A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J(z), the stress intensity factor K(z) and the tri-axial stress constraint level T _z (z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J(z) and T _z (z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.     

Characteristics and generation of elastic turbulence in a three-dimensional parallel plate channel using direct numerical simulation

Direct numerical simulations(DNSs) of purely elastic turbulence in rectilinear shear flows in a three-dimensional(3D) parallel plate channel were carried out,by which numerical databases were established.Based on the numerical databases,the present paper analyzed the structural and statistical characteristics of the elastic turbulence including flow patterns,the wall effect on the turbulent kinetic energy spectrum,and the local relationship between the flow motion and the microstructures' behavior.Moreover,to address the underlying physical mechanism of elastic turbulence,its generation was presented in terms of the global energy budget.The results showed that the flow structures in elastic turbulence were 3D with spatial scales on the order of the geometrical characteristic length,and vortex tubes were more likely to be embedded in the regions where the polymers were strongly stretched.In addition,the patterns of microstructures' elongation behave like a filament.From the results of the turbulent kinetic energy budget,it was found that the continuous energy releasing from the polymers into the main flow was the main source of the generation and maintenance of the elastic turbulent status.     

Theoretical and numerical analysis of electron motion in a three-dimensional undulator field

The results of numerical calculations of electron trajectories in the three-dimensional ideal magnetic field of an undulator are given. These trajectories can be regarded as exact results in our case. It is shown that, in a series of cases, results of the calculation of trajectories using approximate analytical formulas significantly differ from those obtained using numerical methods. The obtained numerical results show that the influence of the undulator on the dynamics of the electron beam is very complicated and cannot be reduced only to the focusing properties of the undulator magnetic field or wiggler.     

Plastic analysis of crack problems in three-dimensional icosahedral quasicrystalline material

Due to their complexity, the basic plastic properties of all quasicrystalline materials are essentially unknown [M. Feuerbacher, C. Thomas, K. Urban, Plastic behaviour of quasicrystalline materials, in Quasicrystals: Structure and Physical Properties, H.R. Trebin, ed., Wiley/VCH, Berlin, 2003]. Plastic deformation of cracks in icosahedral quasicrystals have been analyzed in a strict and systematic form and the crack tip opening displacement (CTOD) and size of the plastic zone around the crack tip was determined exactly. CTOD is suggested as a parameter of plastic fracture for quasicrystalline materials. The present work may also provide a novel methodology for plastic analysis of quasicrystals.     

An ultrasonic method for dynamic monitoring of fatigue crack initiation and growth

Attached ultrasonic sensors can detect changes caused by crack initiation and growth if the wave path is directed through the area of critical crack formation. Dynamics of cracks opening and closing under load cause nonlinear modulation of received ultrasonic signals, enabling small cracks to be detected by stationary sensors. A methodology is presented based upon the behavior of ultrasonic signals versus applied load to detect and monitor formation and growth of cracks originating from fastener holes. Shear wave angle beam transducers operating in through transmission mode are mounted on either side of the hole such that the transmitted wave travels through the area of expected cracking. Time shift is linear with respect to load, and is well explained by path changes due to strain combined with wave speed changes due to acoustoelasticity. During subsequent in situ monitoring with unknown loads, the measured time of flight is used to estimate the load, and behavior of the received energy as a function of load is the basis for crack detection. Results are presented from low cycle fatigue tests of several aluminum specimens and illustrate the efficacy of the method in both determining the applied load and monitoring crack initiation and growth.     

Spring-block approach for crack patterns in glass

Fracture patterns resulting from point-like impact acting perpendicularly on the plane of a commercial sodalime glass plate is modelled by a spring-block system. The characteristic patterns consist of crack lines that are spreading radially from the impact point and concentric arcs intersecting these radial lines. Experimental results suggest that the number of radial crack lines is scaling linearly with the energy dissipated during the crack formation process. The elaborated spring-block model reproduces with success the observed fracture patterns and scaling law.     

Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis

In the past three decades, considerable progress has been made in the investigation of incompressible turbulent boundary layer through experiments, DNS and theoretical works, including: (1) the statistics characteristic and structure of turbulence; (2) the co-herent structures in turbulent flows; (3) turbulence modeling and the large eddy simula-tion (LES). In contrast, the progress was very slow for the compressible, in particular, the super-sonic turbulent boundary layer. Recent works on d…     

A comparative analysis of reticular crack on ceramic plate driven by thermal shock

Reticular crack is generally found on the surface of ceramic material that has been subjected to a thermal-shock condition. In the present study, a quantitative effect of thermal shock and quench temperature has been studied and investigated. Experimental tests were carried out to characterize the reticular crack that has been found in the Ge Kiln, which is a famous art of the ancient Chinese culture. After comparative analysis between thermal-shock cracks and the glaze crack patterns of the Ge Kiln porcelain, it is found that this study is expected to provide a powerful tool for recurrence of the long-lost firing and cooling process of the Ge Kiln porcelain.     

A new statistical dynamic analysis on vegetation patterns in land ecosystems

As complex self-adaptive systems, land ecosystems usually tend to produce intricate vegetation patterns under specific environmental constraints, which have ever puzzled us for decades. In this paper, a universal principle on pattern formation of land ecosystems is highlighted as: a land ecosystem always tries to find an optimal process to acquire maximized flux under a certain constraint or price. The underlying microscopic dynamic mechanism that induces complex vegetation patterns in land ecosystems is then revealed. Based on the Holdridge life zone system, evolutionary dynamic processes and structural classifications of several typical vegetation patterns are then simulated and discussed. Good agreements between theoretical analyses and numerical results are found. This paper demonstrates that the new theoretical analyses and simulation technique can be possibly applied to the whole land ecosystem, not only benefiting academic study on the formation and dynamics of vegetation patterns, but also providing implications for vegetation classification, vegetation protection and soil erosion control.     

Reconstruction of heat flux profile on the HL-2A divertor plate with a three-dimensional analysis model

A three-dimensional analysis model based on the finite element method (FEM) is developed, which can derive the evolution and distribution characteristics of heat flux deposited on the divertor plate from the surface temperature measured by infrared thermography diagnostics. The numerical simulations of surface heating due to localized power bursts and the power deposition calculations demonstrate that this analysis can provide accurate results and useful information about localized hot spots compared with the normal one- and two-dimensional calculations. In this paper, the details of this three-dimensional analysis are presented, and some results in ohmic heating and electron cyclotron resonant heating (ECRH) discharge on HL-2A are given.     

Confocal three-dimensional micro X-ray fluorescence based on synchrotron radiation for mineral analysis

The confocal three-dimensional micro X-ray fluorescence using polycapillary optics and a synchrotron radiation was applied to nondestructively analyze elemental compositions of minerals, and thereby obtain the three-dimensional distributions of elements in the minerals. Such confocal micro X-ray fluorescence had potential applications in the mineral prospecting, identification of jades, differentiation of stones.     

An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation

An analytical approach is presented for the forced vibration analysis of a plate containing a surface crack of variable angular orientation, based on three different boundary conditions. The method is based on classical plate theory. Firstly, the equation of motion is derived for the plate containing the angled surface crack with respect to one side of the plate and subjected to transverse harmonic excitation. The crack formulation representing the angled surface crack is based on a simplified line-spring model. Then, by employing the Berger formulation, the derived governing equation of motion of the cracked plate model is transformed into a cubic nonlinear system. The nonlinear behaviour of the cracked plate model is thus investigated from the amplitude–frequency equation by use of the multiple scales perturbation method. For both cracked square and rectangular plate models, the influence of the boundary conditions, the crack orientation angle, crack length, and location of the point load is demonstrated. It is found that the vibration characteristics and nonlinear characteristics of the plate structure can be greatly affected by the orientation of the crack in the plate. Finally the validity of the developed model is shown through comparison of the results with experimental work.     

基于半波片的偏振跟踪理论分析

分析了卫星量子密钥分配中采用半波片进行偏振跟踪的原理，通过旋转半波片实现对偏振“零”方向的跟踪.针对BB84协议和B92协议，给出了三组共轭基六个光子偏振态的变换关系式，分析了基于偏振跟踪的量子密钥编码原理. 关键词： 量子密钥分配 偏振跟踪 半波片     

Determination of dynamic three-dimensional displacement fields on a shell surface

This paper presents a solution to the problem of dynamic three-dimensional displacement distributions on a curved surface under impact-loading by utilizing photomechanics and the finite-element method. An impulsive force is applied by using a new type of electromagnetic forcing mechanism, which gives good repeatability. The relation between instataneous loading and time that is set for the force-voundary condition in the finite-element calculation of the displacement components is recorded experimentally. It is found that the experimental results are in good agreement with those of the finite-element method.     

Vibration analysis of a rectangular thin isotropic plate with a part-through surface crack of arbitrary orientation and position

In this paper, vibration analysis of a rectangular thin isotropic plate with a part-through surface crack of arbitrary orientation and position is performed by using the Kirchhoff plate theory. Simply supported (SSSS), clamped (CCCC) and simply supported–clamped (SCSC) boundary conditions are considered for the analysis. First, the governing differential equation of a cracked plate is formulated. A modified line spring model is then used to formulate the crack terms in the governing equation. Next, by the application of Burger's formulation, the differential equation is transformed into the well-known Duffing equation with cubic and quadratic nonlinearities. The Duffing equation is then solved by the method of multiple scales (MMS) to extract the frequency response curve. Natural frequencies are evaluated for different values of length, angle and position of a part-through surface crack. Some results are compared with the published literature. Amplitude variation with different values of length, angle and position of a part-through surface crack are presented, for all three types of the plate boundary conditions.     

Direct numerical simulations and analysis of three-dimensional n-heptane spray flames in a model swirl combustor

Three-dimensional n-heptane spray flames in a swirl combustor are investigated by means of direct numerical simulation (DNS) to provide insight into realistic spray evaporation and combustion as well as relevant modeling issues. The variable-density, low-Mach number Navier–Stokes equations are solved using a fully conservative and kinetic energy conserving finite difference scheme in cylindrical coordinates. Dispersed droplets are tracked in a Lagrangian framework. Droplet evaporation is described by an equilibrium model. Gas combustion is represented using an adaptive one-step irreversible reaction. Two different cases are studied: a lean case that resembles a lean direct injection combustion, and a rich case that represents the primary combustion region of a rich-burn/quick-quench/lean-burn combustor. The results suggest that premixed combustion contribute more than 70% to the total heat release rate, although diffusion flame have volumetrically a higher contribution. The conditional mean scalar dissipation rate is shown to be strongly influenced, especially in the rich case. The conditional mean evaporation rate increases almost linearly with mixture fraction in the lean case, but shows a more complex behavior in the rich case. The probability density functions (PDF) of mixture fraction in spray combustion are shown to be quite complex. To model this behavior, the formulation of the PDF in a transformed mixture fraction space is proposed and demonstrated to predict the DNS data reasonably well.     

Stress-intensity coefficients in an infinite plate with a crack in a nonuniform steady field

The stress-strain state around the end of a crack ¦x¦<, y=0 in the elastic plane (x, y) is considered for arbitrary given loads acting on the periphery of the crack and constant load at infinity. At the same time, there is a plane thermalstress state due to a steady heat flux parallel to the considered plane. An analytical expression is found for the stress-intensity coefficients in the given conditions, generalizing the case previously considered. A series of examples is given on the calculation of the intensity coefficients of purely temperature stresses in specific conditions of the thermal state of the elastic body. The results obtained may be used in constructing a theory of the time dependence of the strength in the gross failure of polymer materials.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 7–13, March, 1979.     

Ultrasonic engine based on traveling waves in a plate

Velocity dispersion curves and phase relationships between the surface displacement components are calculated in the case of waves propagating in XZ-, YZ-, and ZY-cut LiNbO₃ plates. The dispersion curves agree with experimental frequency dependences of the excitation efficiency for various modes in the plates. The displacements of ZnS microparticles placed on the surface of the plates qualitatively agree with the analytical phase relationships between the displacement components. Results obtained indicate that the plate may be used as an ultrasonic engine capable of transferring microparticles in various physical and industrial processes.