ANALYSIS OF THE DYNAMIC BEHAVIOR OF A GRIFFITH PERMEABLE CRACK IN PIEZOELECTRIC MATERIALS WITH THE NON-LOCAL THEORY

The dynamic behavior of a Griffith permeable crack under harmonic anti-plane shear waves in the piezoelectric materials is investigated by use of the non-local theory. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near the crack tips. By means of Fourier transform, the problem can be solved with a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. These equations are solved with the Schmidt method and numerical examples are provided. Contrary to the previous results, it is found that no stress and electric displacement singularities are present at the crack tip. The finite hoop stress and the electric displacement depend on the crack length, the lattice parameter of the materials and the circle frequency of the incident waves. This enables us to employ the maximum stress hypothesis to deal with fracture problems in a natural way.

INVESTIGATION OF THE SCATTERING OF ANTI-PLANE SHEAR WAVES BY TWO GRIFFITH CRACKS USING THE NON-LOCAL THEORY

In this paper, the scattering of harmonic antiplane shear waves bytwo finite cracks is studied using the non-local theory. The Fouriertransform is applied and a mixed boundary value prob- lem isformulated. Then a set of triple integral equations is solved using anew method, namely Schimidt's method. This method is more exact andmore reasonable than Erigen's for solving this Kind of problem. Theresult of the stress near the crack tip was obtained. Contrary to theclassical elas- Ticity solution, it is found that no stresssingularity is present at the crack tip, which can explain theProblem of macroscopic and microscopic mechanics.

A Nonlinear Theory of Elastic Plates without Using Kirchhoff-Love Assumptions and Its Application

ＡＮｏｎｌｉｎｅａｒＴｈｅｏｒｙｏｆＥｌａｓｔｉｃＰｌａｔｅｓｗｉｔｈｏｕｔＵｓｉｎｇＫｉｒｃｈｈｏｆ┐ＬｏｖｅＡｓｕｍｐｔｉｏｎｓａｎｄＩｔｓＡｐｐｌｉｃａｔｉｏｎＤｏｃｔｏｒａｌＣａｎｄｉｄａｔｅ：ＳｈｅｎｇＳｈａｎｇｚｈｏｎｇＡｄｖｉｓｏｒ：Ｃ...

INVESTIGATION OF THE SCATTERING OF HARMONIC ELASTIC WAVES BY TWO COLLINEAR SYMMETRIC CRACKS USING THE NON-LOCAL THEORY

The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen's for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.

Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory

The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.

Quantum Theory of the Wannier Phenomenon

We employ a recently amended Born-Oppenheimer (hereafter shortly BO) approximation [1] to treat inelastic scattering of slow electrons from highly excited Rydberg atoms like e- + He(1s ns)→He-** for n ≫ 1. Along these lines we replace the standard BO set of potentials by an evolution operator. In this way we take a momentum-momentum coupling inadvertently disregarded by BO into account. The BO eigenvalue problem is now replaced by an evolution equation. One eigen-evolution has been identified as Wanner channel. That channel describes the diffraction of electron pairs from a potential ridge. That diffraction causes a phase jump of π/2 in the channel evolution. Moreover we present a new conservative attractive force controlling the motion of the electron pair as a whole in the nuclear field whose potential is given by . The coupling constant g has been calculated. That potential foreign to the standard BO approximation manifests itself by an entirely new series of isolated resonances located slightly below the double ionization threshold. This resonance ensemble compares favorably with experimental data. Further we present an evolution which forces the electron pair to the electrostatically unstable top of the potential ridge. That evolution may be regarded as quantum version of Wannier’s converging trajectory, and manifests itself here as Fresnel distribution.

Thermoelastic Analysis of Non-uniform Pressurized Functionally Graded Cylinder with Variable Thickness Using First Order Shear Deformation Theory(FSDT) and Perturbation Method

Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.

Ordered Rate Constitutive Theories for Non-Classical Thermoviscoelastic Fluids with Internal Rotation Rates

The paper presents constitutive theories for non-classical thermoviscoelastic fluids with dissipation and memory using a thermodynamic framework based on entirety of velocity gradient tensor. Thus, the conservation and the balance laws used in this work incorporate symmetric as well as antisymmetric part of the velocity gradient tensor. The constitutive theories derived here hold in coand contra-variant bases as well as in Jaumann rates and are derived using convected time derivatives of Green’s and Almansi strain tensors as well as the Cauchy stress tensor and its convected time derivatives in appropriate bases. The constitutive theories are presented in the absence as well as in the presence of the balance of moment of moments as balance law. It is shown that the dissipation mechanism and the fading memory in such fluids are due to stress rates as well as moment rates and their conjugates. The material coefficients are derived for the general forms of the constitutive theories based on integrity. Simplified linear (or quasi-linear) forms of the constitutive theories are also presented. Maxwell, Oldroyd-B and Giesekus constitutive models for non-classical thermoviscoelastic fluids are derived and are compared with those derived based on classical continuum mechanics. Both, compressible and incompressible thermoviscoelastic fluids are considered.

INVESTIGATION OF A GRIFFITH CRACK SUBJECT TO UNIFORM TENSION USING THE NON-LOCAL THEORY BY A NEW METHOD

Field equations of the non-local elasticity are solved to determine the state of stress in a plate with a Griffith crack subject to uniform tension. Then a set of dual-integral equations is solved using a new method, namely Schmidt's method. This method is more exact and more reasonable than Eringen's a one Sor solving this kind of problem. Contrary to the solution of classical elasticity, it is found that no stress singularity is present ar the crack tip. The significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales. The finite hoop stress at the crack tip depends on the crack length.

Non-equilibrium statistical theory about microscopic fatigue cracks of metal in magnetic field

This paper develops the non-equilibrium statistical fatigue damage theory to study the statistical behaviour of micro-crack for metals in magnetic field. The one-dimensional homogeneous crack system is chosen for study. To investigate the effect caused by magnetic field on the statistical distribution of micro-crack in the system, the theoretical analysis on microcrack evolution equation, the average length of micro-crack, density distribution function of microcrack and fatigue fracture probability have been performed. The derived results relate the changes of some quantities, such as average length, density distribution function and fatigue fracture probability, to the applied magnetic field, the magnetic and mechanical properties of metals. It gives a theoretical explanation on the change of fatigue damage due to magnetic fields observed by experiments, and presents an analytic approach on studying the fatigue damage of metal in magnetic field.

THE SCATTERING OF HARMONIC ELASTIC ANTI-PLANE SHEAR WAVES BY A FINITE CRACK IN INFINITELY LONG STRIP USING THE NON-LOCAL THEORY

In this paper, the scattering of harmonic anti-plane shear wavesby a finite crack in infinitely long strip is studied using thenon-local theory. The Fourier transform is applied and a mixedboundary value problem is formulated. Then a set of dual integralequations is solved using the Schmidt method instead of the first orthe second integral equation method. A one-dimensional non-localkernel is used instead of a two-di- mensional one for the anti-planedynamic problem to obtain the stress occurring at the crack tips.Contrary to the classical elasticity solution, it is found that nostress singularity is present at the crack tip. The non-local dynamicelastic solutions yield a finite hoop stress at the crack tip, thusallowing for a fracture criterion based on the maximum dynamic stresshypothesis. The finite hoop stress at the crack tip depends on thecrack length, the width of the strip and the lattice parameters.

A Nonlinear Dynamical Theory of Non-Classical Plates

In ths paper. a new nonlinear formulation of plates. including shear and rotatory inertia and transverse normal stress effects, is developed by means of general assumptions, of which the von Karman-type formulation and some thick plate theories are special cases. To keep the formulation fairly general, the problem addressed in this paper simultaneously includes: the effects of shear deformation according to the geometric deformation similarity of the crosssection, the rotatory inertia, and the transverse normal stress. The three-dimensional compatible equations are applied to derive the basic equations. Numerical results are given for linear and non-linear analysis of plates.

THE FIRST-ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDER UNIFORM SURFACE LOADING (Ⅲ)──NUMERICAL RESULTS

ased upon the differential equations and their related boundary conditions givenin the previous papers[1, 2], using a global interpolation method, this paper presents anumerical solution to the axisymmetric bending problem of non-Kirchhoff-Love theoryfor circular plate with fixed boundary under uniform surface loading. All the numericalresults obtained in this paper are compared with that of Kirchhoff-Love classicaltheory[3] and E. Reissner's modified theory[4]

Rate Constitutive Theories of Orders n and 1n for Internal Polar Non-Classical Thermofluids without Memory

In recent papers, Surana et al. presented internal polar non-classical Continuum theory in which velocity gradient tensor in its entirety was incorporated in the conservation and balance laws. Thus, this theory incorporated symmetric part of the velocity gradient tensor (as done in classical theories) as well as skew symmetric part representing varying internal rotation rates between material points which when resisted by deforming continua result in dissipation (and/or storage) of mechanical work. This physics referred as internal polar physics is neglected in classical continuum theories but can be quite significant for some materials. In another recent paper Surana et al. presented ordered rate constitutive theories for internal polar non-classical fluent continua without memory derived using deviatoric Cauchy stress tensor and conjugate strain rate tensors of up to orders n and Cauchy moment tensor and its conjugate symmetric part of the first convected derivative of the rotation gradient tensor. In this constitutive theory higher order convected derivatives of the symmetric part of the rotation gradient tensor are assumed not to contribute to dissipation. Secondly, the skew symmetric part of the velocity gradient tensor is used as rotation rates to determine rate of rotation gradient tensor. This is an approximation to true convected time derivatives of the rotation gradient tensor. The resulting constitutive theory: (1) is incomplete as it neglects the second and higher order convected time derivatives of the symmetric part of the rotation gradient tensor;(2) first convected derivative of the symmetric part of the rotation gradient tensor as used by Surana et al. is only approximate;(3) has inconsistent treatment of dissipation due to Cauchy moment tensor when compared with the dissipation mechanism due to deviatoric part of symmetric Cauchy stress tensor in which convected time derivatives of up to order n are considered in the theory. The purpose of this paper is to present ordered rate constitutive theories for deviatoric Cauchy strain tensor, moment tensor and heat vector for thermofluids without memory in which convected time derivatives of strain tensors up to order n are conjugate with the Cauchy stress tensor and the convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n are conjugate with the moment tensor. Conservation and balance laws are used to determine the choice of dependent variables in the constitutive theories: Helmholtz free energy density Φ, entropy density η, Cauchy stress tensor, moment tensor and heat vector. Stress tensor is decomposed into symmetric and skew symmetric parts and the symmetric part of the stress tensor and the moment tensor are further decomposed into equilibrium and deviatoric tensors. It is established through conjugate pairs in entropy inequality that the constitutive theories only need to be derived for symmetric stress tensor, moment tensor and heat vector. Density in the current configuration, convected time derivatives of the strain tensor up to order n, convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n, temperature gradient tensor and temperature are considered as argument tensors of all dependent variables in the constitutive theories based on entropy inequality and principle of equipresence. The constitutive theories are derived in contravariant and covariant bases as well as using Jaumann rates. The nth and 1nth order rate constitutive theories for internal polar non-classical thermofluids without memory are specialized for n = 1 and 1n = 1 to demonstrate fundamental differences in the constitutive theories presented here and those used presently for classical thermofluids without memory and those published by Surana et al. for internal polar non-classical incompressible thermofluids.

The Nature of Inertia Explained Using the Field Theory

Analysis of free fall and acceleration of the mass on the Earth shows that using abstract entities such as absolute space or inertial space to explain mass dynamics leads to the violation of the principle of action and reaction. Many scientists including Newton, Mach, and Einstein recognized that inertial force has no reaction that originates on mass. Einstein calls the lack of reaction to the inertial force a serious criticism of the space-time continuum concept. Presented is the hypothesis that the inertial force develops in an interaction of two masses via the force field. The inertial force created by such a field has reaction force. The dynamic gravitational field predicted is strong enough to be detected in the laboratory. This article describes the laboratory experiment which can prove or disprove the hypothesis of the dynamic gravitational field. The inertial force, calculated using the equation for the dynamic gravitational field, agrees with the behavior of inertial force observed in the experiments on the Earth. The movement of the planets in our solar system calculated using that equation is the same as that calculated using Newton’s method. The space properties calculated by the candidate equation explain the aberration of light and the results of light propagation experiments. The dynamic gravitational field can explain the discrepancy between the observed velocity of stars in the galaxy and those predicted by Newton’s theory of gravitation without the need for the dark matter hypothesis.

CONSTRUCTION OF QUANTUM FIELD THEORY OF DISLOCATIONS BASED ON THE NON-RIEMANNIANPLASTICITY

A new microscopic approach was proposed, which bridges the order gap between the dislocation theory and the crystalline plasticity based on the quantum field theory of dislocations. The Ginzburg-Landau equation was derived rigorously from the quantized Hamiltonian for a crystal body containing a large number of dislocations, which gives the reaction-diffusion (RD) type differential equations. The RD equation describes periodic patterning shown in PSBs, etc.. relationship between the proposed theory and the concepts appeared in the non-Riemannian plasticity was extensively discussed by introducing the gauge field of dislocations. (Edited author abstract) 15 Refs.

非货币激励因素对中小学教师工作满意度的影响——基于云贵川渝的调查

教师工作满意度是影响教师工作效能、促进教师可持续发展的重要因素。研究采用TALIS 2018教师问卷对云贵川渝4个省份的中小学教师展开抽样调查。数据分析显示,该地区教师工作满意度处于较高水平,但内部群体间存在显著性差异。回归分析发现,云贵川渝4省份中小学教师工作满意度受工资薪酬以及其他非货币因素的影响。比较分析发现,云贵川渝初中教师对工资薪酬的接受度高于上海同行,但对社会认可、媒体关注等非货币激励因素的认可程度却低于上海教师,从而使其工作满意度整体水平低于上海。研究认为,坚持教育家精神铸魂强师的同时提升教师工作满意度,需要在巩固提高工资薪酬水平的基础上,进一步从优化教师工作体验、提高教师学历、打通职业晋升渠道、营造尊师重教良好氛围等非货币因素着手,在满足教师内在需求的同时,为加快教育现代化、建设教育强国、办好人民满意的教育提供有力支撑。

基于物质-文化互动视角的传统村落形态识别及优化策略研究:以湖南省郴州市庙下村为例

在乡村振兴战略实施过程中,乡村聚落形态识别及规律分析对传统村落的传承发展与创新保护具有重要意义。本文基于表征与非表征理论和康泽恩形态学理论,从物质-文化互动视角构建涵盖历史形态、结构形态和功能文化形态的传统村落形态识别体系。以湖南省郴州市庙下村为案例,通过实地调研、参与式评估、问卷调查、深度访谈等方式对村落进行调查分析,研究结果表明:(1)从历史形态演化维度来看,受不同时期历史文化与社会文化的影响,庙下村聚落物质形态呈现出限制性扩张、集聚式增长、外延式发展和沿路式扩张4个阶段。(2)从结构形态的特征维度来看,村落内部形成由点、线、面交织的完整有序结构。其中,点要素在东北宗祠附近及中心处集聚,线要素呈交叉纵横的棋盘式布局特征,面要素的功能板块在村落中呈现界限清晰的规则有序布局。(3)不同点、线、面承载的文化空间有所差异。从文化形态维度来看,以乡村聚落内的1 086处现存建筑为评价单元,选取用地类型、建筑年代、建筑质量、建筑风貌、建筑层数和屋顶形式6个评价指标,采用2.5D空间形态表达方式探究文化价值的差异性,庙下村文化价值特征的各方面在空间上均呈现出显著集聚、相似与连续的特征。(4)基于物质-文化形态特征,将庙下村分为传统文化区、现代化生活区和传统生活区等6种功能类型,根据不同区域存在问题以及治理主体差异,进一步从管理策略上归并为保护区、整治区和更迭区,以村民、政府和企业主体构成的行动者网络为逻辑出发点,针对不同区域的开发保护提出建议,为促进传统村落可持续发展提供新视角。

群延迟加权的非凸稀疏时频分析方法及其应用

时频分析方法被广泛应用于机械系统故障诊断,如何有效提高非平稳信号的时频分布可读性成为时频分析的难点。将稀疏理论与时频分析方法相结合,可实现高分辨率的时频表示。在理想脉冲信号模型的基础上,将群延迟算子引入广义极大极小凹正则稀疏时频表示模型,提出基于群延迟加权的非凸稀疏时频表示。首先,建立基于广义极大极小凹正则的非凸稀疏时频模型,并给出保证目标函数凸性的参数条件。其次,推导群延迟算子并建立加权策略,提出前向后向分裂算法以求解加权非凸稀疏时频表示模型。再次,利用仿真信号对所提方法在时频聚集性和重构性等方面的性能进行分析。最后,根据滚动轴承的模拟信号和实验信号进行故障分析,验证了所提出的方法在滚动轴承故障诊断中的有效性。

Research on a non-linear chaotic prediction model for urban traffic flow

In order to solve serious urban transport problems, according to the proved chaotic characteristic of traffic flow, a non linear chaotic model to analyze the time series of traffic flow is proposed. This model reconstructs the time series of traffic flow in the phase space firstly, and the correlative information in the traffic flow is extracted richly, on the basis of it, a predicted equation for the reconstructed information is established by using chaotic theory, and for the purpose of obtaining the optimal predicted results, recognition and optimization to the model parameters are done by using genetic algorithm. Practical prediction research of urban traffic flow shows that this model has famous predicted precision, and it can provide exact reference for urban traffic programming and control.