Modeling the 3-D Rotational and Translational Motion of a Halbach Rotor Above a Split-Sheet Guideway

When a Halbach rotor is simultaneously rotated and translationally moved above a split-sheet aluminum guideway a traveling time-varying magnetic field is created in the air gap. This field induces eddy currents in the guideway that can simultaneously create suspension and propulsion forces. If the rotor is offset from the center then a re-centering guidance force can also be created. As the forces are created in a highly inductive way the use of magnets circumvents any low power factor issues and enables a relatively high lift-to-weight ratio to be attained in comparison to using windings. The conductive and nonconductive regions are modeled by using a steady-state convective A- $phi$ formulation. The Halbach rotor is modeled using a 3-D analytic based model and is coupled to the conductive guideway region using boundary conditions. The steady-state rotation of the Halbach rotor is modeled by incorporating complex terms in the analytic model. The accuracy of the steady-state model is confirmed by comparing it with a 3-D transient finite-element Magsoft Flux model (with no translation) and with experimental results (with both rotation and translation). The effect of the rotor width on performance is also investigated.      

Extended displacement discontinuity Green's functions for three-dimensional transversely isotropic magneto-electro-elastic media and applications

A versatile method is presented to derive the extended displacement discontinuity Green's functions or fundamental solutions by using the integral equation method and the Green's functions of the extended point forces. In particular, the three-dimensional (3D) transversely isotropic magneto-electro-elastic problem is used to demonstrate the method. On this condition, the extended displacement discontinuities include the elastic displacement discontinuities, the electric potential discontinuity and the magnetic potential discontinuity, while the extended forces include the point forces, the point electric charge and the point electric current. Based on the obtained Green's functions, the extended Crouch fundamental solutions are derived and an extended displacement discontinuity method is developed for analysis of cracks in 3D magneto-electro-elastic media. The extended intensity factors of two coplanar and parallel rectangular cracks are calculated under impermeable boundary condition to illustrate the application, accuracy and efficiency of the proposed method.     

Calculating the Forces Created by an Electrodynamic Wheel Using a 2-D Steady-State Finite-Element Method

We present a two-dimensional complex steady-state finite-element method for calculating the lift and thrust or breaking forces created when a magnetic rotor is translationally moved and rotated over a conducting sheet. The method replaces the magnetic rotor with an equivalent current sheet by equating the current sheet's and magnet rotor's magnetic vector potentials. We validate the steady-state method by comparing the forces with transient finite-element models. The utility of this steady-state model is that it enables a study of the effects of parameter changes for such a machine to be undertaken rapidly.     

Effects of magnetic fields on cracks in a soft ferromagnetic material

The 2D problem of a soft ferromagnetic solid with a finite crack under a uniform magnetic field has been studied based on the linear theory of Pao and Yeh. Especially, in this work, the Maxwell stresses induced by the applied magnetic field are taken into account in the boundary conditions not only along the crack surfaces, but also at infinity. Based on these boundary conditions, the related boundary-value problem is solved by using Muskhelishvili’s complex variable method to obtain the complex potentials. Thus, it is found that the obtained complex potentials are constant, which indicates that both magnetic fields and stress are uniform in the solid. This implies that if only a pure magnetic field is applied, it has no effects on a crack in a soft ferromagnetic solid. To confirm this result, the same boundary-value problem is solved by the integral transform technique, which shows the same finding as that by using the complex variable method. This outcome is consistent with available experimental data but different to previously published theoretical results.     

Boundary element analysis for the three-dimensional eddy currentproblem

The numerical implementation of the boundary-element method formulated for 3-D eddy-current problems is presented. In particular, the algorithm for solving these problems, together with the formulation for the magnetic vector potential and the electric potential using the Lorentz gauge, is discussed in detail. Based on accurate calculations of the numerical solution at interior points in the neighborhood of the boundary, the revised integration method shown earlier by the authors (1988) is extended to this 3-D magnetic field analysis for the steady-state     

多晶材质电子结构及热电性能的模拟

发展了一种研究多晶体系电子态以及热电性质的计算机模拟方法。首先采用相场动力学方法模拟多晶材质图案，再利用其模型序参量构造晶界的势函数，用近自由电子近似构造体系的哈密顿量。求解薛定谔方程得到体系的本征态。通过电荷密度的分布研究电子的限域特征,分析模拟结果发现对于晶界为势垒的情况，电子的基态出现在最大晶粒中；而对于晶界为势阱的情况，电子更容易限域在多个晶粒交叉的晶界附近，由得到的本征能级和波函数可以计算出温差导致的电位差，即得到赛贝克系数随温度的变化。结果表明具有导电晶界的多晶体的赛贝克系数要高于具有导电晶粒的多晶体。     

h- and a-formulations for the time-domainmodelling of thin electromagnetic shells

Thin conductive magnetic shells are accounted for by means of two different time-domain magnetodynamic finite-element formulations, namely the magnetic field formulation and the magnetic vector potential formulation. Both approaches are an extension of the classical linear frequency-domain thin-shell approximation. The interface conditions for the magnetic field formulation and the vector potential formulation are expressed in terms of the average current density and the average flux density, respectively, together with a number of higher-order components of these quantities. The proposed time-domain thin-shell approaches are validated by means of a 3D magnetodynamic problem. The results are shown to agree well with those obtained with a fine model, whereas the computation time is significantly reduced.     

An integral-equation/singularity-method approach for 3-D electromagnetic field determination in the end region of a turbine-generator

A mathematical model using an integral-equation/singularity-method approach is derived for determining the magnetic field and electromagnetic forces induced by current-carrying conductors in a region bounded by 3-D material-body surfaces which have complex configurations. Special analytical and numerical techniques that eliminate near-field computational difficulties and bypass the cumbersome matrix manipulations required by other integral-equation approaches are described. A comprehensive computer program package has been developed using this approach for obtaining the 3-D solutions in the end region of a turbine-generator due to armature end windings. Special computational techniques for handling the complex end-winding and surface geometry are described and detailed numerical results are presented for the 3-D field solution and the forces acting on the conductors.     

Carbon Dots Strongly Immobilized onto Carbon Nanohorns as Non-Metal Heterostructure with High Electrocatalytic Activity towards Protons Reduction in Hydrogen Evolution Reaction

Highly performing, non-metal inexpensive electrocatalysts for the production of hydrogen via electrochemical water splitting are called for the replacement of current platinum-based ones. In order to speed up the electrocatalytic hydrogen evolution, abundant active sites but also efficient charge transfer is needed. In this context, 0D carbon dots (CDs) with large specific surface area, low cost, high conductivity, and rich functional groups emerge as promising non-metal electrocatalysts. Additionally, the use of conductive substrates provides an effective strategy to boost their electrocatalytic performance. Herein, the unique 3D superstructure of carbon nanohorns (CNHs), as well as without any metal content in their structure, is used to provide a conductive support of high porosity, large specific surface area, and good electrical conductivity, for the in situ growth and immobilization of CDs, via a simple hydrothermal method. The direct contact of CDs with the 3D conductive network of CNHs promotes charge transfer, accelerating hydrogen evolution. The all-carbon non-metal CDs/CNHs nanoensembleshows an onset potential close to the one of Pt/C, low charge transfer resistance, and excellent stability.     

Permeance computation using indirect boundary integral equation method

An approach using indirect boundary integral equation method is proposed to determine the permeance between ferromagnetic poles in axisymmetric and three-dimensional magnetic systems. A generalised mathematical model is given for both types of magnetic systems. It consists of Fredholm integral equations of the first kind with respect to fictitious magnetic charge density sought in the form of simple layer potential. The system of boundary integral equations is solved using the method of mechanical quadratures. The approach is implemented in its own computer code. Results are presented for axisymmetric poles of electromagnets (cylinders, cones and frustum cones) and for a three-dimensional clapper-type system. Comparisons with known formulas are made and their accuracies are estimated. The approach presented is useful at the stage of preliminary design of magnetic systems. It is also applicable to computation of capacitances and electrical conductances     

Three-dimensional nonlinear magnetic field boundary value problem and its numerical solution

An accurate solution to the nonlinear magnetic field boundary value problem which results when ferromagnetic materials are present is generally very difficult to obtain. Several computer codes based on a magnetic vector potential have been published in the literature. While those codes can be used to solve 2-dimensional problems, difficulties arise in their application to 3-dimensional problems. One difficulty is the complexity of the resulting differential equations which must be solved. This paper treats the more complex 3-dimensional solutions as derived from the concept of a scalar magnetic potential. The most desirable feature of this approach is that the magnetic material characteristics are incorporated directly into one second order nonlinear partial differential equation which can be solved on a digital computer using standard finite difference schemes. In order to add credence to the validity of the technique presented, a simple 3-dimensional magnetic field boundary value problem is posed and solved.     

Evaluation of Surface Impedance Models for Axisymmetric Eddy-Current Fields

We have investigated the range of validity of the perfect electric conductor and of the standard Rytov–Leontovich impedance boundary condition models for the analysis of axisymmetric eddy-current problems. Using these models, we derived approximate expressions for the magnetic vector potential, field quantities, Joule losses, and forces for conducting spheroids placed in external nonuniform magnetic fields produced by coaxial circular turns carrying currents varying sinusoidally with time. We compared our numerical results for the magnetic field intensity at the conductor surface, power losses, and forces (for both prolate and oblate spheroidally shaped conducting objects) with the results from analytical expressions obtained by applying the exact boundary conditions. While the simpler perfect conductor model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained by using the standard surface impedance model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis for electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis for Joule losses.      

An ancillary boundary integral equation for magnetostatic analysis

The boundary element method (BEM) has been established as an effective means for magnetostatic analysis. Direct BEM formulations for the magnetic vector potential have been developed over the past 20 years. There is a less well-known direct boundary integral equation (BIE) for the magnetic flux density which can be derived by taking the curl of the BIE for the magnetic vector potential and applying properties of the scalar triple product. On first inspection, the ancillary boundary integral equation for the magnetic flux density appears to be homogeneous, but it can be shown that the equation is well-posed and non-homogeneous using appropriate boundary conditions. In the current research, the use of the ancillary boundary integral equation for the magnetic flux density is investigated as a stand-alone equation and in tandem with the direct formulation for the magnetic vector potential.     

Effective magnetization and forces due to eddy currents

A simple method for evaluating the effective magnetization due to eddy currents excited by AC magnetic fields in finite conductive objects is presented. The values of magnetization enable the estimation of the forces exerted on the object by the effect of eddy currents. The method relies on assuming a similarity between eddy current magnetization and the magnetization due to diamagnetic effects, which is easier to evaluate. Its validity is checked by comparing results from the eddy current forces with data obtained from conventional but much more complicated methods or from experimental data. The approach may be useful for evaluating the eddy current losses in finite conductive objects excited by AC magnetic fields or the influence of small conductive objects on AC excitation coils. The method combines techniques related to the conventional evaluation of eddy currents in certain 1-D geometries with techniques that approximate behavior of the AC magnetic field in finite objects in a way similar to that followed when the magnetic forces acting on a diamagnetic object are calculated     

Associative Liquid-In-Liquid 3D Printing Techniques for Freeform Fabrication of Soft Matter

Shaping soft materials into prescribed 3D complex designs has been challenging yet feasible using various 3D printing technologies. For a broader range of soft matters to be printable, liquid-in-liquid 3D printing techniques have emerged in which an ink phase is printed into 3D constructs within a bath. Most of the attention in this field has been focused on using a support bath with favorable rheology (i.e., shear-thinning behavior) which limits the selection of materials, impeding the broad application of such techniques. However, a growing body of work has begun to leverage the interaction or association of the two involved phases (specifically at the liquid–liquid interface) to fabricate complex constructs from a myriad of soft materials with practical structural, mechanical, optical, magnetic, and communicative properties. This review article has provided an overview of the studies on such associative liquid-in-liquid 3D printing techniques along with their fundamentals, underlying mechanisms, various characterization techniques used for ensuring the structural stability, and practical properties of prints. Also, the future paths with the potential applications are discussed.     

Verformungsanalyse elektrisch leitender metallischer Bauteile bei Magnetimpulsbearbeitung

In the present study the deformation of conductive metallic systems under the action of electromagnetic fields is investigated. For this purpose, a variational formulation is introduced. The coupling of the propagation of electromagnetic fields and the deformation is taken into account by the introduction of electromagnetic forces. The suggested model allows the numerical analysis of the deformation of electrically conductive metallic systems under magnetic pulse processing.     

Free Vibration of the Axially Loaded System of Two Beams Connected by a Two-Directional Viscoelastic Interlayer

In this paper, the analytical method has been used for solving a problem of free vibration with clamping of an axially loaded sandwich beam. The sandwich beam consists of two external layers connected by a viscoelastic two-directional Winkler interlayer. The upper external layer is described by the Bernoulli–Euler model, which is loaded by a constant axial force. The lower external layer is modeled as the Timoshenko model. The phenomenon of free vibration has been described using a homogenous system of conjugate partial differential equations. After separation of variables in the system of differential equations, the boundary problem has been solved and three complex equations for the definition of frequency and modes of free vibration have been obtained. The free-vibration problem for arbitrarily assumed initial conditions and various axial forces has been considered.     

Mesh independent analysis of shell‐like structures

Mesh independent analysis is motivated by the desire to use accurate geometric models represented as equations rather than approximated by a mesh. The trial and test functions are approximated or interpolated on a background mesh that is independent of the geometry. This background mesh is easy to generate because it does not have to conform to the geometry. Essential boundary conditions can be applied using the implicit boundary method where the trial and test functions are constructed utilizing approximate step functions such that the boundary conditions are guaranteed to be satisfied. This approach has been demonstrated for two‐dimensional (2D) and three‐dimensional (3D) structural analysis and is extended in this paper to model shell‐like structures. The background mesh consists of 3D elements that use uniform B‐spline approximations, and the shell geometry is assumed to be defined as parametric surfaces to allow arbitrarily complex shell‐like structures to be modeled. Several benchmark problems are used to study the validity of these 3D B‐spline shell elements. Copyright © 2012 John Wiley & Sons, Ltd.     

Approximating three-dimensional steady-state potential flow problems using two-dimensional complex polynomials

A new advance in the Complex Variable Boundary Element Method, or CVBEM, is its extension to three-dimension (3D). This advance breaks down the barrier of limiting CVBEM models to two-dimensional (2D) problems, and also opens the door to solving 3D potential problems with other 2D numerical analogs. In this paper, a 3D analog is developed using 2D basis functions of the complex analytic polynomial type. Thus, 2D complex polynomials are being applied to 3D potential problems. This new advance may be of interest to those involved in applied mathematics, complex variables, boundary elements, and numerical solution of partial differential equations of the Laplace of Poisson type.     

STUDY ON PRODUCTIVITY OF HORIZONTAL WELLS WITH SEGMENTAL PERFORATION BASED ON PSEUDO STEADY-STATE FLOW

分段射孔是一种常用的水平井射孔工艺。由于多个射孔段的存在,使得水平井每个射孔段的产能预测变得十分复杂。用Fourier正弦变换、势的叠加原理、三角函数变换、渐进分析求解了圆形封闭地层水平井三维拟稳态渗流问题,得到了水平井的均匀流量产量模型。通过与直井产能对比,求得水平井稳态当量井径,再利用压降叠加原理建立了分段射孔水平井产能计算方法。研究表明,水平井垂向位置影响当量井径;分段射孔时,相同射孔长度下,端部(趾端,跟端)产量最大,而中部井段产量最小;多个射孔段同时投产时,射孔长度对射孔段产量的影响较射孔间距大。此方法可以用于确定水平井射孔段分段产量。