Mathematical Modelling of Cable Stayed Bridges: Existence, Uniqueness, Continuous Dependence on Data, Homogenization of Cable Systems

A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected with the homogenizing procedure is proposed and the existence and uniqueness of a solution are proved.     

考虑随机弱化二阶效应的电缆流变断裂学分析

将电缆视作为ｎ股子束构成的线束，而每股子束由ｍ个平行的受拉元件组成，受拉元件就是渍于树脂基体的聚合物肌绳。未破坏的元件在任一时刻都按照某种规律承载，表现出电缆断裂对持载时间和载荷特征的相依性，从而，电缆的断裂是一个非平衡态不可逆热力学相容的一个非线性动力学演化假设下，我们考虑单个元件受载断裂与线束受载的关系。认识到元件的数目一一大时，线事的破坏时间是近正态分析的。     

FORCED WAVE PROPAGATION IN VISCOELASTIC CABLE WITH SMALL SAG

Based on the linear viscoelastic differential constitutive law and cable structural model, the coupled longitudinal-transverse waves that propagate along a viscoelastic cable with small curvature is investigated. A mathematical model is presented that describes the three-dimensional nonlinear response of a viscoelastic cable. An asymptotic form of this model is obtained for the linear response of cables having small equilibrium curvature. The spectral relation governing the propagating waves is derived using transform methods. The spectral relation is employed in deriving a Green's function that is then used to construct solutions for in-plane response under distributed harmonic excitation. Analysis of forced response reveals the existence of two types of periodic waves that propagate through the cable, one characterizing extension-comprehensive deformation and the other characteristic transverse deformation. Project supported by the National Natural Science Foundation of China (No. 59635140).     

单层平面索网幕墙结构的风振响应分析及实用抗风设计方法

单层平面索网玻璃幕墙结构是广泛应用于大型公共建筑中的一种新型结构形式,由于其具有柔性大、质量轻、阻尼小、自振频率低的特点,属风敏感结构。由于单索幕墙具有较高的几何非线性,本文采用基于随机振动理论的模态叠加频域方法进行了单索幕墙结构的风振响应分析。将模态叠加频域方法的计算结果和非线性时程分析方法的精确计算结果进行了比较,证明了该方法的准确性。并且本文通过分析各阶模态对单索幕墙结构风振响应的贡献,得到脉动风荷载下结构的振动以第一阶模态为主的结论。根据该结论本文采用频域方法推导了单索幕墙结构的位移均方差和索内力均方差的实用计算公式,同时考虑单索幕墙的结构特点提出了基于结构响应的单索幕墙结构实用抗风设计方法。     

大跨度斜拉桥动力特性分析

本文提出一种计算大距度钢桁梁斜拉桥动力特性的方法。文中分别采用桁段有限单元、空间梁元、空间杆元计算斜拉桥中桁架，桥塔、拉索的刚度矩阵与质量矩阵，采用子空间迭代法求解特征方程，所得结果可供设计参考。     

空间曲线索的平衡方程及单索几何判定

空间曲线索平衡方程可在理想柔索假定的基础上进行推导,也可以由空间曲线梁平衡方程退化得到。本文给出后者的连续化分析过程并进行了初步的讨论,目的在于将空间曲线索的各种力学模型统一起来。采用理想柔索假定后单索只能是平面曲线,自然坐标系和整体直角坐标系下平面曲线索的平衡方程是等价的。同时,针对以往单索连续化分析中几何判定的不足,基于空间曲线的弧长独立参数概念,指出单根理想柔索本质上为静不定和动不定体系。     

预应力索-桁架结构形状优化设计

就预应力索-桁架结构形状优化设计问题,考虑了施加预应力阶段、预应力与荷载共同作用阶段的性态约束条件,建立了设计变量包括截面尺寸、索力值、杆件及索节点坐标的形状优化数学模型;在求解方法上将设计变量分为两个子空间:第一子空间为索力值和截面尺寸优化设计空间,第二子空间为形状优化设计空间; 第一子空间给出新的求解方法以减轻结构重量,第二子空间用节点渐进法优化结构形状和布索位置以增加结构刚度.算例表明,该方法能使结构重量逐步减轻,结构刚度不减,形状逐步达到最优.     

预应力钢桁架结构分析中的摩擦滑移索单元

为精确模拟预应力钢桁架中连续长索在支撑点的滑动,本文创建了一种考虑摩擦力影响的新单元。被称为摩擦滑移索单元的新单元有三个节点,中间节点为支撑点。本文首先利用弹性悬链线的解析解,建立了弹性悬链线单元,并推导了单元两端点的张拉刚度。摩擦滑移索单元由两个弹性悬链线单元组合而成,根据支撑点处索的滑动方向、索力差、滑动摩擦力和滑移刚度调整两索段的原长,使支撑点两侧的索力满足给定的摩擦关系。算例验证了新单元算法的正确性和高效性,对设计的预应力钢桁架的分析,显示了张拉过程中及使用荷载作用下新单元在结构分析中的应用。新单元可直接用于常规的有限元分析,研究在工作状态或施工中存在连续长索滑移的索结构。     

Exploring the effect of radiation crosslinking on the physico‐mechanical,dynamic mechanical and dielectric properties of EOC–PDMS blends for cable insulation applications

This work focuses on the effect of electron beam irradiation on the physico‐mechanical, dynamic mechanical and dielectric properties of blends based on ethylene octene copolymer (EOC) and poly dimethyl siloxane (PDMS) rubber. It is found that electron beam irradiation caused considerable improvement in the physico‐mechanical properties; the tensile strength was enhanced by nearly 35% for 70:30 EOC:PDMS blend. Phase morphology of the blends analyzed before irradiation by scanning electron microscopy (SEM) exhibited droplet/matrix morphology with sizes of the PDMS rubber domain varying from 0.55 µm to 0.47 µm as the amount of PDMS rubber decreased from 30 wt% to 10 wt%. This reduction in the PDMS rubber domain has been correlated with the physico‐mechanical properties of the blends. Further, the dynamic mechanical properties and creep behavior of these EOC:PDMS blends before and after irradiation has been studied. It is inferred that the 70:30 blend after radiation crosslinking shows a 17% decrease in the creep compliance, i.e. higher creep resistance compared to neat blends. All the radiation crosslinked blends exhibited lower dielectric constant, lower dielectric loss and higher electrical resistivity as compared to the virgin blends which makes it suitable for cable insulating application. Copyright © 2016 John Wiley & Sons, Ltd.     

Research on mechanical and dielectric properties of XLPE cable under accelerated electrical‐thermal aging

Research into the electrical‐thermal aging properties of cross‐linked polyethylene (XLPE) cable has great significance, because of its wide application. This study conducted accelerated electrical‐thermal aging tests on 10‐kV XLPE cable in order to assess the cable's mechanical and dielectric properties. After being aged by applying 34.8‐kV AC voltage at the four temperatures of 90, 103, 114, and 135°C, the cable samples were taken out in five stages according to the aging time and cut into slices. The slices were conducted experiments to test the breaking elongation, tensile strength, gel content, breakdown voltage, and frequency spectrums of the dielectric constant and dielectric loss. The results demonstrate that the mechanical strength and gel content of XLPE vary greatly under different aging temperatures, a finding that is associated with the crystallization characteristics of the material. The breakdown voltage shows a slight decreasing trend with aging time. The dielectric constant decreases with aging time in high‐frequency areas (10³–10⁶ Hz), while the dielectric loss factor increases with aging time at low frequencies (10^?2–0 Hz). These two parameters can be used to characterize the degree of aging in cable. Copyright © 2016 John Wiley & Sons, Ltd.