the third geometry, the disciplines of the peak values change as the radius of curvature increases are totally different.

Elliptical kinematics of the accretive surface growth

The stresses within the soft tissue are not constant for some shell surfaces. They vary with position along the mantle edge. In this paper, we show that elliptical geometry is more convenient to describe this type of surface. Thus, we introduce the elliptical kinematics along an initial curve and construct some accretive surfaces with an elliptical cross-section. In fact, these surfaces are not only curves with an elliptical cross-sectional curve, but also the material points of the surface follow an elliptical trajectory during their formation. This situation can be easily explained through elliptical motion and elliptical quaternion algebra. Then, we investigate the relationship between velocity and eccentricity of the surfaces and compare it to the case of circular motion. Furthermore, we visualize some examples to support the theoretical results through the MAPLE program.

Scattering by Various Cylindrical Posts Located Inside a Parallel-Plate Waveguide

The electromagnetic scattering of modes propagating inside a parallel-plate waveguide by cylindrical posts of various cross-sections is studied. Exact solutions are obtained for metallic posts of the circular and elliptical cross-sections. Numerical results are displayed and discussed.

Моделирование механических и физических свойств пучка углеродных нанотрубок при поперечном сжатии с использованием цепной модели с редуцированным числом степеней свободы

The paper studies a bundle of oriented carbon nanotubes (CNTs) under the transverse loading under the plane deformation conditions within the framework of a molecular dynamics model with a reduced number of degrees of freedom. The model takes into account CNT wall stretching and bending, as well as van der Waals interactions. Each CNT is represented by a ring of atoms with two degrees of freedom in the plane of the ring. The discrete nature of the model allows describing the large curvature of the CNT wall and the destruction of CNTs at very high pressure. CNT crystal equilibrium structures are obtained under the strain-controlled biaxial loading. Separate CNTs of a sufficiently large diameter have two equilibrium states: with a round and collapsed cross section. Small-diameter CNTs in the free state can only have a circular cross section. The study identified the presence of two phase transitions observed during biaxial compression of a CNT bundle. The first transformation similar to phase transition of the second order leads to ellipticization of CNT cross sections. As a result of the second transition of the first order, bundled CNTs appear in the beam, the proportion of which gradually increases with the increase in compressive strain. The authors calculated beam elasticity constants such as Young’s moduli, shear modulus, and Poisson’s ratios. The study shows that one of the equilibrium structures (with elliptical CNT cross sections) has the property of a partial auxetic, that is, it has a negative Poisson’s ratio under uniaxial loading in a certain direction. The proposed chain model can be effectively applied to analyze physical and mechanical properties of bundles of single-walled or multi-walled CNTs under the plane deformation conditions, and after simple modifications, it can be used to similar structures made of other two-dimensional nanomaterials.

A review on acoustic performance analysis of reactive muffler

This paper highlights on acoustic performance analysis of different types of reactivemufflers. The performance of the muffler is measured in terms of insertion loss(IL), transmissionloss (TL), leveldifference (LD)or noise reduction (NR). The transmission loss (TL) is one of the important parametermostly used for acoustic performance analysis of muffler.The transmission loss of the muffler is determined with incident power by decomposition theory and transmitted power by plane wave approximation assuming anechoic termination. The exhaust noise generated by the vehicle must be within limit as prescribed by pollution control board norms to meet the customer expectations.The exhaust system noise makes a huge contribution to the exterior noise. To attenuate the noise generated from the vehicle different types of reactive muffler are used as per target frequency of engine.This paper presents a review on the acoustic performance of reactive muffler with simple expansion chamber-circular, elliptical&rectangular cross section, muffler with Extended Inlet and Extended outlet, conicalmuffler, muffler with perforated pipe, muffler with baffle plate, Plug muffler, Split stream rushing muffler and muffler with corrugated pipe.

Study on the penetration of elliptical cross-section projectiles into concrete targets: theory and experiment

To better understand the penetration mechanism of the elliptical cross-section projectile (ECSP) into semi-infinite concrete target, penetration experiments using three types of ECSPs with different shape ratios (1, 1.25 and 1.61) and with striking velocities ranged from 550 m/s to 1050 m/s were conducted. Penetration depths, penetration trajectory and mass erosion rates of the projectile were obtained after the experiments. The experiment results show that the penetration performance and ballistic stability of the ECSP are equivalent to those of the circular cross-section projectile (CCSP). Based on the theory of complex variable function and conformal transformation, a semi-analytical model which can calculate the cavity boundary stress distribution of elliptical section cavity controlled by the displacement boundary condition was established and the model was validated by comparing the model degenerate solution with Kirsch problem results. Theoretical calculation results show that the radial stress of elliptical section cavity increases progressively from the minor axis to the major axis. In addition, a formula combining with the semi-analytical theoretical model and the local interaction theory was developed. The predicted penetration depths were compared with 30 groups of experiment data with different projectile parameters and striking velocities and coincide quite well with the corresponding experimental data. Finally, the influence of shape ratio and caliber-radius-head (CRH) on the penetration performance of projectile and the application prospect of ECSPs on hypersonic weapon platform were studied.

On the shape factor in iceberg deterioration by forced convection

The present paper concerns the conventional use, in offshore ice engineering, of the convective heat transfer equation presented by White, et al. (1980) for iceberg keel degradation due to forced convection. The equation describing loss of iceberg keel mass involves a shape factor which depends on both the actual shape of the keel and on the governing convective heat transfer law applicable across the boundary layer over the keel. Two shape factor values from White et al. (1980) depend on a binary overall shape classification: tabular and non-tabular icebergs. Since the relative mass loss varies linearly with the shape factor, any uncertainty in it propagates directly into the mass loss model. The formulation proposed in White et al. (1980) is justified for very wide icebergs in a flow which can be presented as two-dimensional. However, it is not clear whether all arbitrary icebergs in arbitrary flow may be represented by the same shape factor values and how the shape factor over an ensemble of tabular or non-tabular icebergs would vary. The present work provides further insight into the quantification of the shape factor. For this, the model provided in White et al. (1980) is applied to several analytical geometrical shapes in either two-dimensional flow or three-dimensional axisymmetric flow. The iceberg keel is presented either by half of a cylinder with elliptic cross-section or by half of a spheroid, i.e., a body of revolution. The shape factor values for the analytical shapes have been found to be around 12%–20% lower than the shape factors given in White et al. (1980). The values reported here for the elliptic deep half-cylinder can be used as conservative limit for engineering estimations of the iceberg deterioration rate due to forced convection.

Three dimensional flow over elliptic cylinders arrays in octagonal arrangement

A numerical study of flow characteristics around eight elliptic cross-section cylinders in an octagonal configuration is presented. The axis ratio of elliptic cylinder is taken as 1:2. Three spacings between the cylinders (0.07 m, 0.14 m and 0.2 m), two angles of attack (α=0° and α=15°) and two Reynolds numbers (Re=4060 and Re=45800) are considered to investigate the parametric influences. The flow is modelled using three-dimensional large eddy simulation. Simulations are performed by utilizing ANSYS Fluent software. The results comprise of flow patterns and force coefficients (drag and lift). It is seen that both the drag and lift forces acting on the cylinders vary with the spacings values, angle of attack and Reynolds numbers. The lift force peaks at α=15° and Reynolds number 45800. The drag force on the upstream cylinder reaches its peak at α=0° and Reynolds number 4060. It is observed that the drag on the upstream cylinders decreases as the value of the Reynolds number increases. Contours of velocity and subgrid turbulent viscosity are also presented. Moreover, it is concluded from the present study that the effect of change in the Reynolds number on flow characteristics is more significant as compared to the change in the spacing between the cylinders.

Lateral Impact Response of Elliptical Hollow and Partially Concrete-Filled Cold-Formed Steel Columns Under Static Axial Compression Load

In recent years, the use of partially concrete-filled steel tubular (PCFST) columns has been considered due to their cost-effectiveness and reduction of structural weight in bridge piers and building columns. One of the critical discussions about these columns is their impact resistance. In this article, the dynamic response of hollow and PCFST columns with elliptical cross-section under simultaneous loading of static axial compressive load and lateral impact load is presented using finite element modeling in ABAQUS software (FEA). To ensure the accuracy of the numerical modeling, the analysis results are compared with the results of previous works. The effects of different parameters such as impact velocity, the height of the impact location, the impact direction, the impact block mass, the size and shape of the impact block are investigated in this paper. The results of the numerical analysis showed that the partially filled specimens had better performance than the hollow specimens. The changes in impact direction and impact block mass parameters have a significant effect on the failure of the columns, especially when they are under high impact velocity. Changing the impact velocity significantly affects the impact resistance of specimens. However, the size and shape of the impact block did not have a significant effect on the displacement of the column against the impact loading.

The Predictive Value of Elliptical Neck Parameters and Oversizing Ratio for Type Ia Endoleaks after Endovascular Aneurysm Repair

PurposeTo assess the predictive value of geometric parameters for type Ia endoleak (T1AEL) after endovascular abdominal aortic aneurysm repair and to determine the range of optimal oversizing ratio (OSR) in patients with an elliptical cross-section of the aneurysm neck. Materials and MethodsA propensity score-matched case-control study was conducted. Case patients were those who were diagnosed with T1AEL and control patients were those who did not have T1AEL after endovascular aneurysm repair during the period from 2012 to 2018. Geometric and oversizing parameters were compared based on both 2-dimensional (2D) and 3-dimensional measurements. Net reclassification improvement was used to measure the prediction increment of an elliptical model (major axis OSR, neck length, and severe neck angulation) compared with that of the conventional model (OSR 2D, neck length, and severe neck angulation). ResultsNineteen case patients and 111 control patients were included. The median OSR 2D of patients with T1AEL was 17% (interquartile range, 15%–22%), but the median major axis OSR was only 7% (interquartile range, 5%–12%). For the geometric parameters, axis difference had the highest area under the curve (AUC) (0.74; 95% CI, 0.63–0.84) for predicting T1AEL. For the elliptical oversizing parameters, the major axis OSR had an AUC of 0.89 (95% CI, 0.78–0.97), with a cutoff value of 13%. The elliptical model had a higher discriminating ability for T1AEL than the conventional model (AUC 0.91 vs 0.86, respectively; P = .045), with an improved reclassification ability (net reclassification improvement, 27.93%; 95% CI, 19.22%–36.64%; P < .0001). ConclusionsElliptical aneurysm neck cross-section, assessed by the difference between axis dimensions in the plane orthogonal to the centerline, was associated with an increased risk of T1AEL. The prescription of major axis oversizing of at least 13% can significantly reduce the risk of T1AEL formation in patients with an elliptical aneurysm neck.

Saint-Venant torsion of orthotropic piezoelectric elliptical bar

The object of this paper is the Saint-Venant torsion of a solid elliptical cylinder made of orthotropic homogeneous piezoelectric material. We find the shape of the homogeneous orthotropic piezoelectric elliptical cross section which does not warp under the applied torque. The sizes of the orthotropic piezoelectric solid elliptical cross section, which has the maximum value of torsional rigidity for a given cross-sectional area, are also determined.

A comprehensive study on the characterization of chaotic advection flow and heat transfer in a twisted pipe with elliptical cross-section

Chaotic advection flow is one of the most useful methods to enhance mixing and heat transfer simultaneously in the laminar flow which is generated by spatially chaotic trajectories of the fluid particles. The present study aims to characterize the behavior of chaotic advection flow and heat transfer in a twisted pipe. The considered geometry consists of three 90° bends with an elliptical cross-section; the angle between curvature planes of consecutive bends is 90°. Numerical simulations are performed for both steady-state and pulsatile (unsteady) inlet velocity conditions with the Reynolds numbers in the range of 200 ≤ Re ≤ 450, wall temperatures 310 ≤ Tw(K) ≤ 340, velocity amplitude ratios (the ratio of peak oscillatory velocity component to the mean flow velocity) 1 ≤ β ≤ 3, and Womersley numbers 2.1118 ≤ α ≤ 7.9018. Mixing and heat transfer are analyzed both qualitatively and quantitatively for various considered conditions. The results revealed that the elliptical cross-section has a considerable impact besides the chaotic configuration on mixing and heat transfer enhancement. In the steady-state flow, the desirable system efficiency can be achieved either by increasing the wall temperature or decreasing the Reynolds number. Moreover, in the pulsatile flow, the Womersley numbers in the range of 2.1118 ≤ α ≤ 3.9509 provide a favorable condition to augment the mixing and heat transfer in the twisted pipe.