Analytic torsion and Ruelle zeta functions for hyperbolic manifolds with cusps

In this paper we derive a relationship of the leading coefficient of the Laurent expansion of the Ruelle zeta function at s=0 and the analytic torsion for hyperbolic manifolds with cusps. Here, the analytic torsion is defined by a certain regularized trace following Melrose [R.B. Melrose, The Atiyah-Patodi-Singer Index Theorem, Res. Notes Math., vol. 4, A.K. Peters, Ltd., Wellesley, MA, 1993]. This extends the result of Fried, which was proved for the compact case in [D. Fried, Analytic torsion and closed geodesics on hyperbolic manifolds, Invent. Math. 84 (3) (1986) 523-540], to a noncompact case.     

A New Solution with Torsion in Model of dS Gauge Theory of Gravity

A new static de Sitter solution with torsion in the model of de Sitter gauge theory of gravity is obtained. The torsion only contains O(3)-symmetric tensor part according to irreducible decomposition. Some properties of the new solution are discussed.     

基于扭秤的激光干涉差动测量微小冲量方法

基于扭秤测量冲量原理,结合激光干涉法差动测量角度的方法,提出一种基于扭秤的激光干涉差动测量微小冲量的方法。介绍系统的基本组成和测量过程,给出扭秤结构设计参数,并对系统参数进行了标定,结合设计参数与标定结果,对系统的分辨率、量程和精度进行了校核,在典型的测量环境下,对激光烧蚀靶材所形成的Ns量级微小冲量进行了测量,给出了典型的测量结果并进行分析。结果表明:所提出的基于扭秤的激光干涉差动测量微小冲量方法,系统分辨率可达10-7Ns量级,测量范围跨5个数量级,最大可以测量10-2Ns量级冲量,测量精度优于95%。     

Tension–torsion fracture experiments – Part II: Simulations with the extended Gurson model and a ductile fracture criterion based on plastic strain

An extension of the Gurson model that incorporates damage development in shear is used to simulate the tension–torsion test fracture data presented in Faleskog and Barsoum (2013) (Part I) for two steels, Weldox 420 and 960. Two parameters characterize damage in the constitutive model: the effective void volume fraction and a shear damage coefficient. For each of the steels, the initial effective void volume fraction is calibrated against data for fracture of notched round tensile bars and the shear damage coefficient is calibrated against fracture in shear. The calibrated constitutive model reproduces the full range of data in the tension–torsion tests thereby providing a convincing demonstration of the effectiveness of the extended Gurson model. The model reinforces the experiments by highlighting that for ductile alloys the effective plastic strain at fracture cannot be based solely on stress triaxiality. For nominally isotropic alloys, a ductile fracture criterion is proposed for engineering purposes that depends on stress triaxiality and a second stress invariant that discriminates between axisymmetric stressing and shear dominated stressing.     

圆中空夹层钢管混凝土柱扭转实验研究

以名义含钢率、外钢管强度和空心率为主要变化参数,设计了6根圆中空夹层钢管混凝土和1根双层空钢管试件,对其进行了扭转试验研究。试验结果表明:在加载过程中,钢管和混凝土变形协调,共同工作;试件表现出很好的塑性性能;试件名义含钢率和外钢管强度越大,试件抗扭承载力也越大;空心率越大,试件抗扭承载力也越大;圆中空夹层钢管混凝土比双层空钢管抗扭承载力有明显的提高。同时用有限元方法对试件扭矩-转角全过程曲线进行计算,计算结果与试验结果吻合良好。     

Group Invariant Solutions of the Plastic Torsion of Rod with Variable Cross Section

Based on the theory of Lie group analysis, the full plastic torsion of rod with arbitrary shaped cross sections that consists in the equilibrium equation and the non-linear Saint Venant-Mises yield criterion is studied. Full symmetry group admitted by the equilibrium equation and the yield criterion is a finitely generated Lie group with ten parameters. Several subgroups of the full symmetry group are used to generate invariants and group invariant solutions. Moreover, physical explanations of each group invariant solution are discussed by all appropriate transformations. The methodology and solution techniques used belong to the analytical realm.     

Determination of the thermal noise limit in test of weak equivalence principle with a rotating torsion pendulum

Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise.     

Nonlinear stability and dynamics of composite skew plates under nonuniform loadings using differential quadrature method

The buckling, postbuckling and postbuckled vibration behaviour of composite skew plates subjected to nonuniform inplane loadings are presented here. The skew plate is modelled using first order shear deformation theory accounting for von-Kármán geometric nonlinearity and initial geometric imperfections. The different types of nonuniform loads that have been considered in this study are concentrated load, partial load and parabolic load. The explicit analytical expressions for prebuckling stress distributions within composite skew plate subjected to three different types of nonuniform inplane loadings are developed by solving plane elasticity problem using Airy's stress function approach. It is observed that the inplane normal stress distributions within the skew plate due to above nonuniform loadings do not become uniform even at mid-section. The generalized differential quadrature (GDQ) method is used to solve the nonlinear governing partial differential equations. It is observed that the postbuckled load carrying capacity of skew plate under concentrated loading is the lowest compared to other nonuniform and uniform loadings.     

开口厚壁截面短构件的约束扭转1）

为了分析开口厚壁截面短构件的约束扭转问题,采用统一分析梁模型与有限节线法,对T形和L形厚壁截面短构件约束扭转时横截面的翘曲和应力分布情况等问题进行了分析研究.算例计算结果表明：开口厚壁截面短构件存在与其横截面形心位置不一致的扭转（弯曲）中心,构件在不过扭转中心的外力作用下会产生弯扭耦合变形,其横截面将产生不均匀翘曲,横截面上的翘曲正应力和扭转剪应力均呈非线性分布.     

两类特殊三次空间Bézier曲线的挠率特征分析

空间Bézier曲线的挠率在几何造型中被广泛应用. 文中利用笛卡尔符号法则讨论了两种特殊三次空间Bézier曲线的挠率单调性问题, 最后得出当空间三次Bézier曲线的控制边相等且中间控制边和相邻两控制边的夹角相等时, 挠率仅有一个极小值; 而当两夹角相等但控制边长成等差数列时, 文中给出了挠率单调及极值存在的充分条件.