Flexural and eigen-buckling analysis of steel-concrete partially composite plates using weak form quadrature element method

Flexural and eigen-buckling analyses for rectangular steel-concrete partially composite plates(PCPs)with interlayer slip under simply supported and clamped boundary conditions are conducted using the weak form quadrature element method(QEM).Both of the derivatives and integrals in the variational description of a problem to be solved are directly evaluated by the aid of identical numerical interpolation points in the weak form QEM.The effectiveness of the presented numerical model is validated by comparing numerical results of the weak form QEM with those from FEM or analytic solution.It can be observed that only one quadrature element is fully competent for flexural and eigen-buckling analysis of a rectangular partially composite plate with shear connection stiffness commonly used.The numerical integration order of quadrature element can be adjusted neatly to meet the convergence requirement.The quadrature element model presented here is an effective and promising tool for further analysis of steel-concrete PCPs under more general circumstances.Parametric studies on the shear connection stiffness and length-width ratio of the plate are also presented.It is shown that the flexural deflections and the critical buckling loads of PCPs are significantly affected by the shear connection stiffness when its value is within a certain range.

The weak form market efficiency investigation of American, European and Asian stock markets

This paper investigates the empirical validity of the Weak Form Efficient Market Hypothesis for American, European and Asian stock markets. Random Walk Hypothesis is used to prove weak form efficiency in American, European and Asian stock indices. ADF and PP Unit Root Tests have been used to test unit root in time series of daily data of American, European and Asian stock indices. Results show that sample of stock markets are weak-form efficient in terms of the Random Walk Hypothesis.

Planar Weak Form Quadrature Beam Elements Based on Absolute Nodal Coordinate Formulation: A Structural Mechanics Approach

A planar nonlinear weak form quadrature beam element of arbitrary number of axial nodes is proposed on the basis of the absolute nodal coordinate formulation (ANCF). Elastic forces of the element are established through geometrically exact beam theory, resulting in good consistency with classical beam theory. Two examples with strong geometrical nonlinearity are presented to verify the effec-tiveness of the formulation.

Is the“Weak Form”of CLT Being Adoptedin China ?

This paper, based on the hi sto rical background of CLT(communicative language teaching), mainly addresses the k ey issues concerning the weak form of CLT. This is an area few people have paid attention to in the past few years in China. Therefore, its main concepts and f e atures are discussed with relevance to literature and an empirical study on four novice teachers of English. Finally, the research shows that the weak form of CLT is being conducted in Chinese secondary schools.

Analysis of thin plates by the weak form quadrature element method

The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the par- tial derivatives at the integration sampling points are then approximated using differential quadrature analogs. Neither the grid pattern nor the number of nodes is fixed, being adjustable according to convergence need. The C~ continuity conditions char- acterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined. Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method. It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.

Nonlinear Bifurcation and Post-buckling Analysis of Cylindrical Composite Stiffened Laminates Based on Weak Form Quadrature Element Method

This paper presents a weak form quadrature element formulation in the analysis of nonlinear bifurcation and post-buckling of cylindrical composite stiffened laminates subjected to transverse loads.A total Lagrangian updating scheme is used in combination with arc-length method,and the branch-switching method is adopted to identify the whole post-buckling procedure of the laminates.The formulation of the shell model and beam model are based on the basic concept of Ahmad.The coincidence of discrete nodes and integration points in quadrature element endows it with compactness and conciseness in the nonlinear buckling analysis of the cylindrical stiffened laminates.Several numerical examples are firstly presented to verify the effectiveness and accuracy of present formulation.Parametric studies on the effects of the height-to-breadth ratio,lamination schemes,positions,distribution,number of the stiffeners on the bifurcation and post-buckling behavior are performed.

Weak WT_2-class of differential forms and weakly A-harmonic tensors

In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.

Second-Order Finite Difference/Spectral Element Formulation for Solving the Fractional Advection-Diffusion Equation

The main aim of this paper is to analyze the numerical method based upon the spectral element technique for the numerical solution of the fractional advection-diffusion equa-tion.The time variable has been discretized by a second-order finite difference procedure.The stability and the convergence of the semi-discrete formula have been proven.Then,the spatial variable of the main PDEs is approximated by the spectral element method.The convergence order of the fully discrete scheme is studied.The basis functions of the spectral element method are based upon a class of Legendre polynomials.The numerical experiments confirm the theoretical results.

A Study of the Elastodynamic Problem by Meshless Local Petrov-Galerkin Method Using the Laplace-Transform

The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial differential equation and using the moving least square (MLS) method to construct shape function. This method is a more effective alternative than the finite element method for computer modelling and simulation of problems in engineering;however, the accuracy of the present method depends on a number of parameters deriving from local weak form and different subdomains. In this paper, the meshless local Petrov-Galerkin (MLPG) formulation is proposed for forced vibration analysis. First, the results are presented for different values of as, and aq?with regular distribution of nodes nt=55. After, the results are presented with fixed values of?as?and aq?for different time-step.

广义弱形式自由单元法

自由单元法(FrEM)是一种单元配点法,吸收了有限元法等参单元的插值稳定性与无网格法使用灵活的优点,具有稳定性好和灵活性高的性能.FrEM在每个配置点只需要一个通过自由选择周围节点而形成的独立的等参单元,不需要考虑单元之间节点的相互连接关系,这种自由性使得人们可以按照学科性质形成所需要的单元,因而FrEM既适用于固体力学,也适用于流体力学问题的求解.然而,FrEM所用单元需要至少有一个内部节点(用于方程的配点),以致有限元法中单元节点相连的网格不能在FrEM中直接使用.文章基于对应于配置点的等参单元形函数在与其不相连的边界上为0的特性和配置点等效节点力平衡关系,提出了一种广义弱形式自由单元法(GFrEM).该方法是一种使用单元逐点建立配置方程的单元配点法,具有如下特点:(1)突破了现有自由单元法中单元需要内部节点的限制,因而可以使用线性单元和高阶单元;(2)突破了现有自由单元法中一个配置点使用一个单元的限制,可以使用与配置点相连的任意多个单元;(3)可以使用任意形式的规则单元和多边形/多面体单元;(4)如果使用单元节点相连的传统有限元法网格,则GFrEM自然演变为传统的有限元法.论文将给出几个固体力学方面的应用算例,展示所提方法的有效性.

弱电网下构网型双馈风电机组直流动态分析及优化控制策略

当双馈风电机组接入弱交流电网时,转子侧和网侧变流器均采用无锁相环的构网型控制策略可以提高发电系统的并网稳定性。然而,对直流端口而言,网侧变流器在构网型控制下的直流电压抗扰能力有所降低,机组出力波动时直流电压的动态特征不容忽视。为此,文中首先建立了考虑交直流侧动态耦合特征的构网型双馈风电机组的小信号模型。基于系统模型研究了不同电网强度和风机转速下直流电压控制的稳定性,根据耦合传递函数矩阵分析了不同条件下定子功率变化对直流电压的耦合影响。利用小信号模型分析了定子功率对直流电压的交、直流耦合路径,并分别设计了解耦优化策略。理论分析表明,所提策略可以降低有功功率加载对直流电压的耦合作用,优化直流侧动态特性。最后,利用硬件在环实验平台验证了理论分析的正确性及所提控制策略的有效性。

Bell’s Ternary Quadratic Forms and Tunnel’s Congruent Number Criterion Revisited

Bell’s theorem determines the number of representations of a positive integer in terms of the ternary quadratic forms x2+by2+cz2 with b,c {1,2,4,8}. This number depends only on the number of representations of an integer as a sum of three squares. We present a modern elementary proof of Bell’s theorem that is based on three standard Ramanujan theta function identities and a set of five so-called three-square identities by Hurwitz. We use Bell’s theorem and a slight extension of it to find explicit and finite computable expressions for Tunnel’s congruent number criterion. It is known that this criterion settles the congruent number problem under the weak Birch-Swinnerton-Dyer conjecture. Moreover, we present for the first time an unconditional proof that a square-free number n 3(mod 8) is not congruent.

我国碳交易市场的弱式有效性检验及趋势分析

文章基于各碳交易市场日均交易价格数据,采用RS分析法和ADF检验法对中国八个试点省市的碳排放权交易市场和全国碳市场进行研究,以检验市场是否达到弱式有效水平,并追踪有效性特征随时间的演变。结果表明:各试点碳交易市场以及全国碳市场均未达到弱式有效水平,总体仍处于发展阶段。随着政策的完善、市场参与者的增加和技术的进步,预期市场效率将得到提升。本文为研究碳金融市场的演进提供了理论基础,还为全国统一碳排放权交易市场的建设提供了政策效果的评估和反馈,以消除内部阻碍碳排放权流动的约束,提高资源配置效率。

高阶高度非线性强耦合偏微分方程组数值解实现方法——以渗蚀强耦合偏微分方程组为例

为实现高阶高度非线性强耦合偏微分方程组(Partial Differential Equations,PDEs)的数值求解,本文以渗蚀强耦合PDEs为典型案例,剖析了PDEs的高阶高度非线性,结合空间映射,基于弱形式建模与分离式算法,实现了渗蚀强耦合PDEs的数值求解,并验证了求解方法的可行性与可靠性。研究表明:强耦合是导致PDEs非线性特性的充分条件;非弱形式建模难以妥善解决高阶高度非线性强耦合PDEs数值收敛性问题;分离式求解算法对于高阶高度非线性强耦合PDEs的初始条件更具包容性。

构网型直驱风电机组间控制相互作用研究

构网型风电控制技术具有很好的弱电网适应性,可以有效避免风电并网次超同步振荡问题。但是虚拟同步控制引入固有的低频特征模式,接入强电网时会发生低频振荡,同时多台构网型风电机组并联运行时存在控制器相互作用。针对此问题,采用特征模式分析方法,研究了基于虚拟同步控制方法的构网型直驱风电机组并联运行时的控制相互作用及主导低频特征模式稳定性。揭示了虚拟惯量控制参数及系统运行方式对构网型风电机组并联运行低频振荡特性的影响。通过详细时域仿真验证了分析结果的正确性。

考虑土壤非线性的接地网有限元分析

随着超特高压电网的出现和系统容量的不断扩大,入地故障电流也随之不断增加,此时接地装置周围土壤在散流过程中将呈现明显的非线性特性。为此,针对大幅值故障电流下土壤的非线性特性,提出一种计算接地装置特性的有限元模型。对有限元计算中的无穷边界问题引入空间坐标变换方法,通过改变介质参数将电场控制在有限范围内,在保证计算精度的基础上降低了计算量;对于由接地导体与土壤分界面处介质突变引起的病态方程,采用有限元方程的弱解形式,降低了微分方程对场量连续性的要求,加快了方程的收敛速度;针对大幅值入地电流下土壤的非线性特性,在有限元计算中令单元土壤电阻率为该单元电场强度的函数,采用非线性有限元算法加以考虑。将此模型对典型接地装置的仿真结果与相关实测及文献计算结果对比,验证了其分析接地装置非线性特性的有效性。

基于有限元弱解式的棒–板长空气间隙先导放电空间电场仿真研究

对棒–板长空气间隙先导放电过程的空间电场分布以及带电离子浓度等特征参数进行仿真计算研究。建立棒–板长空气间隙放电的二维模型,导出流注–先导放电的二阶偏微分方程,通过有限元弱解形式(weakform)数值计算方法求解先导放电过程中产生的电子、正、负离子浓度与空间电场的大小。仿真结果显示:气体放电所产生的空间电荷对空间电场分布影响显著;间隙距离1.5m的棒–板长空气间隙下,外加500kV、250/2500μs正极性操作电压时的先导放电起始条件为,流注头部带电离子浓度达到4×1013cm-3数量级,空间电场最低达到10kV/cm;先导放电形成后,先导通道内电场约为1～2kV/cm,先导起始时间在400μs左右且以3×104m/s速度传播;有限元弱解形式能有效消除计算离子流中的数值振荡,使偏微分方程求解迅速收敛。

基于偏微分弱解式方程的三维电磁力计算及其在接触器中的应用研究

为了研究接触器电磁力建立的瞬态过程,以及接触器中的能量损耗关系,提出了一种基于PDE弱解式方程的三维电磁力计算方法,通过加权残值法将微分形式的麦克斯韦(Maxwell)方程转化成弱解式矢量方程,得到矩阵形式的控制方程。基于该方程研究了磁路的静态和动力学响应。利用麦克斯韦应力张量,研究了不同电流和间隙时三维电磁力的稳态分布。利用阶跃响应研究了三维电磁力的动态建立过程,并研究了不同磁导率和电导率对于磁通密度以及电磁力动态响应的影响。仿真结果表明,减小电导率可以降低磁通密度的瞬态响应峰值;提高铁心磁导率可以增加电磁力稳态输出值。通过对电磁力的瞬态响应过程研究发现,磁路中主要能量损耗来源于空气,其损失比例峰值达到90%。

无网格法及其最新进展

无网格法具有许多独特的优点,因此有人认为无网格法将成为继有限元法之后新一代的数值方法.到目前为止,已提出了不下十几种无网格法,这些无网格法各有不同的优缺点.本文评述几种主要无网格法(着重应用于固体力学中的基于弱式的无网格法),将它们适当地分类,论述典型的无网格形状函数的构造方法,介绍无网格法的发展现状,评价已提出无网格法的优缺点,并比较典型无网格法的相同和不同点,以及讨论无网格法发展所面临的问题等.最后就无网格法的发展趋势进行了展望.