From Lie algebra crossed modules to tensor hierarchies

The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity rely on a pairing – the embedding tensor – between a Leibniz algebra and a Lie algebra. Two such algebras, together with their embedding tensor, form a triple called a Lie-Leibniz triple, of which Lie algebra crossed modules are particular cases. This paper is devoted to showing that any Lie-Leibniz triple induces a differential graded Lie algebra – its associated tensor hierarchy – whose restriction to the category of Lie algebra crossed modules is the canonical assignment associating to any Lie algebra crossed module its corresponding unique 2-term differential graded Lie algebra. This shows that Lie-Leibniz triples form natural generalizations of Lie algebra crossed modules and that their associated tensor hierarchies can be considered as some kind of ‘lie-ization’ of the former. We deem the present construction of such tensor hierarchies clearer and more straightforward than previous derivations. We stress that such a construction suggests the existence of further well-defined Leibniz gauge theories.     

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。     

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.     

参数灵敏度分析的神经网络方法及其工程应用

在系统分析中，参数灵敏度分析不仅为判断各系统参数的重要性大小提供了依据，量化的灵敏度指标也是后续参数估计的前提。然而，在多效实际系统中，系统参数与系统状态间的显式函数关系不易得到，导致一阶灵敏度指标无法直接求取。简化的单因素分析方法亦存在模型粗糙、精度不高的缺点。本文研究采用人工神经网络的高精度泛化映射，通过少量样本的训练，建立复杂系统中多个系统参数与系统状态间的近似映射关系，继而推导得到统一的灵敏度计算列式。简单结构的神经网络方法和解析方法的对比计算显示了方法的有效性和可靠性。最后，应用该法对某斜拉桥结构的荷载参数和刚度参数进行了考查，得到一般性结论。     

THEORETICAL AND EXPERIMENTALRESEARCH ON DYNAMIC BEHAVIOR OF GUYED MASTS UNDER WIND LOAD

I. INTRODUCTION Wind-induced vibration is the critical factor for the safety of guyed masts. Many dynamic modelshave been proposed in the literature[1 , 2]. However, there are obvious de?ciencies in many of theseprevious works owing to the poor cabl…     

斜拉索各参数取值对索力测定结果的影响

为了确保频率法测定斜拉索索力的精度，以某斜拉桥中的拉索为例，采用平面非线性有限元法探讨了斜拉索各参数取值对索力值的影响，并讨论了各参数的合理取值．利用分析结果找到了不同的测试单位在该斜拉桥的索力联测中存在较大索力偏差的原因，可对施工过程中的索力精确测定提供帮助．分析结果同样适用于悬索桥和悬挂屋顶等索结构的索力测定．     

Resonant non-linear normal modes. Part II: activation/orthogonality conditions for shallow structural systems

The general conditions, obtained in Lacarbonara and Rega (Int. J. Non-linear Mech. (2002)), for orthogonality of the non-linear normal modes in the cases of two-to-one, three-to-one, and one-to-one internal resonances in undamped unforced one-dimensional systems with arbitrary linear, quadratic and cubic non-linearities are here investigated for a class of shallow symmetric structural systems. Non-linear orthogonality of the modes and activation of the associated interactions are clearly dual problems. It is known that an appropriate integer ratio between the frequencies of the modes of a spatially continuous system is a necessary but not sufficient condition for these modes to be non-linearly coupled. Actual activation/orthogonality of the modes requires the additional condition that the governing effective non-linear interaction coefficients in the normal forms be different/equal to zero. Herein, a detailed picture of activation/orthogonality of bimodal interactions in buckled beams, shallow arches, and suspended cables is presented.