Finite element analysis of 3-D eddy currents

The authors review formulations of three-dimensional (3-D) eddy current problems in terms of various magnetic and electric potentials. The differential equations and boundary conditions are formulated to include the necessary gauging conditions and thus to ensure the uniqueness of the potentials. Different sets of potentials can be used in distinct subregions, thus facilitating an economic treatment of various types of problems. A novel technique for interfacing conducting regions with an electric vector and a magnetic scalar potential to eddy-current-free regions with a magnetic vector potential is described. Finite-element solutions to several large eddy-current problems are presented     

Transient 3D eddy currents using modified magnetic vectorpotentials and magnetic scalar potentials

A package named VECTOR for solving 3-D eddy current problems is presented. The package is a developmental version of the commercial package CARMEN and in the same way solves the vector diffusion equation, involving a modified vector potential, within conductors and the scalar Poisson equation, using a magnetic scalar potential, in non-eddy-current regions. It has been shown that this set of equations yields a unique solution for both the magnetic vector potential (and hence the currents) and the fields (which are derived from the magnetic potentials by differentiation). This package has recently been extended to solve transient problems, using simple time-stepping techniques. Some results using the package for problems with analytic solutions are given     

The PE2D package for transient eddy current analysis

The PE2D package is a suite of programs for solving, by the finite element method, the electro-magnetic and electrostatic problems which are described by the Laplace, Poisson, Helmholtz or diffusion equation in two dimensions. This paper describes the package and illustrates its use in solving transient eddy-current problems.     

Finite element modeling of absolute eddy current probe signals

Finite element analysis techniques are applied to the problem of predicting signals from an absolute eddy current probe in the tube sheet region of a PWR steam generator for the purpose of optimizing the probe coil geometry and determining the feasibility of using such a probe to characterize the condition of the tube and tube sheet crevice.     

Finite element modelling of closed cracks in eddy current testing

The eddy current inspection of small fatigue cracks in Ti–6AL–4V is evaluated in both a finite element model and experiments. The crack was created in a fatigue process and an eddy current measurement was carried out as the resulting crack was subjected to different levels of static load. The signal showed a strong dependency of the time between the creation of the fatigue crack and the eddy current measurement. This dependency is proposed to be related to oxides forming on the crack faces. The oxide is favourable for the detection of fatigue cracks. The narrow width of the fatigue crack is important to consider in eddy current inspection and as static loads are applied across the crack faces, electrical connections arise within the crack, which has a strong influence on the eddy current signal. Four different models of the contact behaviour were implemented within the finite element model. It is shown that the electrical connections that arise within small fatigue cracks, as well as the influence from the narrow opening as tensile loads are applied, can be predicted by a finite element model of the eddy current method.     

3D机织复合材料多向接头有限元分析

为了探究3D机织复合材料桁架接头的机械性能,采用有限元软件ANSYS对3D机织复合材料多向接头所在桁架总体进行有限元模拟,模拟中根据纤维走向对多向接头不同轴向圆管建立相应坐标系,并赋予材料属性,使用MPC多点约束法施加载荷.求解分析后结果表明:模拟结果与实测结果中最大应变的位置与数值基本吻合,确定了模拟的有效性;将最大应力与破坏应力对比发现接头在当前载荷下可能发生轻微破坏,破坏位置应位于副管顶部;通过模拟判断了实测中发生轻微响声的原因;将4种角联锁结构的多向接头模拟结果对比发现,带有衬经结构的复合材料为多向接头最佳材料.此次模拟补充了实测中无法得到的数据,为接头的优化设计和实际使用提供一定的帮助.     

Finite element modelling of tow geometry in 3D woven fabrics

A finite element model of a 3D woven angle interlock fabric undergoing compaction based on the multi-element digital chain technique has been developed. The aim was to create a kinematic model to predict the internal architectural features in a commercial off-the-shelf code. A statistical analysis of yarn crimp and resin channel size was carried out on sections from the model at increasing levels of compaction and compared to laboratory-manufactured samples with the same weave style. Results show a good correlation between overall mean crimp values in the warp, weft and weaver yarns as well as reasonable accuracy in the frequency distribution of local crimp angles. The trend in resin channel size with respect to increasing levels of compaction was also good but significant discrepancies in the absolute dimensions of a resin channel were present due to limitations in controlling the yarn bundle internal interactions in the model.     

Finite element modelling and physics of remote field eddy currentresponses for axially aligned cracks

A simplified physical model for two-dimensional (2-D) finite element analysis of axially aligned crack responses for the remote field eddy current (RFEC) technique is proposed. Two formulations are applied to model the problems. Reasonable agreement between calculated results and some preliminary experimental results is achieved. A hypothesis, based on the physical model, is presented. It explains the RFEC signals from axially aligned cracks and makes some predictions of possible features for future verification     

A normalization scheme for comparing eddy current differential probe signals using a finite element formulation

A first-order finite element formulation is used to model an eddy current differential bobbin coil probe scanning a tube with axisymmetric flaws. A multifrequency signal normalization scheme is developed to allow direct comparison between experimental measurements of the differential bobbin coil probe signal and finite element calculations of the probe coil impedance. Results demonstrate that both magnitude and phase of the differential bobbin coil impedance are useful in characterizing flaws in tubing for multifrequency scans.     

Intelligent sensing for non-destructive testing using eddy currents

When a metallic surface is tested by the eddy-current technique, defects produce events on the electrical signal coming from the sensor whose particular signature is a function of different factors such as the shape, size and position of any defects. Thanks to the introduction of modern digital signal processing methods, the quality of detection of events in the signal may be appreciably improved. The reliability of the decision mechanism, entrusted with reducing non-detection and limiting false alarms, is then increased and allows consideration of automatic testing. The work presented here was done jointly by the Institut de Recherches de la Sidérurgie Française (IRSID) of the Usinor-Sacilor group and the aboratoire d' Automatique et de Recherche Appliquée (LARA) of the Centre de Recherche en Automatique de Nancy (CRAN).     

朗之万换能器振动模式的有限元三维分析

本文主要运用3D有限元分析方法来分析应用于水下声纳的朗之万换能器的振动模式,频率从40KHz-160KHz.限于篇幅,本文只从理论计算上分析了以下三种情况即换能器总长度大于其直径;换能器总长度与其直径相当;换能器的总长度小于其直径.计算结果显示出换能器纵向振动与径向振动两种模式的情况以及其耦合情况,并且表明在实际应用中可以采用激励压电片的直径大于或等于换能器的纵向长度的这种情况.     

Meshless method for numerical modeling of pulsed eddy currents

Meshless methods have attracted great attention due to their advantage in geometric representation. In this paper, a meshless element-free Galerkin method is applied for the first time to solve pulsed eddy-current problems. Detailed mathematical derivations and the numerical implementation are discussed. The model is validated against analytic solutions for two canonical cases.     

Inversion scheme based on optimization for 3-D eddy current flaw reconstruction problems

An inversion scheme based on first-order optimization is developed for eddy current flaw reconstruction problems with arbitrary specimen, probe and defect shapes. As an essential component of this scheme, a new 3-D forward solver is introduced for the purpose of rapid flaw signal prediction in the inversion loop. This forward solver, whose numerical formulation is basically a discrete reaction variational technique, relies on a reaction data set in the form of an equation system, constructed before entering the inversion loop by a finite element electromagnetic field simulator. The anomalous region is subdivided into small subregions, called flaw cells, and a flaw is represented by a complete set of current dipole density pulses defined in these flaw cells. The coefficient matrix of the equation system consists of reactions between the dipole current density pulses while the elements of the right-hand-side vector are reactions between the pulses and the probe coils. The gradient of the error function, which represents the sensitivity with respect to the flaw parameters, can also be computed quickly from the same pre-calculated reaction dataset, thereby ensuring the efficient implementation of a first-order optimization algorithm. In order to avoid being trapped in a local minimum of the error function, good initial flaw estimates are generated by a neural network signal processing system developed recently by the authors. Various reconstruction examples demonstrate the efficiency of the reconstruction system.     

三维整体中空复合材料压缩性能的有限元分析

利用有限元软件ANSYS, 建立了三维整体中空复合材料结构模型, 进行压缩力学性能分析。利用该模型, 以芯材高度、 芯材密度和材料特性(弹性模量)为参数, 详细研究了其对材料压缩性能的影响, 并对其影响特征进行了分析和讨论。结果表明: 三维整体中空复合材料在受压状态下, 芯材与上下面板相接处应力最大, 最容易发生压缩破坏; 材料的压缩性能随着芯材密度、 材料弹性模量的增加而提高, 随着芯材高度的增加而下降。该研究结果可为整体中空复合材料的结构优化提供参考。      

Finite element analysis of transient free convection flow over vertical plate

A finite element method is used to study the heat-transfer response of an incompressible, laminar, transient free convection flow over a semi-infinite vertical plate. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved using the Newton–Raphson iteration. The resulting first-order ordinary differential equations with respect to time are solved using the implicit Euler scheme. Numerical results for the details of the velocity and temperature contours and profiles as well as heat transfer rate in terms of Nusselt number which are shown on graphs have been presented.     

Finite element modeling of transient ultrasonic waves in linear viscoelastic media

Linear viscoelasticity offers a minimal framework within which to construct a causal model for wave propagation in absorptive media. Viscoelastic media are often described as media with `fading memory,' that is, the present state of stress is dependent on the present strain and the complete time history of strain convolved with appropriate time-dependent shear and bulk stress relaxation moduli. An axisymmetric, displacement-based finite element method for modeling pulsed ultrasonic waves in linear, homogeneous, and isotropic (LHI) viscoelastic media is developed that does not require storage of the complete time history of displacement at every node. This is accomplished by modeling stress relaxation moduli as discrete or continuous spectra of decaying exponentials and relaxation times. Details of the construction and computation of the time-dependent stiffness matrix are presented. As an application of the finite element method, a finite number of exponentials (amplitudes and relaxation times) are employed to represent a typical model for a continuous relaxation spectrum. It is demonstrated that a small number of discrete exponentials are required to model ultrasonic wave propagation of a typical band-limited pulse in a model material accurately. Previous work has shown this model to be consistent with other analytic models for wave propagation in viscoelastic media