Modeling of electrical field modified by injected space charge

This paper presents the numerical solution of the coupled Poisson equation and charge conservation equation. We present an algorithm to obtain the distributions of electric field and charge density resulting from a corona discharge in the two-dimensional hyperbolic blade-ground plate configuration. We use finite elements method (FEM) to determine the potential distribution, finite volume method (FVM) and method of characteristics (MOC) to determine the distribution of charge density. The structured mesh is redefined at each iteration step to decrease artificial numerical diffusion. For solving the conservation equation, MOC with redefinition of structured mesh appears to be the best technique.     

Calculation of the ion flow field of AC-DC hybrid transmission lines

A simulation method to calculate the ion flow field of AC-DC hybrid lines is proposed. The charge simulation method (CSM) and the finite element method (FEM) are applied to calculate the electric field, while a time-dependent upwind differential algorithm is applied to calculate the migration of space charges. Furthermore, a variable time-step discretisation method is introduced to accelerate the computational process. The calculation results of ground level electric field and ion current density of a reduced-scale AC-DC hybrid line model are compared with previous experimental and calculating works. Satisfactory agreement is obtained between our calculation results and the experimental ones. As an application, the ion flow field of a hybrid 1000 kV AC/800 kV DC transmission line is simulated and analysed.     

Optimisation of an alternating current multi-conductor system

In this paper, we consider a multi conductor system for the transport of electric energy. Not only the electric field between the conductors, but also the internal field distribution inside the conductors is taken into account. Whereas the first one is governed by the Laplace potential equation, the latter one is governed by the AC diffusion equation in order to include the eddy current effects. Both sets of equations are solved using the Boundary Element Method. At last the geometrical layout of the multi conductor system will be optimized using a genetic algorithm. The criterion for the optimization process is the minimization of the global electric losses of the multi conductor system.     

Symmetric coupling of multi‐zone curved Galerkin boundary elements with finite elements in elasticity

The coupling of Finite Element Method (FEM) with a Boundary Element Method (BEM) is a desirable result that exploits the advantages of each. This paper examines the efficient symmetric coupling of a Symmetric Galerkin Multi‐zone Curved Boundary Element Analysis method with a Finite Element Method for 2‐D elastic problems. Existing collocation based multi‐zone boundary element methods are not symmetric. Thus, when they are coupled with FEM, it is very difficult to achieve symmetry, increasing the computational work to solve the problem. This paper uses a fully Symmetric curved Multi‐zone Galerkin Boundary Element Approach that is coupled to an FEM in a completely symmetric fashion. The symmetry is achieved by symmetrically converting the boundary zones into equivalent ‘macro finite elements’, that are symmetric, so that symmetry in the coupling is retained. This computationally efficient and fast approach can be used to solve a wide range of problems, although only 2‐D elastic problems are shown. Three elasticity problems, including one from the FEM‐BEM literature that explore the efficacy of the approach are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

A general 3D BEM/FEM coupling applied to elastodynamic continua/frame structures interaction analysis

This paper presents a procedure for coupling general finite element models with three‐dimensional bodies modelled by the Boundary Element Method (BEM). Shells, plates and frames are modelled by the Finite Element Method (FEM) and coupled to the BEM domain directly or by means of rigid blocks. The coupling is used for the analysis of buildings connected to half‐space by means of rigid footings, piles or plates in bending and other problems where combinations of different types of sub‐domains are required, composite domains for instance. Several numerical examples are analysed to demonstrate the robustness and accuracy of the proposed scheme. Copyright © 1999 John Wiley & Sons, Ltd.     

A coupled mechanical‐charge/dipole molecular dynamics finite element method,with multi‐scale applications to the design of graphene nano‐devices

A new Molecular Dynamics Finite Element Method (MDFEM) with a coupled mechanical‐charge/dipole formulation is proposed. The equilibrium equations of Molecular Dynamics (MD) are embedded exactly within the computationally more favourable Finite Element Method (FEM). This MDFEM can readily implement any force field because the constitutive relations are explicitly uncoupled from the corresponding geometric element topologies. This formal uncoupling allows to differentiate between chemical‐constitutive, geometric and mixed‐mode instabilities. Different force fields, including bond‐order reactive and polarisable fluctuating charge–dipole potentials, are implemented exactly in both explicit and implicit dynamic commercial finite element code. The implicit formulation allows for larger length and time scales and more varied eigenvalue‐based solution strategies. The proposed multi‐physics and multi‐scale compatible MDFEM is shown to be equivalent to MD, as demonstrated by examples of fracture in carbon nanotubes (CNT), and electric charge distribution in graphene, but at a considerably reduced computational cost. The proposed MDFEM is shown to scale linearly, with concurrent continuum FEM multi‐scale couplings allowing for further computational savings. Moreover, novel conformational analyses of pillared graphene structures (PGS) are produced. The proposed model finds potential applications in the parametric topology and numerical design studies of nano‐structures for desired electro‐mechanical properties (e.g. stiffness, toughness and electric field induced vibrational/electron‐emission properties). Copyright © 2014 John Wiley & Sons, Ltd.     

Model of corona discharge from a thin point in a space-charge-limited current regime

Exact self-similar solutions for the problem of electric field and charge density distribution in the external region of a unipolar corona discharge from a thin point emitter have been found. The obtained solutions are valid outside the framework of the traditional Deutsch approximation based on the small influence of a volume charge on the shape of equipotential surfaces. The value of a saturated discharge current is estimated assuming that the corona discharge is generated by a certain part of the point.     

Electric Potential Measurements in Gaseous Insulating Materials by Corona Probe in a Controlled Environment

The experimental determination of electric potential in gaseous insulating materials is performed using a corona probe. This method can be used to measure point values of electric potential from dc to ac at industrial frequency values. The proposed method, after an initial calibration of the probe, allows the determination of the amplitude of the electric potential at the point in space where the tip of the probe is located. The measurement is performed by adjusting the feeding potential of the probe until a complete corona suppression is obtained. To discriminate the corona effect of the probe from other possible corona sources, a device for probe current detection is proposed. The corona probe method has been verified by measuring electric potential, under both dc and 50-Hz ac conditions, in known field configurations and in natural and controlled environments. Finally, the proposed method has been applied to determine the space distribution of the electric potential around high-voltage insulating structures under dc and 50-Hz voltages in a natural environment.     

长条型非球面反射镜轻量化及支撑结构优化研究

针对轻型光学空间遥感器的长条型非球面反射镜,首先进行了轻量化研究,然后针对支撑结构的初步设计方案,采用有限元法进行了静力学分析和计算,以对镜面面型精度的影响为评价指标,进行了有效的多次迭代优化,最终确定了满足要求的支撑结构方案。     

Dynamic behavior of frame structures by boundary integral procedures

The Boundary Element Method is applied to synthesize a set of Boundary Integral Equations representing the uncoupled axial and flexural dynamic behavior of rectilinear Bernoulli–Euler beam elements in the frequency domain. In the sequence, these structural elements are coupled by the sub-region technique to model two-dimensional frame structures, in which the axial and flexural behaviors are coupled. This methodology is used to accurately recover modal data, eigenfrequencies and eigenmodes, of two frame structures. The usual Boundary Element procedure is recast to deliver simultaneously the values of variables at the element boundaries and at an arbitrary number of internal nodes. The inclusion of internal nodes allow to recover the structure eigenmodes and makes feasible the coupling of the assembled systems with a surrounding environment, for instance, an acoustic field. The results obtained are compared with a standard Finite Element eigenvalue analysis. It is shown that for increasing response frequencies, the Boundary Element scheme delivers modal data within a degree of accuracy, which is only obtained by the conventional Finite Element Method with considerable finer meshes.     

On the fluctuations in positive glow corona

Current knowledge of fluctuations in the steady glow current of the positive rod-to-plane corona at normal air density is reviewed. New work has been extended to investigate how the frequency and amplitude of these fluctuations change with the air density and humidity. The air density has been changed both by decreasing the pressure and by increasing the temperature. The pressure has been decreased down to 0.6 bar, and the temperature has been increased up to 200degC. A method is proposed for calculating the frequency of fluctuations in any rod-plane gap with known field distribution. The method is based on assessment of the space charges developed in a positive glow corona that fill not only the ionisation zone around the rod but also the inter-electrode spacing. These space charges result in an electric field that affects the frequency of these fluctuations. The calculated frequency values agree reasonably with those measured for different rod diameters     

DOMAIN DECOMPOSITION WITH BEM AND FEM

The Finite Element Method and the Boundary Element Method are two different structure analysis methods with a totally different numerical character. Therefore, it makes no sense to couple these two methods pointwise at the interface. In contrast to a lot of coupling strategies in the past, in this paper a method is constructed where we have coupling of the two different methods in a weak form. As a result we can analyse the given structure with two different grids independent of each other. On this account, we see that the big advantage of the proposed method is in its ablity to couple BEM and FEM. The construction of a robust and reliable numerical algorithm depends on the adaptive control of symmetry and definiteness of the coupling matrix. Therefore, we use an iterative method for solving the boundary integral equation by expanding the Calderon projector in a Neumann series. Numerical results show the preciseness and efficiency of the method. © 1997 John Willey & Sons Ltd.     

A computational investigation and smooth-shaped defect synthesis for eddy current testing problems using the subregion finite element method

Eddy Current Testing (ECT) plays a key role in detecting cracks and defects in conductors. The present study examines for the first time how the subregion method as an effective mathematical and computational technique can be admixed with Finite Element Method (FEM) to study multiple defects parameters for ECT issues. Separating a defect region from the entire domain in any computational technique will save both time and storage space. Examples of different types of defects are presented in this article . A tangible result of processing time reduction by 90% has been achieved which has led us to consider the subregion FEM method as an effective method in solving different Nondestructive Evaluation (NDE) problems. An agreement between our results and others using classical FEM has been achieved which could lead to using this technique in online and field testing problems. The presented subregion FEM algorithm was verified experimentally with good agreement by testing Aluminum (T6061-T6) samples with defects. A Tunneling Magnetoresistive (TMR) sensor was used to measure the component of the magnetic field from normal to the sample top surface. A major component of minimizing processing time was achieved, which could lead to using this technique in online and field testing problems.     

结构外声场分析中的无限元法

无限元法在声场分析中逐渐开始应用,本文研究了声场分析的无限元法的基本理论,比较了边界元法与无限元法的优缺点,分析了无限元法收敛精度的相关因素,通过对无限元法在结构外声场分析中实际应用的几个相关参数的计算,主要包括坐标原点的选取、无限元阶数、坐标矢量的定义等,总结了无限元法应用时重要参数的几条规律,对无限元法在声场分析领域的应用推广具有一定的理论与实用价值。     

Analysis of the Electric Field and Ion Current Density Under Ultra High-Voltage Direct-Current Transmission Lines Based on Finite Element Method

The corona generated from high-voltage direct-current transmission lines can induce the ion around the lines, which will increase the electric field and the ion current density and influence the environment nearby. Based on the finite-element method, an iterative algorithm to analyze the electric field and the ion current density at the ground level generated from the bundled conductors of bipolar lines is proposed. After the validity of the method is testified, some examples are analyzed. The method has been used to design plusmn800 kV transmission lines system in China     

Nodal sensitivities as error estimates in computational mechanics

Summary This paper proposes the use of special sensitivities, called nodal sensitivities, as error indicators and estimators for numerical analysis in mechanics. Nodal sensitivities are defined as rates of change of response quantities with respect to nodal positions. Direct analytical differentiation is used to obtain the sensitivities, and the infinitesimal perturbations of the nodes are forced to lie along the elements. The idea proposed here can be used in conjunction with general purpose computational methods such as the Finite Element Method (FEM), the Boundary Element Method (BEM) or the Finite Difference Method (FDM); however, the BEM is the method of choice in this paper. The performance of the error indicators is evaluated through two numerical examples in linear elasticity.     

The DRM‐MD integral equation method: an efficient approach for the numerical solution of domain dominant problems

This work presents a multi‐domain decomposition integral equation method for the numerical solution of domain dominant problems, for which it is known that the standard Boundary Element Method (BEM) is in disadvantage in comparison with classical domain schemes, such as Finite Difference (FDM) and Finite Element (FEM) methods. As in the recently developed Green Element Method (GEM), in the present approach the original domain is divided into several subdomains. In each of them the corresponding Green's integral representational formula is applied, and on the interfaces of the adjacent subregions the full matching conditions are imposed. In contrast with the GEM, where in each subregion the domain integrals are computed by the use of cell integration, here those integrals are transformed into surface integrals at the contour of each subregion via the Dual Reciprocity Method (DRM), using some of the most efficient radial basis functions known in the literature on mathematical interpolation. In the numerical examples presented in the paper, the contour elements are defined in terms of isoparametric linear elements, for which the analytical integrations of the kernels of the integral representation formula are known. As in the FEM and GEM the obtained global matrix system possesses a banded structure. However in contrast with these two methods (GEM and non‐Hermitian FEM), here one is able to solve the system for the complete internal nodal variables, i.e. the field variables and their derivatives, without any additional interpolation. Finally, some examples showing the accuracy, the efficiency, and the flexibility of the method for the solution of the linear and non‐linear convection–diffusion equation are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

Static boundary element analysis of piles submitted to horizontal and vertical loads

In this paper a numerical model for the analysis of the interaction between soil and piles, with or without rigid caps, subjected to horizontal and vertical loads is presented. The piles are modelled here by the Finite Element Method (FEM) and the soil by the Boundary Element Method (BEM). In this formulation the pile is represented as one finite element and the displacements and tractions along the shaft are approximated by polynomial functions. Some examples are presented and the results obtained with this formulation are very close to those obtained with other formulations and with experimental results.     

Lower bound limit analysis by bem: Convex optimization problem and incremental approach

The lower bound limit approach of the classical plasticity theory is rephrased using the Multidomain Symmetric Galerkin Boundary Element Method, under conditions of plane and initial strains, ideal plasticity and associated flow rule. The new formulation couples a multidomain procedure with nonlinear programming techniques and defines the self-equilibrium stress field by an equation involving all the substructures (bem-elements) of the discretized system. The analysis is performed in a canonical form as a convex optimization problem with quadratic constraints, in terms of discrete variables, and implemented using the Karnak.sGbem code coupled with the optimization toolbox by MatLab. The numerical tests, compared with the iterative elastoplastic analysis via the Multidomain Symmetric Galerkin Boundary Element Method, developed by some of the present authors, and with the available literature, prove the computational advantages of the proposed algorithm.