THE CLOSED-FORM SOLUTION OF VECTOR FINITE ELEMENT INTEGRAL EQUATIONS FOR THREE DIMENSIONAL ELECTROMAGNETIC ANALYSIS

In this paper,a set of closed-form formulas for vector Finite Element Method(FEM) to analyze three dimensional electromagnetic problems is presented on the basis of Gaussian quadrature integration scheme.By analyzing the open region problems,the first-order Absorbing Boundary Condition(ABC) is considered as the truncation boundary condition and the equation is carried out in a closed-form.Based on the formulas,the hybrid Expanded Cholesky Method(ECM) and MultiFrontal algorithm(MF) is applied to solve finite element equations.Using the closed-form solution,the elec-tromagnetic field of three dimensional targets can be studied sententiously and accurately.Simulation results show that the presented formulas are successfully and concise,which can be easily used to analyze three dimensional electromagnetic problems.

Slope stability analysis under seismic load by vector sum analysis method

The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.

Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method

A novel,highly efficient and accurate adaptive higher-order finite element method(hp-FEM)is used to simulate a multi-frequency resistivity loggingwhile-drilling(LWD)tool response in a borehole environment.Presented in this study are the vector expression of Maxwell’s equations,three kinds of boundary conditions,stability weak formulation of Maxwell’s equations,and automatic hpadaptivity strategy.The new hp-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation.Numerical experiments show that the new hp-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom,which provides more accurate results than those obtained using the adaptive h-FEM.The numerical results illustrate the high efficiency and accuracy of the method at a given LWD tool structure and parameters in different physical models,which further confirm the accuracy of the results using the Hermes library(http://hpfem.org/hermes)with a multi-frequency resistivity LWD tool response in a borehole environment.

内孤立波作用下缓波形立管动力特性研究

我国南海活跃着大量内孤立波,严重威胁海洋工程作业的安全。本文采用向量式有限元方法分析内孤立波作用下深海缓波形钢悬链立管动力特性,建立考虑触地段土反力和内孤立波载荷的缓波形钢悬链立管动力模型,根据mKdV方程求解内孤立波载荷,基于向量式有限元梁单元编制Fortran计算程序。分析不同入射角内孤立波作用下立管的位移极值、张力及弯矩变化趋势,并比较缓波形立管与简单钢悬链立管在内孤立波作用下的动力特性。结果表明:内孤立波作用下,缓波形钢悬链立管会有较大的位移响应,特别是顶部悬垂段会有较大的水平位移;缓波形立管比简单钢悬链立管有更显著的张力变化幅值,有更加复杂的弯矩变化趋势。

Uncertain eigenvalue analysis of the dielectric-filled waveguide by an interval vector finite element method

Eigenvalues of the dielectric-filled waveguide are of great importance to its transmission characteristic analysis and optimization design, which could be easily affected by spatially uncertain dielectric parameters. For the sake of quantifying their influence on eigenvalues of the dielectric-filled waveguide and overcoming the limitation of less samples, an interval vector finite element method(IVFEM) is proposed to acquire the lower and upper bounds of the eigenvalues with spatial uncertainty of the medium parameters. Firstly, the uncertain dielectric material properties are described by the interval field model and the corresponding interval Karhunen-Loève(K-L) approximate method. Secondly, by inserting the interval uncertainties into the constitutive relationship of the standard generalized eigenvalue equations of the dielectric-filled waveguide, an interval standard generalized eigenvalue equation is then formulated. At last, the lower and upper bounds of the eigenvalues are calculated according to the first-order perturbation method, which can be used to estimate the transmission properties of the waveguide efficiently. Three kinds of the dielectric-filled waveguides are analyzed by the proposed IVFEM and verified by Monte Carlo simulation method.

磁矢量势的全球电磁感应时间域三维有限元正演计算方法

全球电磁感应测深方法能获得地球深部电导率结构分布,目前被广泛应用于地球内部结构与热状态研究.地磁台站与地磁卫星观测的电磁感应数据为时间序列信号,在时间域分析全球电磁感应数据,特别是分析频谱极宽的磁暴脉冲响应,具有天然的优势.然而,当前的全球电磁感应数据解释技术一般在频率域进行,缺少时间域中的研究成果.为了弥补缺少时间域全球电磁感应数据解释方法的问题,本文开发了一种基于磁场矢量势的全球电磁感应时间域三维有限元并行正演求解方法,具备高精度快速计算源于地球外部时变电流源的地球感应电磁场时间序列的能力,特别适合于计算与分析频谱极宽的磁暴脉冲电磁感应时变响应.首先,建立基于磁场矢量势的全球电磁感应时间域微分控制方程,结合磁层外部电流源的物理属性建立边界条件和初始条件,从而构建出全球电磁感应时间域初始边界值问题.然后,利用四面体矢量有限元技术和无条件稳定的隐式后退欧拉公式,分别实现磁场矢量势的空间域和时间域离散,进而获得不同时刻的实系数大型有限元线性方程组,借助于高性能并行直接求解器,快速高精度地求解不同时刻的磁场矢量势与感应磁场.最后,利用理论模型验证本文算法的正确性.利用Dst磁暴环电流指数建立的时间域电流源与真实地球三维电性模型,研究"澳科一号"后续卫星200 km轨道对中国和澳大利亚下方地幔转换带高导体的探测能力,结果表明这些地幔转换带异常体在200 km卫星轨道高度能产生明显异常.综上所述,本文开发的时间域全球电磁感应方法不仅具备精确快速计算全球感应电磁场时间序列响应的能力,还能为反演与解释"澳科一号"等我国地磁卫星观测数据提供技术支持.

新型双层半插入式交替极永磁电机的解析建模

为了提高永磁电机的电磁转矩,提出一种新型双层半插入式交替极永磁电机模型。内层为交替极磁极,外层为表贴式永磁体,内外层永磁均为径向磁化。采用二维子域模型法,将求解域划分为定子槽、定子槽口、气隙、外层永磁和内层永磁共5个子域。根据拉普拉斯和泊松方程,通过分离变量法获得各子域矢量磁位的通解,再根据边界条件并求解矩阵方程,获得各子域矢量磁位的直流分量和谐波系数。以一台8极9槽新型电机为例,计算了电机的气隙磁密、空载感应电动势和电磁转矩,结果表明,在永磁用量相同的前提下,与传统的表面插入式电机相比,新型电机具有更高的电磁转矩。最后,用有限元法验证了解析模型的正确性。

采用向量式有限元的拉索参数振动模拟

拉索的参数振动主要是由连接拉索端部的结构振动引起的,当端部振动频率与拉索的自振频率满足一定倍数关系时,拉索端部激励容易激发较大拉索参数振动。由于参数振动存在复杂的非线性振动特征,传统的解析方法难以应用于实际工程。本文发展了模拟拉索参数振动的向量式有限元方法,对斜拉索在动边界条件下的振动进行分析,对比控制方程的数值解以验证结果的准确性。并基于向量式有限元模型对端部支座轴向运动激励下产生的主共振区和主参数共振区特性进行讨论,分别研究了拉索倾角、阻尼比以及风荷载协同作用对参数振动的影响。研究结果表明向量式有限元可以有效模拟复杂工况下的拉索参数振动,有利于实际工程应用。

基于第三类边界条件的大地电磁三维矢量有限元任意各向异性正演

地球内部介质的各向异性对地球物理场解译有很大影响,研究各向异性介质中大地电磁响应具有重要的意义.边界条件是影响电磁场正演精度的一个关键因素,其中第一类边界条件需要将底面边界设置在离异常体足够远的地方,面临着计算规模大、求解速度慢的问题.相比第一类边界条件,第三类边界条件具有计算规模更小、计算精度更高的优点,在三维各向同性正演中被广泛使用.然而,各向异性使得第三类边界条件理论变得更为复杂,目前尚未见到采用第三类边界条件的大地电磁三维各向异性正演.本文推导出各向异性介质中三维矢量有限元底界面的第三类边界条件,通过模型计算对算法的可靠性和精度进行了验证.结果表明,当精度相同时,第三类边界条件的计算规模可以更小;而当底界面离异常体较近时,第三类边界条件有着更高的精度.

持续受压锈蚀柱构件轴压性能预测

以往研究表明,如果柱构件在锈蚀过程中持续受压,轴压性能会发生变化。提出了单轴混凝土的受压应力-应变曲线折减模型,该模型使用四个折减系数来描述持续受压柱内部钢筋锈蚀后混凝土的力学行为。使用支持向量回归(Support Vector Regression,SVR)模型对既有试验数据进行回归,并采用十折交叉验证法评估SVR的泛化能力。将SVR预测的混凝土折减后的应力-应变关系输入受压柱有限元模型,模拟锈蚀柱构件的静力加载过程,有限元模拟结果与试验结果接近,说明提出的方法能够较好地预测持续受压锈蚀柱构件轴压性能。

FLOW AROUND A CIRCULAR CYLINDER USING A FINITE-VOLUME TVD SCHEME BASED ON A VECTOR TRANSFORMATION APPROACH

Flows around a circular cylinder displaying an unsteady vortex shedding process at the Reynolds numbers of 1000,3900 and 1×104 are studied using a finite-volume Total Variation Diminishing（TVD） scheme for solving the Unsteady Reynolds-Averaged Navier-Stokes（URANS） equations.An Elemental Velocity Vector Transformation（EVVT） approach is proposed for the local normal and tangential velocity transformation at the interfaces of main and satellite elements.The presented method is validated by comparing with the available experimental data and numerical results.It is shown that the two-dimensional TVD finite volume method with the Renormalization Group（RNG） turbulence model can be used to determine hydrodynamic forces and captures vortex shedding characteristics very well.

基于向量式有限元的岸边集装箱起重机地震响应分析

由于岸边集装箱起重机结构在地震下的运动较复杂,为了研究其在地震载荷下的跳轨行为,文中基于向量式有限元理论以典型巴拿马岸边集装箱起重机为例建立模型,提出改进的轮轨接触模型,并施加EI Centro地震波计算岸桥整机动力学特性。结果表明,地震波对岸边集装箱起重机垂直方向的位移影响更大,海侧门腿与陆侧门腿相比更难以发生抬腿,得出的结论可为今后更多的大型港口设备的抗震设计提供了思路。

磁悬浮无轴离心泵叶轮转子动力学特性

为了实现磁悬浮无轴离心泵在高速工况下的稳定悬浮,探究离心泵水力激振力对叶轮转子悬浮特性的影响.对于电机系统,采用虚位移方法构建电机处于转子偏心状态下的悬浮力数学模型并采用有限元法(FEM)进行验证;对于离心泵系统,应用计算流体力学(CFD)方法进行离心泵内部流场数值模拟,重点探究叶轮处于不同轴向、径向悬停位置下的水力激振力特性,同时探究叶轮在不同转速工况下的运行特性;结合现代控制理论中的矢量控制策略,在Matlab/Simulink环境下实现磁悬浮无轴离心泵叶轮转子的动态稳定悬浮.研究结果表明:在体积流量14 m3/h和扬程20 m的工况下,当电机在转速0~6000 r/min运行时,叶轮转子径向偏移小于250μm,远小于转子和定子间气隙4 mm,可见所建立的磁悬浮无轴离心泵系统能实现高可靠性的悬浮运行.

三腔道软体驱动器弯曲预测方法的研究

三腔道软体驱动器为软体驱动器最具应用潜力的结构特征之一,现有三腔道软体驱动器空间变形力学特性研究中,仍缺乏一个简单有效的变形预测方法。针对这一问题,在分析三腔道软体驱动器空间变形原理的基础上,提出矢量方程法;然后,基于三腔道软体驱动器的单个腔道通入气压形变效果的基础上,结合矢量方程法建立了气压与软体驱动器末端空间位置和变形轨迹的非线性数学模型;最后,开展对三腔道软体驱动器的有限元仿真及实验验证。结果表明,基于矢量方程法所建立的数学模型能够较好地预测软体驱动器空间变形轨迹,为三腔道软体驱动器空间变形提供了一种研究方法。

Impact of aperture on dynamic response of sandwich plates with aluminium face-sheets and PMI core based on an alternative finite element formulation and experiments

Apertures generally exist in the sandwich structures attributing to mechanical connection and lightweight, which might induce failure of such structures. Thus, it is required to realize the impact of aperture on mechanical behaviors of sandwich structures. If transverse shear deformations are unable to be described accurately, the reasonable prediction of dynamic behaviors of the form-core sandwich plates with apertures will meet severe challenges due to a large difference of transverse shear modulus at the adjacent layers. Thereby, such issue is less studied by using the efficient models and experimental testing, so an alternative sinusoidal-type finite element formulation is to be proposed to precisely predict dynamic response of the form-core sandwich structures with apertures. The proposed finite element formulation can meet beforehand compatible conditions of transverse shear stresses at the interfaces of adjacent laminates. In order to appraise strictly capability of the proposed model, experimental tests on natural frequencies of three groups of specimens with different apertures have been carried out. Moreover, four specimens in each group are tested to reduce the testing errors, which is less reported in the published literature. In addition,three-dimensional Finite Element Method(3-D FEM) is also selected to account for the good performance of the present model. Finally, the impact of aperture diameter on the natural frequencies of the sandwich structures is both experimentally and numerically investigated, which can serve as a reference for other researchers.

Response simulation and theoretical calibration of a dual- induction resistivity LWD tool

In this paper, responses of a new dual-induction resistivity logging-while-drilling （LWD） tool in 3D inhomogeneous formation models are simulated by the vectorfinite element method （VFEM）, the influences of the borehole, invaded zone, surroundingstrata, and tool eccentricity are analyzed, and calibration loop parameters and calibrationcoefficients of the LWD tool are discussed. The results show that the tool has a greater depthof investigation than that of the existing electromagnetic propagation LWD tools and is moresensitive to azimuthal conductivity. Both deep and medium induction responses have linearrelationships with the formation conductivity, considering optimal calibration loop parametersand calibration coefficients. Due to the different depths of investigation and resolution, deepinduction and medium induction are affected differently by the formation model parameters,thereby having different correction factors. The simulation results can provide theoreticalreferences for the research and interpretation of the dual-induction resistivity LWD tools.

基于电场矢量波动方程的三维可控源电磁法有限单元法数值模拟

从可控源电磁法的基本原理出发,推导了基于电场矢量波动方程的三维边值问题,利用广义变分原理,把边值问题转换为变分问题,并引入散度条件,避免了伪解的出现,使有限元计算在理论上更加完备.在准静态近似条件下,把水平电偶极子在空中和大地的远区电场闭合表达式作为有限元计算中的区域外边界条件,解决了边界条件加载的困难;把应用于地震模拟中的伪delta函数引入到可控源电磁法中的三维有限元模拟中,消除了源点的奇异性,提高了方程组的稳定性.通过对均匀大地和层状介质模型的模拟,检验了程序的正确性,并对典型的地质体模型进行了数值模拟,分析了其变化规律.

基于参数辨识的变压器绕组变形在线监测方法

变压器绕组变形导致的内部匝间故障已经上升至事故率的首位,对电网安全性危害极大。为此,提出一种变压器绕组变形在线监测工程方法。利用以傅里叶为理论基础的动态向量模型,在保持高精度的条件下简化变压器电磁暂态模型,并讨论不同运行状态下模型参数辨识解的个数。当变压器空载合闸时辨识出绕组电阻参数,在变压器稳态运行时利用已辨识出的电阻参数修改参数辨识模型,并辨识漏感参数。利用绕组变形与漏电感参数之间的关系,实现对变压器绕组变形在监测。建立了变压器绕组变形的仿真模型,使用有限元方法计算变压器绕组变形的短路电感值,验证了变压器绕组在线监测方法的有效性。

井环境对阵列感应测井响应的影响分析

阵列感应测井资料经常出现与井眼环境有关的质量问题.采用三维矢量有限元法分别在椭圆形井眼、仪器偏心及斜井条件下的阵列感应测井原始响应进行了模拟,并对环境校正和合成聚焦后的数据进行了分析.结果表明,线圈距较短的原始测量信号更易受井眼椭圆度、仪器偏心、泥浆电阻率及与地层电阻率反差的影响;而合成聚焦后的浅探测曲线虽然经过了环境校正和合成聚焦等数据处理,但仍然受这些因素的影响,这反映出阵列感应测井的数据处理是不完善的或采用的校正模型是理想化的;在井斜影响方面,浅探测曲线受井斜角大小影响相对较小,深探测曲线在井斜角为60°以上时受其影响较大而必须进行进一步处理.

矢量有限元素法在随钻电阻率测井模拟中的应用

在三维非均匀介质中,提出一种新型的矢量有限元素法(FEM),用来模拟随钻(LWD)电阻率测井仪器的响应。在斜井和水平井中,成层的介质空间被离散成多个四面体单元,每个四面体有6个矢量棱边元。在三维地层模型中,未知数个数可以超过一百万个,采用代数多重网格结合多重前线解法,使用个人计算机即可求解这样大规模的线性方程。通过已发表的时域有限差分法(FDTD)的数值结果和实际测井数据,对仿真结果的有效性进行了双重验证。由此开发的算法已应用到模拟井眼、偏心、倾角、围岩校正和其他一些三维的测井响应中。所提方法也能为LWD电阻率测井仪器的设计提供理论支持。