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.

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.

Numerical simulation of three-dimensional fracturing fracture propagation in radial wells

A fracture propagation model of radial well fracturing is established based on the finite element-meshless method.The model considers the coupling effect of fracturing fluid flow and rock matrix deformation.The fracture geometries of radial well fracturing are simulated,the induction effect of radial well on the fracture is quantitatively characterized,and the influences of azimuth,horizontal principle stress difference,and reservoir matrix permeability on the fracture geometries are revealed.The radial wells can induce the fractures to extend parallel to their axes when two radial wells in the same layer are fractured.When the radial wells are symmetrically distributed along the direction of the minimum horizontal principle stress with the azimuth greater than 15,the extrusion effect reduces the fracture length of radial wells.When the radial wells are symmetrically distributed along the direction of the maximum horizontal principal stress,the extrusion increases the fracture length of the radial wells.The fracture geometries are controlled by the rectification of radial borehole,the extrusion between radial wells in the same layer,and the deflection of the maximum horizontal principal stress.When the radial wells are distributed along the minimum horizontal principal stress symmetrically,the fracture length induced by the radial well decreases with the increase of azimuth;in contrast,when the radial wells are distributed along the maximum horizontal principal stress symmetrically,the fracture length induced by the radial well first decreases and then increases with the increase of azimuth.The fracture length induced by the radial well decreases with the increase of horizontal principal stress difference.The increase of rock matrix permeability and pore pressure of the matrix around radial wells makes the inducing effect of the radial well on fractures increase.

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 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.

Dynamic Analysis and Numerical Simulation of a Kind of Arrestor Arresting Buckle Propagation by FEM

For exact estimation of efficiency of a buckle arrestor, it is necessary to take the effect of structural inertia into account in the analysis of buckle propagation on elastic structures after meeting arrestors. Under this consideration, this paper deals with the dynamics of buckle arrest and its numerical simulation on the basis of the beam system model used by Chater and Hutchinson (1983). The FEM combined with an improving are-length control method is adopted to solve the dynamic equations describing the arresting of buckle propagation. A new group of parameters for arrestor design which differs greatly from that by the quasi-static analysis is obtained. The present results support the conclusion that the inertia of the beam cannot be neglected in such analysis.

Numerical study of detonation shock dynamics using generalized finite difference method

The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.

Solution of a problem of thermal stresses in a non-homogeneous thermoelastic infinite medium of isotropic material by finite difference method

The present work deals with a new problem of thermoelasticity for an infinitely long and isotropic circular cylinder of temperature dependent physical properties.The inner and outer curved surfaces of the cylinder are subjected to both the mechanical and thermal boundary conditions.A finite difference model is developed to derive the solution of the problem in which the governing equations are uncoupled linear partial differential equations.The transient solution at any time can be evaluated directly from the model.In order to demonstrate the efficiency of the present model we consider a suitable material and obtain the numerical solution of displacement,temperature,and stresses inside the cylinder for the homogeneous-dependent material properties of the medium.The results are analyzed with the help of different graphical plots.

FINITE ELEMENT MODELLING OF COMPLEX 3D STATIC AND DYNAMIC CRACK PROPAGATION BY EMBEDDING COHESIVE ELEMENTS IN ABAQUS

This study proposes an algorithm of embedding cohesive elements in Abaqus and develops the computer code to model 3D complex cragk propagation in quasi-brittle materials in a relatively easy and efficient manner. The cohesive elements with softening traction-separation relations and damage initiation and evolution laws are embedded between solid elements in regions of interest in the initial mesh to model potential cracks. The initial mesh can consist of tetrahedrons, wedges, bricks or a mixture of these elements. Neither remeshing nor objective crack propagation criteria are needed. Four examples of concrete specimens, including a wedgesplitting test, a notched beam under torsion, a pull-out test of an anchored cylinder and a notched beam under impact, were modelled and analysed. The simulated crack propagation processes and load-displacement curves agreed well with test results or other numerical simulations for all the examples using initial meshes with reasonable densities. Making use of Abaqus＇s rich pre/post- processing functionalities and powerful standard/explicit solvers, the developed method offers a practical tool for engineering analysts to model complex 3D fracture problems.

Conjugate Gradient Method to Solve Fluid Structure Interaction Problem

In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for the fluid. Conjugate gradient method gives suitable numerical results according to some papers.

A sweeping preconditioner for Yee＇s finite difference approximation of time-harmonic Maxwell＇s equations

This paper is concerned with the fast iterative solution of linear systems arising from finite difference discretizations in electromagnetics. The sweeping preconditioner with moving perfectly matched layers previously developed for the Helmholtz equation is adapted for the popular Yee grid scheme for wave propagation in inhomogeneous, anisotropic media. Preliminary numerical results are presented for typical examples.

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。

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。

基于数值模拟的高边坡加固效果分析

福州市某高边坡削坡后存在安全隐患问题,需要对其进行加固处理并验证加固方案的效果。在对该高边坡进行稳定性分析的基础上,选取一个代表性剖面构建边坡三维网格模型,采用有限差分法分析边坡加固前后在天然工况和暴雨工况下的塑性区和位移量。在天然工况和暴雨工况下,边坡加固后的塑性区面积相比加固前有明显的减少;天然工况下边坡加固前和加固后的最大位移量分别为29.6 mm和10.8 mm,暴雨工况下边坡加固前和加固后的最大位移量分别为54.9 mm和27.9 mm;坡面6个监测点加固后的位移量相比加固前的位移量均大幅下降。数值模拟结果表明,格构梁加锚杆的加固方案可有效抑制边坡变形,提升边坡整体稳定性。该研究对类似高边坡加固方案设计和验证具有一定参考价值。

用UDEC模拟爆炸波在节理岩体中的传播

离散元程序 UDEC与有限差分程序 AUTODYN- 2 D相结合 ,用于模拟节理岩体中爆炸波的传播和节理对波传播的影响 .AUTODYN- 2 D用来模拟地下爆炸过程及生成的爆炸波 ,并输入到 UDEC,然后用 UDEC来模拟爆炸波在节理岩体中的传播 .研究表明 ,UDEC与 AUTO-DYN- 2

地震波传播的哈密顿表述及辛几何算法

地震波传播过程本质上是能量在传播过程中逐步损耗直至殆尽的过程 ,而在实际应用中 ,常在无能量损耗假设下 ,用弹性波动方程或标量波动方程描述它 .在哈密顿 (Hamil ton)体系表述下 ,地震波传播过程即为一个无限维的哈密顿系统随时间的演化过程 .若不计能量损耗 ,波场演化过程实质上为一个单参数连续的辛变换 ,因而对应的数值算法应为辛几何算法 .本文首先从地震波标量方程出发 ,给出哈密顿体系下地震波传播的表述 ,即任意两个时刻的波场是通过辛变换联系起来的 .随后 ,把波场在时间和相空间离散化后 ,给出了用于波场计算的一些辛格式 ,如显式辛格式、隐式辛格式和蛙跳辛格式 .并进一步讨论了有限差分格式和辛格式的异同 .然后 ,应用显式辛格式和同阶的有限差分方法给出了同一理论速度模型下的波场和Marmousi速度模型下的单炮记录 .数值结果表明 ,辛算法是一类可行的波场模拟的数值算法 .在时间步长较小时 ,有限差分方法是辛算法的一个很好近似 .文中的理论和方法 。