新书介绍

《张量分析及其应用》一书,内容包括n维仿射空间和三维真伪欧氏空间中的张量代数和张量分析、曲面上的张量和曲面论,Riemann空间中的张量分析,以及张量在经典力学、连续介质力学、电磁场理论、相对论中的应用,还介绍了作者将张量应用到一些工程问题中的研究成果。例如透平机械内部流动、轴承润滑和壳体理论等。 本书的特点是,充分运用局部仿射标架和共轭标架以及行列式张量的特性,尤其是引入了S——族坐标系,使得在解决透平机械内部流动、润滑理论的广义Reynold方程和壳体理     

基于深度张量投影网络的机械故障诊断方法研究

针对现有的、基于深度卷积神经网络的故障诊断方法利用池化层对高阶输入张量降维时容易破坏张量数据,造成数据信息丢失,以及网络结构相对复杂的不足,构造了一种深度张量投影网络。该网络利用张量投影层代替传统卷积神经网络中的池化层,在对输入的高阶张量数据进行降维时,不会对张量数据造成破坏,避免了特征信息的丢失,提高了模型对故障的识别准确率;并且张量投影层是一种维度可变的降维层,可以简化网络结构。在此基础上,结合高阶谱和深度张量投影网络各自的优点,提出了基于深度张量投影网络的机械故障诊断方法。在提出的方法中,利用高阶谱提取故障信号特征,将得到的高阶张量谱图输入到构建的深度张量投影网络模型中进行高阶张量降维和识别。提出的方法成功应用到齿轮箱故障诊断中。实验结果表明,所提方法能够更好地保留原始故障信息,有效识别不同类型的故障,准确率优于传统深度卷积神经网络故障诊断方法。     

浅谈环状管网小负荷当量化和提高可靠性的措施

本文介绍了小负荷当量化对既有环状管网计算的简化方案,有利于提高环状管网可靠性计算和水力计算的运算效率。最后,在上述研究的基础上论述了几种提高环状管网可靠性的措施。     

改进的张量投票法算实现红外人体破碎目标复原

运用张量投票算法对红外人体破碎目标进行复原不能满足红外行人检测的实时性要求.针对该算法计算量大,运行时间长提出了改进的张量投票算法.首先,将强度阈值转化为距离阈值来滤除超出投票场的大部分点.然后,根据圆形投票场两点相互投票作用的对称性,减少强度的再次计算.最后,通过强度阈值进行精细滤除.实验仿真结果表明,改进的张量投票算法在保证复原效果不变的同时,减少了计算量,缩短了运行时间.     

计算平板平面度的简化表格

资料[1]介绍了计算平板平面度的简化公式,应用它来计算平面度确实提高了工作效率。借助(1)的思路,本文利用另外形式的简化公式,建立一个简化的计算表格。该表格就其计算工作量而言和(1)的方法相差无几,而在实用中却有如下的优点:计算步骤简单,明瞭;运算数目排列整齐,容易校对;计算结果一目了然。因此,简化表格不仅容易掌握而且进一步提高了工作效率。图1为过平板某条基线的截面图形。基线端点为 O、n。它们对于平板的理想平面 A_0的偏差是δh_0、δh_n(此二数值的确定可参考[1])。在 On     

非线性常微分方程高阶谐波平衡法傅里叶展开的简化

简化了一种求取非线性常微分方程高阶谐波解的近似解析计算方法。对平方和立方非线性项的傅里叶展开过程进行改进和简化,使计算过程变为两次矩阵运算即可完成展开过程,且两次矩阵运算过程一致,易于编程。以Duffing方程为算例,计算结果与数值方法一致,运算效率有所提高。     

发光二极管主波长的优化计算方法

从发光二极管主波长的定义出发,比较分析了计算发光二极管主波长的3种方法,并提出了一种优化的计算方法。先将色品图划分为10个区域,再结合线性插值运算,可以减少运算次数、提高寻找速度,简化了求主波长的计算过程,同时使主波长计算结果的精确度优于0．1nm。     

桥梁结构时变可靠度计算的新方法

为提高桥梁结构时变可靠度的计算效率,该文提出了新的计算方法。该方法基于结构时变可靠度分析的基本理论,利用Taylor级数展开,将可靠度计算从传统的积分运算形式转换为代数运算的形式,从而简化计算过程,提高计算效率。为了考虑桥梁初始承载力和衰减过程的不确定性,该文基于全概率方法,给出了计算劣化结构时变可靠度的显式公式。通过将该文方法应用于某钢筋混凝土桥梁进行时变可靠度分析,并与Monte Carlo模拟方法进行对比,表明了该文方法的准确性和高效性。     

制冷剂R142b热物性计算程序的一种简易可视化

根据国内外有关资料，对制冷工质R142b热物性数据进行了分析，得到了其热力性质简化计算模型；用Visual Basic 6．0对R142b热物性程序作了可视化研究，运算证明计算程序比较简单、实用，计算量小，精度能满足一般使用要求。     

强非线性振动系统的通用化求解程序及应用

基于研究强非线性振动系统的待定固有频率法,应用Mathematica符号运算语言,编写适用于计算多自由度系统稳态渐近解的通用化程序。在将传统理论向高维复杂系统进行推广的同时,进一步实现应用过程中涉及常微分耦合系统简化、高阶规范形计算等具体运算环节的系统化与程序化,极大地提高了理论推导的效率。基于提出的程序化方法,研究一类碳纳米管强非线性振动系统,计算其规范形和稳态渐近解,并据此讨论阻尼系数和激振力对于振动幅值的影响。最后将定量分析结果与数值结果进行对比,验证了程序化方法的有效性。     

Strongly orthotropic continuum mechanics and finite element treatment

Despite successful application to orthotropic analysis, any Lagrangian strain tensor that is symmetric can be classified as an isotropic metric, while the infinitely orthotropic case can be accurately dealt with using one‐dimensional elements, structural tensors or kinematic constraints. In this paper, we present a strongly orthotropic continuum mechanics basis that models the exact kinematic behavior of the intermediary class of materials and also show its application to multi‐axial media and treatment using the finite element method. By asserting that mechanistic strain metrics must be material property dependent and satisfy equilibrium, we are able to derive a novel orthotropic linear strain tensor that is asymmetric and thus capable of describing all levels of orthotropy, while maintaining generality to the well‐established isotropic approach. Subsequently formulated are a material principal rotation tensor, extended orthotropic compliance tensor and an extended Mohr's plot for strain relying on an additional metric denoted as aspectual strain. Using the developed finite element formulation, it is shown that identical stress results to conventional theory for an orthotropic linear problem are predicted, while offering a more informative analysis. A second numerical example demonstrates the unique capability of this approach to solve the erroneous response of strongly orthotropic materials under trellis shear as compared with a number of conventional and contemporary approaches and thus its ability to produce kinematically exact results. Copyright © 2008 John Wiley & Sons, Ltd.     

The plastic potential in the theory of anisotropic elastic-plastic solids

In the paper the yield condition is proposed for the most general anisotropic material. It is one of the possible generalizations of the Huber-Mises-Hencky yield condition for the case of anisotropy. The body considered is anisotropic elastically as well as plastically. It is assumed that the plastic anisotropy tensor is a definite function of the elastic anisotropy tensor. The corresponding flow function is a part of the strain energy and its value remains unchanged when all normal components of stress are increased by the same value. The theory of the eigen states for fourth order tensors is used. The plastic anisotropy tensor proposed has the same deviatoric eigen states as the elastic anisotropy tensor. The proposed yield condition reduces to that of Huber-Mises-Hencky when the anisotropy is vanishingly small. The method presented in this paper can be also applied to describe other types of plastic anisotropy tensor.     

Application of metric tensors to conformal arrays

Using the metric tensor g ^{the author derives the scattering parameters appearing in the field equations of the uniform theory of diffraction (UTD). The method presented allows us to derive these field parameters in terms of tensors whose general form can be applied to high-frequency electromagnetic scattering problems or more specifically to the analysis of conformal arrays. All the parameters in the field solutions are related to the array manifold properties that are derived via the use of the metric tensor are shown. The expressions for the Frenet-field tensors and the generalised Fock parameter and the shortest path propagated by the fields along the array manifold using the metric tensor in the calculus of variations are determined. The method enables UTD mutual coupling calculations to be performed for various phased array manifolds.}     

Structure-preserving space-time discretization of a mixed formulation for quasi-incompressible large strain elasticity in principal stretches

In this paper, we propose an energy and momentum consistent time-stepping scheme for nonlinear elastodynamics. The algorithm is based on a mixed Hu-Washizu–type variational principle that is inspired by the concept of polyconvexity and relies on a tensor cross product of second-order tensors. In addition, we introduce a new algorithmic stress formula in its eigenvalue representation to model the transient behavior of hyperelastic bodies of Ogden-type materials. Finally, several numerical examples show the superior performance of the proposed formulation in terms of numerical robustness and stability.     

“Practical” components of vectors and tensors

A concept of “practical” components for general vectors and tensors is introduced which provides a more versatile and useful alternative to the traditional physical components.Practical components have direct application in practical analysis. They give the magnitude of measurable quantities in orthogonal directions orientated as required to the given vector and tensor coordinates whether these are orthogonal or oblique.The algebra of practical components is well ordered and complements that of formal tensor theory. Although attention is directed to three- and two-dimensional vectors and tensors as encountered in structural mechanics, both the concept and method are valid for n-dimensional space as well as for other branches of mathematical physics.     

An element-wise scheme to analyse local mechanical anisotropy in fibre-reinforced composites

ABSTRACT

Herein, the general constitutive equation of bi-phasic materials equipped with orientation tensor is presented in direct notation. The formulation is refined by some correction factors specific to natural fibre-reinforced composites; then, a planar case is derived. The necessity of local information is emphasised through the introduction of auxiliary maps, which included volume fraction and orientation data. A semi-analytical homogenisation method is introduced through finite element analysis. Auxiliary maps are shown to be a better alternative to the overall orientation of fibres. Global calculations are insensitive to local variations whilst appropriate auxiliary maps offer refined results. Considering the multidisciplinary application of orientation tensors, the proposed scheme can be used in all areas where local information cannot be disregarded.     

Distribution of directional data and fabric tensors

Distribution of directional data is characterized by what is termed fabric tensors. A formal least square approximation is applied, and three kinds of fabric tensors are defined in connection with the choice of a basis of the space of functions on a unit sphere or a unit circle. All the resulting equations are Cartesian tensor equations, and they are interpreted in terms of the representation theory of the rotation group and the potential theory in electrodynamics. It is also shown how this characterization is related to the spherical harmonics expansion or the Fourier series expansion. Finally, a method of statistical test is presented in the Cartesian tensor form to check the true form of the distribution. A physical example is also given to illustrate the proposed technique.     

Calculation of permittivity tensors for invisibility devices by effective medium approach in general relativity

Permittivity tensors of arbitrary shaped invisibility devices were obtained using an effective medium approach in general relativity. As special cases, analytical expressions for the permittivity tensors of invisibility cloaks for the elliptic cylinder, prolate spheroid, and the confocal paraboloid geometry are derived. In the case of a elliptic cylinder, it was found that the point of infinite light speed in the electromagnetic space becomes two points in physical space in the zz component of the permittivity tensor. This result is different from the case of a perfect cylinder in which there is a line of cloak at which the speed of light becomes infinite. In the cases of prolate spheroid and confocal paraboloid, the point of infinite light speed in the electromagnetic space becomes a line in physical space for the first two tensor components and the third component of the permittivity tensor becomes singular at the line of cloak.     

Damage Constitutive Equations and its Application to Fiber Reinforced Composites under Transverse Impact

Two continuous field variables, called as continuity tensor and damage variable tensor, are used to describe the anisotropic responses of an elastic-brittle material under transverse impact load. Based on the continuum damage mechanics, anisotropic damage constitutive equations in both full and incremental forms are proposed here. The expressions of effective elastic module tensor, damage variable tensor and damage propagation force tensor are further derived, and the methods for determining the tensors are explained in detail. An example of strain and damage response of a fiber reinforced composite laminated plate under transverse impact load is employed to demonstrate the application of this theory. In the example, the damage variable coupled with geometric large deformation of laminated plate is also considered. The calculating results illustrate the influence of damage on strain field in the impacted laminated plate.     

张量积空间中框架的一种新构造

因为非张量积且较实用的高维小波基不多见,常常用低维的小波基作张量积来构造高维小波基。本文中,我们利用算子论的方法,研究了两个Hilbert空间中的框架张量以及张量积空间中框架的关系。将高维空间中的框架表示可以转化为低维空间中的框架张量,同时也可以把高维空间中的向量用低维空间的框架张量来表示。