Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.

An efficient locally one-dimensional finite-difference time-domain method based on the conformal scheme

An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.

The dimension split element-free Galerkin method for three-dimensional potential problems

This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

An improved three-dimensional full-vectorial finite-difference imaginary-distance beam propagation method

A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling terms （CCTs） are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.

DYNAMIC ANALYSIS OF ARREST OF BUCKLE PROPAGATION ON A BEAM ON A NONLINEAR ELASTIC FOUNDATION BY FEM

Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.

Three-Dimensional Numerical Simulation of Stably Stratified Flows over a Two-Dimensional Hill

Stably stratified flows over a two-dimensional hill are investigated in a channel of finite depth using a three-dimensional direct numerical simulation (DNS). The present study follows onto our previous two-dimensional DNS studies of stably stratified flows over a hill in a channel of finite depth and provides a more realistic simulation of atmospheric flows than our previous studies. A hill with a constant cross-section in the spanwise (y) direction is placed in a 3-D computational domain. As in the previous 2-D simulations, to avoid the effect of the ground boundary layer that develops upstream of the hill, no-slip conditions are imposed only on the hill surface and the surface downstream of the hill;slip conditions are imposed on the surface upstream of the hill. The simulated 3-D flows are discussed by comparing them to the simulated 2-D flows with a focus on the effect of the stable stratification on the non-periodic separation and reattachment of the flow behind the hill. In neutral (K = 0, where K is a non-dimensional stability parameter) and weakly stable (K = 0.8) conditions, 3-D flows over a hill differ clearly from 2-D flows over a hill mainly because of the three-dimensionality of the flow, that is the development of a spanwise flow component in the 3-D flows. In highly stable conditions (K = 1, 1.3), long-wavelength lee waves develop downstream of the hill in both 2-D and 3-D flows, and the behaviors of the 2-D and 3-D flows are similar in the vicinity of the hill. In other words, the spanwise component of the 3-D flows is strongly suppressed in highly stable conditions, and the flow in the vicinity of the hill becomes approximately two-dimensional in the x and z directions.

Alternating Group Explicit Iterative Methods for One-Dimensional Advection-Diffusion Equation

The finite difference method such as alternating group iterative methods is useful in numerical method for evolutionary equations and this is the standard approach taken in this paper. Alternating group explicit (AGE) iterative methods for one-dimensional convection diffusion equations problems are given. The stability and convergence are analyzed by the linear method. Numerical results of the model problem are taken. Known test problems have been studied to demonstrate the accuracy of the method. Numerical results show that the behavior of the method with emphasis on treatment of boundary conditions is valuable.

基于差分法的双排抗滑桩结构内力计算

为研究有连梁双排抗滑桩快速有效的内力计算模型,在对有连梁双排桩进行受力分析的基础上,将有连梁双排抗滑桩结构简化为在桩顶连系梁零弯矩处断开的2根单桩结构,通过对双排桩受力进行叠加得到前后排桩桩顶连梁传递的弯矩与剪力,基于有限差分法建立了有连梁双排抗滑桩受荷段、嵌固段全桩内力计算模型,进而对有连梁双排抗滑桩桩体内力进行了计算。同时,通过大型室内模型试验内力实测结果对所计算结果进行了对比验证。结果表明:(1)模型试验结果与所建计算模型得到的桩顶位移与桩身弯矩值吻合较好,说明简化计算模型具有一定的适用性;(2)二者的后排桩最大弯矩出现位置略有偏差,计算得到的最大弯矩位置更接近实际桩体破坏位置,进一步验证了全桩内力计算模型的可靠性;(3)所建有限差分计算模型避免了将受荷段与嵌固段利用连续条件进行迭代的复杂运算过程,大大提升了计算效率,为实际工程提供了一种快速高效的有连梁双排桩内力计算方法。

基于DNN的煤矿富水区探测反演方法研究

提出了一种基于DNN的煤矿富水区探测反演算法,该算法可以快速准确地实现煤矿富水区二维分布模型的重建。首先,利用时域有限差分方法(FDTD)获得不同分布模型的数值解;随后,依据数据样本搭建网络框架,网络的输入主要为电场分量,输出为相应的模型电导率参数。通过对神经网络进行训练,得到网络的最优系数,随后对富水区分布进行反演预测;结果表明:DNN算法在单个小目标异常体反演中,可以有效克服BP神经网络模型失效的问题,且对于多目标异常体的反演效果更加准确。另外,相同数据集下,DNN的训练耗时与预测耗时也少于BP神经网络。实验结果表明,该算法可以有效提高煤矿富水区探测效率。

Three-dimensional beam propagation method based on the variable transformed Galerkin's method

A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin's method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.

二维复杂弹性空腔的边光滑有限元建模及分析

在弹性空腔结构上敷设被动约束层阻尼(passive constraint layer damping, PCLD)可达到减振降噪的效果,针对这类复杂结构建立了二维复合弹性空腔的边光滑有限元耦合动力学模型。其中,PCLD结构采用两节点四自由度的PCLD梁单元,声场采用边光滑有限元模型。以二维全敷设复合矩形空腔模型为数值算例,以精细网格下的有限元法结果作为参考解,对比研究了在相同背景网格下,边光滑有限元法和有限元法的频响结果,发现前者更接近参考解,说明同样的计算成本下,边光滑有限元法具有更高的精确性,特别是在中频计算中。最后,分析了PCLD结构对某汽车驾驶舱的降噪效果,以及黏弹层和约束层厚度参数的影响规律,发现黏弹层厚度增大,可一定程度上降低空腔噪声,而约束层厚度增大,并不能在整个频段得到很好的降噪效果。

细观非连续介质的应力波传播研究

固体介质,如岩石、混凝土、贝壳和多孔材料等均具有细观非连续、宏观连续的特性,揭示这种细观非连续性对材料动力学响应的影响规律,对于材料设计、安全防护等具有重要意义。从广义Taylor公式出发,推导了分数阶定义下的非连续介质的一维波动方程,引入等效分数阶简化了控制方程。利用有限差分法得到了控制方程的数值解,结果表明:控制方程中的等效分数阶阶数越小,计算得到的波形衰减的程度越大。为了验证方程的可靠性,并进一步研究非连续介质的波传播规律,在考虑多孔材料、岩石等介质的结构特征的基础上,基于ABAQUS软件建立了随机多孔介质模型。分析发现:多孔介质的波传播受到介质细观非连续程度、材料属性和输入波脉宽的影响,但对应的等效分数阶阶数只与介质细观非连续程度相关,因此,其可以作为评价非连续介质动态响应的一个依据。等效分数阶阶数随着孔隙率的增加而减小,孔洞相对数量分布大致相同的情况下,其统计关系近似呈线性关系。研究结果可为研究多孔材料、贝壳等细观非连续介质的波动传播提供新思路。

某失稳边坡的稳定性及加固效果研究

以某公路失稳边坡为研究对象,采用Bishop法计算了边坡5个代表性剖面的稳定性系数,根据稳定性计算结果提出了“削坡+锚杆格构梁+排水沟+坡面绿化”的边坡治理措施。为验证治理措施的有效性,以稳定系最差的I-I’剖面为例建立三维网格计算模型,利用有限差分法计算了天然工况和暴雨工况下边坡位移量分布结果。数值模拟结果显示,边坡加固前,在天然工况和暴雨工况下的最大水平位移量分别为26.3 mm和28.9 mm,最大竖向位移量分别为19.2 mm和22.1 mm;边坡加固后在天然工况和暴雨工况下的最大水平位移分别为10.7 mm和11.5 mm,最大竖向位移分别为14.3 mm和16.8 mm。在天然工况和暴雨工况下,加固后对比加固前坡面位移分别降低了40.56%和39.83%,坡体位移分别降低了54.37%和58.13%。对比加固前和加固后的坡体位移结果可知锚杆格构梁加固有效抑制了坡体变形。加固后的坡体地表位移监测结果均在安全范围内,表明所提出的边坡加固措施对该边坡具有良好的加固效果。本研究可为类似边坡加固工程提供一定的参考。

换流变压器阀侧套管局部放电电磁波传播规律的仿真研究

换流变压器阀侧套管的主绝缘一般采用多层金属缠绕且内部填充环氧浸纸结构,其内部电磁波的传播路径以及衰减规律尚不清晰,严重制约了阀侧套管非接触式在线监测技术的发展。目前以射频、特高频法为代表的非接触式局部放电检测方法可通过研究设备内部电磁波的传播衰减规律,从而实现对设备绝缘状态的有效监测。为研究电磁波在阀侧套管内部的传播衰减规律,该文构建实际±800kV换流变压器阀侧套管时域有限差分三维模型,对局放激发的电磁波在阀侧套管内部和外部的传播路径及规律进行仿真分析。结果表明:(1)阀侧套管的外部空间中电磁波的频带范围为1.5~2.5GHz,电磁波首波出现在法兰处,并已结合实验证明此范围;(2)电磁波在阀侧套管内部的传播路径为电容屏间的环氧浸纸和外侧的SF6填充区域,电磁波在电容屏间独立传播,传出电容芯子后相互叠加,频带分布于0.75~2.5GHz;(3)电磁波在阀侧套管外部的时空分布特性具体表现为电磁波的电场强度随着时间和距离增加呈现衰减趋势,具体衰减规律与距离成非线性关系,电磁波经过电容芯子后的衰减范围为14.11~47.47dB/m,在外部空间中的衰减范围为2.74~13.07dB/m。结果可为换流变压器阀侧套管局部放电的监测与诊断提供一定技术基础。

三维表面裂纹扩展轨迹与数值仿真研究

针对三维表面裂纹扩展形态和轨迹难以预测的特点,基于ANSYS有限元分析软件,利用三维裂纹扩展仿真方法,开发三维裂纹扩展程序,研究典型的三维表面单裂纹与三维非等大共面表面双裂纹扩展轨迹,实现了任意三维多裂纹扩展轨迹的数值模拟。主要研究内容与结论如下:针对三维表面单裂纹模型,当初始裂纹形状c/a>1时,最深处的应力强度因子值大于自由表面处应力强度因子值,随着裂纹的不断扩展,前缘会渐渐趋于稳定的圆形。而对于三维非等大共面表面双裂纹,较大的裂纹扩展速率大于较小的裂纹。开始时2条裂纹均沿光滑的样条曲线扩展,后来受到另一条裂纹的影响,在彼此接近处,由于应力放大作用,此部位的应力强度因子变大,扩展速率也会高于裂纹前缘其他部位。

多级线性加载下软土一维非线性固结分析

多级加载是一种常见的加载形式,目前软土一维非线性固结方面的研究鲜有考虑多级加载。为研究多级加载下软土一维非线性固结规律,构建考虑多级线性加载和土体非线性的固结模型。利用有限差分法获得固结方程的解答,并通过与现有解答对比验证了所得解答的正确性。进而分析荷载形式和土体非线性对固结特性的影响,结果表明:与瞬时加载或单级加载相比,采用多级线性加载可以充分让土体超静孔隙水压力消散并且可以降低超静孔隙水压力峰值。第一级荷载对土体固结影响最大,工程中采用多级荷载时,应控制第一级荷载的加载量及加载速率,以避免土体发生破坏。

非定常Stokes方程的混合有限元法的高精度逼近

针对二维非定常Stokes方程,采用Taylor-Hood混合有限元法进行数值模拟。首先,利用虚功原理将方程转化为变分形式;其次,将求解区域均匀划分为有限个三角形单元,在每个逻辑单元建立与等参单元之间的联系,为速度u选取二次元基函数,为压力p选取线性基函数,从而构造空间尺度的有限元空间;然后,构造时间尺度的全离散θ-型隐格式,选取θ=0.5的Crank-Nicolson六点对称有限差分格式;最后,原问题转化为常微分方程求其数值解,并通过数值算例检验该方法的可行性与有效性。理论构造和数值结果均验证,非定常问题在空间层、时间层离散分别使用线性有限元和二次有限元计算均可得到稳定的一致收敛结果,且二次有限元的精度更高、收敛更快。为了更直观生动地展示实验结果,文章最后给出了精确解与有限元解的三维误差图。

基于电流密度模型的自然电场二维正反演研究

为推动自然电位数据解释,本文基于二维电流密度模型开展了自然电位二维正反演研究。首先,基于有限差分法实现了二维自然电位正演计算,并通过与解析解对比,其最大误差不超过2%,验证了正演算法的有效性。在此基础上,建立了关于电流密度的线性正则化反演算法,该正则化算法通过合理选用正则化因子对数据噪声具有一定适应性。通过含5%噪声的合成数据反演测试结果显示,预测数据与合成数据拟合较好。实测数据的反演测试结果显示,反演预测数据与实测数据拟合较好,验证了反演算法的有效性。该反演算法能有效恢复地下电流密度分布,对地下场源的进一步定位提供了有效信息,将有利于进一步提升自然电位数据的解释效果。