NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD,the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1- and L2-norm space estimates and the O((△t)2) estimate for time variable are obtained.

A Local Discontinuous Galerkin Method with Generalized Alternating Fluxes for 2D Nonlinear Schrödinger Equations

In this paper,we consider the local discontinuous Galerkin method with generalized alter-nating numerical fluxes for two-dimensional nonlinear Schrödinger equations on Carte-sian meshes.The generalized fluxes not only lead to a smaller magnitude of the errors,but can guarantee an energy conservative property that is useful for long time simulations in resolving waves.By virtue of generalized skew-symmetry property of the discontinuous Galerkin spatial operators,two energy equations are established and stability results con-taining energy conservation of the prime variable as well as auxiliary variables are shown.To derive optimal error estimates for nonlinear Schrödinger equations,an additional energy equation is constructed and two a priori error assumptions are used.This,together with properties of some generalized Gauss-Radau projections and a suitable numerical initial condition,implies optimal order of k+1.Numerical experiments are given to demonstrate the theoretical results.

高速飞轮与电机耦合动力学模型研究

基于替代映射方法分别建立主动磁轴承和永磁同步电机的非线性模型,并与飞轮转子动力学模块、PID控制器等组件结合,构造高速飞轮转子与电机耦合的非线性动力学系统模型。仿真结果表明,替代映射方法计算得到的永磁同步电机齿槽转矩数值与有限元模型结果之间误差较小,具有良好的精度,可正确描述其基频到多次倍频的振动特性。永磁同步电机转子偏心作用力随着转子振幅的增大而增强,会显著削弱主动磁轴承对飞轮转子的控制能力。基于前人“双弹簧”模型,结合永磁同步电机替代映射模型,建立包含主动磁轴承和永磁同步电机的“三弹簧”模型。仿真计算结果表明,永磁同步电机转子偏心作用力改变了飞轮转子的第二临界转速的频率和振幅,作用力较大和位置偏置会造成第二临界转速附近的运动失稳。

某混凝土联方网壳结构抗连续倒塌设计

进站的高速铁路列车如果发生脱轨事故,可撞击雨棚柱并导致雨棚结构连续倒塌。考虑该风险,进行郑州南站混凝土联方网壳雨棚结构抗连续倒塌设计。建立结构多尺度有限元模型,采用拆除构件法分析拆除柱后剩余结构动力行为。结果表明,原结构拆除边柱、次边柱和中柱三种工况下,结构发生局部破坏,破坏面积分别为775、2074、547m^(2);但破坏没有蔓延,结构没有发生连续倒塌。为提高结构抗倒塌性能,针对拆除柱后剩余结构受力特点,修改原结构设计,修改后拆除边柱、次边柱和中柱工况下,结构的破坏面积分别是775、0、0m^(2),即拆除次边柱和中柱工况下雨棚结构没有发生局部破坏。

NONTRIVIAL SOLUTION OF A NONLINEAR SECOND-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.

ADFE METHOD WITH HIGH ACCURACY FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized, by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by. using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H-1 and L-2 norm space estimates and O((Deltat)(2)) estimate for time variant are obtained.

NONLINEAR APPROXIMATION OF A VARIATION OF L^1 UNDER THE LOCAL HAAR CONDITION

In this paper, we discuss the nonlinear approximation of a variation of L1 under the local Haar condition. Theorems on characterizations (including alternations), unicity and strong unicity of the nonlinear approximation are obtained, the associated linear problem equivalent to the nonlinear approximation are given.

Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites

The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current（AC） and direct-current（DC） electric field E app = E 0（1 ＋ sin ωt）.The dielectric profile of the cylindrical inclusions is modeled by function ε i（r） = C k r k（r ≤ a）,where r is the radius of the cylindrical inclusion,and C k,k,a are parameters.In the dilute limit,the local potentials and the effective nonlinear responses at all harmonics are derived.Meanwhile,the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field.It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field.Moreover,the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable,and the maximum of the electric field inside the cylinder is at its center.

Applications of Extended Hyperbolic Function Method for Quintic Discrete Nonlinear SchrSdinger Equation

By using the extended hyperbolic function method, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soliton solution, bright and dark soliton solution, alternating phase bright soliton solution, alternating phase dark soliton solution, and alternating phase bright and dark soliton solution, if a special relation is bound on the coefficients of the equation.

One Approach to Construction of Bilateral Approximations Methods for Solution of Nonlinear Eigenvalue Problems

In this paper a new approach to construction of iterative methods of bilateral approximations of eigenvalue is proposed and investigated. The conditions on initial approximation, which ensure the convergence of iterative processes, are obtained.

AN A.D.I.GALERKIN METHOD FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION USING PATCH APPROXIMATION

An A. D. I. Galerkin scheme for three-dimensional nonlinear parabolic integro-differen-tial equation is studied. By using alternating-direction, the three-dimensional problem is reduced to a family of single space variable problems, the calculation is simplified; by using a local approxima-tion of the coefficients based on patches of finite elements, the coefficient matrix is updated at each time step; by using Ritz-Volterra projection, integration by part and other techniques, the influence coming from the integral term is treated; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity is treated. For both Galerkin and A. D. I. Galerkin schemes the con-vergence properties are rigorously demonstrated, the optimal H^1-norm and L^2-norm estimates are obtained.

ADI Finite Element Method for 2D Nonlinear Time Fractional Reaction-Subdiffusion Equation

In this paper, an alternating direction Galerkin finite element method is presented for solving 2D time fractional reaction sub-diffusion equation with nonlinear source term. Firstly, one order implicit-explicit method is used for time discretization, then Galerkin finite element method is adopted for spatial discretization and obtain a fully discrete linear system. Secondly, Galerkin alternating direction procedure for the system is derived by adding an extra term. Finally, the stability and convergence of the method are analyzed rigorously. Numerical results confirm the accuracy and efficiency of the proposed method.

常规混凝土框剪结构连续倒塌动力响应分析

多高层办公建筑主要采用混凝土框剪结构,其在局部结构构件失效下的整体结构连续倒塌可能引发严重的经济损失和社会影响。该文针对常规结构布置的典型框剪结构开展了动力连续倒塌分析,总结其规律为结构毁伤下的连续倒塌快速评估提供依据。主要工作包括:按照不同抗震设防烈度、跨度、层数设计了18个典型结构布置的框剪结构,并采用纤维梁单元和分层壳单元建立了整体结构的数值模型库;采用非线性动力拆除构件法对整体结构开展了计算分析,获得结构系统在局部构件失效下的动力响应;对比分析不同结构的连续倒塌动力响应,研究不同参数对连续倒塌后果的影响。

考虑光伏的备用容量替代配置优化模型

在新能源环境下,负荷需求与新能源发电的不确定性对备用容量对提出了更高的要求,新能源与备用替代日益受到关注。根据电量不足期望值(expected energy not supplied,EENS)与备用容量的关系,确定了电力系统备用总量,并采用优先分配方式在多类型的发电机组中分配备用容量。基于EENS与运行成本,构建光伏发电系统替代火电机组的综合替代效益评价指标,以综合替代效益评价指标的数值最小化为目标函数,构建考虑光伏发电系统替代火电机组参与备用运行的电力系统备用容量优化模型。并用分段线性理论对具有二次特性的目标函数进行线性化处理,采用分支定界算法求解构建的非线性整数规划问题。以IEEE-30系统作为实例,计算结果表明,光伏发电系统替代火电机组参与备用运行,可以降低综合替代效益及备用容量。

主要设计参数对规则RC框架结构抗连续倒塌性能的影响

连续倒塌是指由意外事件造成工程结构的局部破坏并形成连锁反应,最终导致结构大范围破坏甚至整体倒塌,其中结构系统的冗余承载力对其抗连续倒塌性能具有显著影响。为满足工程快速评估的需要,分析、总结了主要设计参数对规则框架结构抗连续倒塌性能的影响规律。按照规范设计了18个典型钢筋混凝土(RC)规则框架,分别考虑了不同抗震设防烈度、结构总楼层数、结构跨度3个主要设计参数对结构冗余承载力的影响;采用纤维梁模型建立了所有典型框架的有限元模型,其中梁采用T形截面建模考虑有效翼缘宽度范围内楼板的贡献;采用非线性动力拆除构件法分析了框架在不同部位发生初始破坏时的连续倒塌响应,以及主要设计参数对结构连续倒塌影响的规律。

一类带p-Laplacian算子的分数阶微分方程边值问题解的存在性

该文运用Leray-Schauder非线性择抉和Krasnosel skiis不动点定理,讨论了一类在一致分数阶导数定义下含p-Laplacian算子的分数阶微分方程边值问题∅p(Tαx(t))′=f(t,x(t)),0≤t≤1,x(0)=Tαx(0)=0,x(1)=μ∫η0x(t)d t解的存在性.其中,1<α≤2,μ≥0,0<η≤1,∅p(s)=|s|p-2 s,(∅p)-1=∅q,p>1,p^(-1)+q^(-1)=1,Tα是一致分数阶导数,f:[0,1]×ℝ→ℝ是给定的连续函数.

一种非线阵双基线干涉仪无线电监测技术

针对复杂无线电磁环境和多样应用场景下,传统无线电监测设备已经无法实现对非法无线电干扰信号源快速准确监测的问题,利用正交偶极子天线阵元俯仰维波束合成定向天线子阵列高增益、双基线干涉仪高测向精度的特点,提出一种基于国产化非线阵双基线干涉仪的无线电监测设备。结合非线阵双基线干涉仪测向技术和信息化设备安全自主可控要求,对设备使用的硬件、软件进行国产化替代应用验证,证实其满足瞬时360°全方位高灵敏度和高精度测向技术要求。它具备不受使用地形环境限制、机动灵活等特点,能够适应车载、便携和无人机载等多平台无线电监测要求,破解了制约无线电监测设备自主可控发展的难题。

PARALLEL COMPUTING METHOD OF PURE ALTERNATIVE SEGMENT EXPLICIT-IMPLICIT DIFFERENCE SCHEME FOR NONLINEAR LELAND EQUATION

The research on the numerical solution of the nonlinear Leland equation has important theoretical significance and practical value. To solve nonlinear Leland equation, this paper offers a class of difference schemes with parallel nature which are pure alternative segment explicit-implicit(PASE-I) and implicit-explicit(PASI-E) schemes. It also gives the existence and uniqueness,the stability and the error estimate of numerical solutions for the parallel difference schemes. Theoretical analysis demonstrates that PASE-I and PASI-E schemes have obvious parallelism, unconditionally stability and second-order convergence in both space and time. The numerical experiments verify that the calculation accuracy of PASE-I and PASI-E schemes are better than that of the existing alternating segment Crank-Nicolson scheme, alternating segment explicit-implicit and implicit-explicit schemes. The speedup of PASE-I scheme is 9.89, compared to classical Crank-Nicolson scheme. Thus the schemes given by this paper are high efficient and practical for solving the nonlinear Leland equation.

钢筋混凝土框架结构抗连续倒塌设计方法的研究

首先简要介绍了国外抗连续倒塌设计规范的主要设计方法和分类设计体系,然后重点对钢筋混凝土框架结构抗连续倒塌拆除构件设计法和拉结强度设计法进行较为深入的分析研究。在基于非线性动力分析的拆除构件设计法进行分析的基础上,对基于线弹性静力分析的拆除构件法的原理和设计参数进行了分析和验算,提出适合我国工程结构的设计参数。分析了国外规范拉结强度设计法应用于按我国规范设计的框架结构的不适用性及其原因,并对国外规范拉结强度设计法中基本拉结强度的计算模型所存在的不足进行了改进,提出了考虑空间传力路径等因素的拉结强度设计法。通过算例对该文建议的线弹性静力拆除构件设计法和拉结强度设计法进行了设计验证。

异步电动机定子磁链与电磁转矩的逆系统解耦控制方法

为了实现脉宽调制电压源型逆变器供电的异步电动机调速系统定子磁链和电磁转矩的动态解耦控制,基于逆系统理论提出了一种新型的解耦控制策略。根据异步电动机调速系统的动态数学模型,证明了其逆系统的存在性,在此基础上得到了逆系统的输入输出方程。把得到的逆系统和异步电动机调速系统相级联,从而将多变量、非线性、强耦合的控制对象解耦成了两个一阶线性子系统,分别称为转矩子系统和磁链子系统,利用线性控制理论对各个调节器进行了设计,实现了定子磁链和电磁转矩对各自参考值的全局渐进跟踪。使用Matlab软件进行了仿真实验,实验结果验证了控制方案的可行性。