Construction analysis on integral lifting of steel structure by the vector form intrinsic finite element

A newnumerical method based on vector form intrinsic finite element（VFIFE） is proposed to simulate the integral lifting process of steel structures. First, in order to verify the validity of the VFIFE method, taking the steel gallery between the integrated building and the attached building of Nanjing M obile Communication Buildings for example, the static analysis was carried out and the corresponding results were compared with the results achieved by the traditional finite element method. Then, according to the characteristics of dynamic construction of steel structure integral lifting, the tension cable element was employed to simulate the behavior of dynamic construction. The VFIFE method avoids the iterative solution of the stiffness matrix and the singularity problems. Therefore, it is simple to simulate the complete process of steel structure lifting construction.Finally, by using the VFIFE, the displacement and internal force time history curves of the steel structures under different lifting speeds are obtained. The results show that the lifting speed has influence on the lifting force, the internal force, and the displacement of the structure. In the case of normal lifting speed, the dynamic magnification factor of 1. 5 is safe and reasonable for practical application.

Vector form Intrinsic Finite Element Method for the Two-Dimensional Analysis of Marine Risers with Large Deformations

Robust numerical models that describe the complex behaviors of risers are needed because these constitute dynamically sensitive systems. This paper presents a simple and efficient algorithm for the nonlinear static and dynamic analyses of marine risers. The proposed approach uses the vector form intrinsic finite element(VFIFE) method, which is based on vector mechanics theory and numerical calculation. In this method, the risers are described by a set of particles directly governed by Newton's second law and are connected by weightless elements that can only resist internal forces. The method does not require the integration of the stiffness matrix, nor does it need iterations to solve the governing equations. Due to these advantages, the method can easily increase or decrease the element and change the boundary conditions, thus representing an innovative concept of solving nonlinear behaviors, such as large deformation and large displacement. To prove the feasibility of the VFIFE method in the analysis of the risers, rigid and flexible risers belonging to two different categories of marine risers, which usually have differences in modeling and solving methods, are employed in the present study. In the analysis, the plane beam element is adopted in the simulation of interaction forces between the particles and the axial force, shear force, and bending moment are also considered. The results are compared with the conventional finite element method(FEM) and those reported in the related literature. The findings revealed that both the rigid and flexible risers could be modeled in a similar unified analysis model and that the VFIFE method is feasible for solving problems related to the complex behaviors of marine risers.

Coupled Cross-Flow/in-Line Vortex-Induced Vibration Responses of a Catenary-Type Riser Subjected to Uniform Flows

A three-dimensional numerical scheme was developed to investigate the vortex-induced vibration(VIV)of a catenary-type riser(CTR)in the in-line(IL)and cross-flow(CF)directions.By using the vector form intrinsic finite element method,the CTR was discretized into a finite number of spatial particles whose motions satisfy Newton’s second law.The Van der Pol oscillator was used to simulate the effect of vortex shedding.The coupling equations of structural vibration and wake oscillator were solved using an explicit central differential algorithm.The numerical model was verified with the published results.The VIV characteristics of the CTR subjected to uniform flows,including displacement,frequency,standing wave,traveling wave,motion trajectory,and energy transfer,were studied comprehensively.The numerical results revealed that the multimode property occurs in the CF-and IL-direction VIV responses of the CTR.An increase in the flow velocity has slight effects on the maximum VIV displacement.Due to structural nonlin-earity,the double-frequency relationship in the CF and IL directions is rarely captured.Therefore,the vibration trajectories display the shape of an inclined elliptical orbit.Moreover,the negative energy region is inconspicuous under the excitation of the uniform flow.

ADAPTIVE PINNING SYNCHRONIZATION OF COUPLED NEURAL NETWORKS WITH MIXED DELAYS AND VECTOR-FORM STOCHASTIC PERTURBATIONS

In this article, we consider the global chaotic synchronization of general cou- pled neural networks, in which subsystems have both discrete and distributed delays. Stochastic perturbations between subsystems are also considered. On the basis of two sim- ple adaptive pinning feedback control schemes, Lyapunov functional method, and stochas- tic analysis approach, several sufficient conditions are developed to guarantee global syn- chronization of the coupled neural networks with two kinds of delay couplings, even if only partial states of the nodes are coupled. The outer-coupling matrices may be symmetric or asymmetric. Unlike existing results that an isolate node is introduced as the pinning target, we pin to help the network realizing synchronization without introducing any iso- late node when the network is not synchronized. As a by product, sufficient conditions under which the network realizes synchronization without control are derived. Numerical simulations confirm the effectiveness of the obtained results.

Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.

Notes on Canonical Forms of Integrable Vector Nonlinear Schr?dinger Systems

We present canonical forms of integrable vector nonlinear Sehr6dinger systems. Mathematically, it is enough to focus on these canonical forms.

ON THE DECOMPOSITION OF COMPLEX VECTOR SPACES AND THE JORDAN CANONICAL FORM OF COMPLEX LINEAR TRANSFORMATIONS

New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.

AN ALGORITHM FOR JORDAN CANONICAL FORM OF A QUATERNION MATRIX

In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a practical algorithm for Jordancanonical form J of a quaternion matrix A, but also provide a practical algorithm forcorresponding nonsingular matrix P with P- 1 AP = J.

INVARIANT FORM AND INTEGRAL INVARIANTS ON KAHLER MANIFOLD

The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential

基于向量式有限元的网壳结构地震易损性分析

为解决网壳结构地震易损性研究中,增量动力分析(incremental dynamic analysis,IDA)所面临的结构非线性分析耗时长且求解困难的问题,提出了一种基于向量式有限元的IDA方法。首先,以一个Kiewitt-8型单层球面网壳为例,验证了向量式有限元方法求解结构地震响应的准确性,其次选取12个不同参数的Kiewitt-8型单层球面网壳为研究对象,并考虑材料不确定性进行IDA分析,以地震峰值加速度与结构最大节点位移比为参数,绘制了结构在地震作用下的IDA曲线和轻微破坏、严重破坏及倒塌这三种性态下的易损性曲线。结果表明:向量式有限元能高效且准确的求解网壳结构的地震响应,屋面质量和矢跨比的增加均会增加三种性态点的超越概率;对于本文的网壳结构算例,求解时间仅为传统有限元方法的1/15,误差在3%以内,屋面质量和矢跨比的改变导致地震危险性最大增加了75%。

Local integrable differential systems and their normal forms

In this paper we first summarize our results published in recent years and their sketch proofs on local integrability,which are on the characterization of local integrability and on the existence of analytic normalization of analytically integrable differential systems. Then we present a new result on the equivalent characterization of the existence of the first integrals of an analytic differential systems near a nonhyperbolic singularity. Finally we pose some open problems on this subject.

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。

Reduced Vector Helmholtz Wave Equation Analysis on the Wave-Number Side

The resolvent helps solve a PDE defined on all of wave-number space, . Almost all electromagnetic scattering problems have been solved on the spatial side and use the spatial Green’s function approach. This work is motivated by solving an EM problem on the Fourier side in order to relate the resolvent and the Green’s function. Methods used include Matrix Theory, Fourier Transforms, and Green’s function. A closed form of the resolvent is derived for the electromagnetic Helmholtz reduced vector wave equation, with Dirichlet boundary conditions. The resolvent is then used to derive expressions for the solution of the EM wave equation and provide Sobolev estimates for the solution.

A Short Vector Solution of the Foucault Pendulum Problem

The paper studies the motion of the Foucault Pendulum in a rotating non-inertial reference frame and provides a closed form vector solution determined by vector and matrix calculus. The solution is determined through vector and matrix calculus in both cases, for both forms of the law of motion (for the Foucault Pendulum Problem and its “Reduced Form”). A complex vector which transforms the motion equation in a first order differential equation with constant coefficients is used. Also, a novel kinematic interpretation of the Foucault Pendulum motion is given.

Complex Spacetime Frame: Four-Vector Identities and Tensors

This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.

船舶岸电变流器用构网型电流矢量控制

船舶岸电变流器作为靠港船舶新的供电电源,可极大地降低船舶靠港时船用同步发电机重质柴油燃烧所带来的NOx、SOx和柴油颗粒等污染物。为保证船舶供电的连续性,岸电侧与船电侧电源多采用预同步方式完成不断电切换,然而可能会因两侧电压非理想的相位差而诱发电流冲击,进而导致岸电与船电电源切换失败。因此,该文首先提出船舶岸电变流器用构网型电流矢量控制策略,其实施于锁相环确定的船电两相同步旋转坐标系中,可在无预同步的前提下完成岸电变流器无冲击自整步并入船电系统,同时通过幅频电压-矢量电流级联闭环完成对船舶岸电变流器输出电压幅值和频率的有效调控。然后,建立构网型电流矢量控制数学模型,并基于此分析控制带宽对控制系统相位稳定裕度、电压跟踪能力以及对负载电流的抗扰能力。最后,通过Satrsim MT 8020硬件在环测试,验证了所提构网型电流矢量控制策略的有效性。

THE VECTOR FIELDS ADMITTING ONE-PARAMETER SPATIAL SYMMETRY GROUP AND THEIR REDUCTION

For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding ( n - 1)-form. In partic ular, while n = 3, an important result can be directly got which is given by Me,ie and Wiggins in 1994.

LAGRANGIAN VECTOR FIELD ON KOHLER MANIFOLD

In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.

基于多线性材料硬化的向量式有限元C型薄壁型钢屈曲分析

C型薄壁型钢在实际工程中较常见,在力的作用下容易发生屈曲失效。传统有限元法预测结构屈曲变形已经有一套较为成熟的方案,但程序较烦琐。基于向量式有限元(VFIFE)方法编制了三角形壳单元的Fortran计算程序。通过Matlab软件编写前处理与后处理程序,将计算结果与经典的双曲壳屈曲计算结果对比,考察其正确性。考虑几何非线性问题与材料非线性问题,引入多线性材料硬化模型,计算了不同尺寸的C型薄壁型钢在轴压荷载下的屈曲特性。根据位移-轴力曲线判断屈曲荷载,通过后处理程序绘制出屈曲发生后的变形,并与现有的试验结果对比。结果表明:引入多线性材料硬化模型的向量式有限元方法能够较好地预测结构屈曲荷载以及屈曲变形,为预测结构的屈曲变形提供一种新的、可靠参考。

基于图向量的一般图的广义谱刻画

给定一个图G,如果对于任意的图H,H和G同谱且它们的补图也同谱蕴含它们同构,则称图G是由广义谱确定的。在文献[12]中,作者给出了一个简单的算术条件判断一个图是由广义谱确定的,即对于给定n个顶点的图G,令其邻接矩阵和道矩阵分别为A=A(G)和W(G)=[e,Ae,…,A^(n-1)e](e为全-1向量),如果2^(-[n/2])detW(G)是无平方因子的奇数,则图G是由广义谱确定的。Qiu等^([7])通过引入图向量,给出一个与图G有关的新矩阵,将广义谱确定概念推广到一般的Φ-DS,并证明了一类正则图是Φ-DS的。本文在文献[7]的基础上,给出了判断一类一般图是Φ-DS的一个简单准则,推广了文献[12]中的结论,并通过数值实验验证了该准则的有效性。