CHARACTERISTICS OF SUBDIFFERENTIALS OF FUNCTIONS

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CHARACTERIZATION OF POWDER FLOWABILITY USING MEASUREMENT OF ANGLE OF REPOSE

In response to the need in industry for a quick and reproducible method of measuring the flowability of powders in processes involving transport and storage, the apparently simple idea of measuring angle of repose has been revived. The simple tester first used has evolved over a number of years into the present version which is shown to be capable of handling quite small samples of powders that are even slightly cohesive. Experimental data are presented and results shown to compare consistently with the better known Hausner ratio.     

THE THEORY OF SIMILARITY AND THE PROFILE OF VERTICAL DISTRIBUTION OF CONCENTRATION OF SAND PARTICLES

In this article,we treat the problem of two-dimensionaluniform steady channel flow of turbid water with theory ofsimilarity.Under the condition of similarity of turbulentfluctuation velocity and fluctuation of concentration ofsand particles,we obtain the profile of the vertical dis-tribution of concentration of sand particles.This profileof vertical distribution of concentration of sand particlesis slightly different from that obtained by diffusion theory,and departs from that obtained by gravitational theory.     

TORSIONAL RIGIDITY OF SHELLS OF REVOLUTION

In this paper,the general equations of equilibrium for axisymmetrical deformationincluding the torsional deformation of revolutional shells are derived.It is shown that theshearing stress distribution due to torsion is independent of other stress componentsincluding those of membrane stress and bending stress.In this paper,the torsional deformation is considered to be represented by membraneaction only,and also by the combined action of bending membrane deformation.It is shownthat the main contribution of torsional rigidity is that related to membrane action.     

THEORY OF ELASTICITY OF AN ANISOTROPIC BODY FOR THE BENDING OF BEAMS

A theory of elasticity for the bending of orthogonal anisotropic beams has been developed by analogy with the special case, which can be obtained by applying the theory of elasticity for bending of transversely isotropic plates to the problems of two deminsions. In this paper, we present a method to solve the problems of bending of orthogonal anisotropic beams and a new theory of the deep-beam whose ratio of depth to length is larger. It is pointed out that Reissner's theory to account for the effect of transverse shear deformation is not very approximate in the components of stress,     

QUASICONTINUUM SIMULATION OF NANOINDENTATION OF NICKEL FILM

A large-scale atom simulation of nanoindentation into a thin nickel film using thequasicontinuum method was performed. The initial stages of the plasticity deformation of nickelwere studied. Several useful results were obtained as follows: (1)The response of the load versusindentation depth—on the load versus indentation depth curve, besides the straight parts cor-responding to the elastic property of nickel, the sudden drop of the load occurred several times;(2) The phenomena of dislocation nucleation—the dislocation nucleation took place when theload descended, which makes it clear that dislocation nucleation causes the drop of the load;(3)The mechanism of the dislocation emission—the Peierls-Nabarro dislocation model and a pow-erful criterion were used to analyze the dislocation emission. And the computational value was ingood agreement with the predict value; (4) The density of geometrically necessary dislocations.A simple model was used to obtain the density of geometrically necessary dislocations beneaththe indenter. Furthermore, the influence of the boundary conditions on the simulation results wasdiscussed.     

BLOW-UP OF SOLUTIONS OF NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS OF GENERALIZED NERVE CONDUCTION TYPE

This paper deals with the two type of mixed problems with respect to Neumannboundary and Dirichlet boundary for nonlinear pseudo-hyperbolic equations of generalizednerve conduction typeu_1-△u_1=F(x,t,u,(?)u,u_t,(?)i_t)when the nonlinear part F(x.t,u,(?)u,u_t,(?)u_t)and the initial values satisfy someconditions,the blow-up properties of the solutions are obtained.     

COMPUTER SIMULATION OF THE MOTION OF THE BULLET BELT OF AIRPLANE GUN

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APPLICATION 0F THE THEORY OF BRANCHING OF SOLUTIONS OF NONLINEAR EQUATIONS IN THE ESTIMATION OF POLE PERTURBANCE OF LINEAR CLOSED-LOOP SYSTEMS

When the state and input matrices of a multivariable lineartime-invariant system are perturbed.the problem of the es-timation of pole perturbance of closed-loop system is con-sidered by making use of the theory of branching of solutionsfor nonlinear equations.     

ANALYSIS OF THE MOTION OF A GYRO-THEODOLITE

With the method of analytical mechanics,this paper studies the motions of a gyro-theodolite under the action of (1) the torque of gravity only,(2)the torque applied by theband suspension.(3)the torque of the band suspension with air damping considered,theequations of motion are then established and their solutions are found.Furthermore,analysis of the law of motion and the behaviour of gyro-theodolite during the orientation ismade.     

Numerical method for the shape reconstruction of a hard target

IntroductionAninverseproblemofconsiderableimportanceinvariousfieldsofengineeringtechnology ,suchasnondestructivetesting ,medicalimaging ,remotesensingandseismicimaging ,istodeterminetheshapeofascatteringobjectfromitsfar_fieldeffectsontheacousticscatteringwaves.However,thiskindofproblemisparticularlydifficulttosolvesinceitisbothnonlinearandill_posed[1].Fortunately ,therehavebeenseveralmethodsdevelopedforsolvingnumericallytheinverseproblemduringthelastdecade .Ofparticularimportancearenonlinearop…     

An inversion integral for crack-scattering data

The inverse problem of determining the size, shape and orientation of a flat crack from high-frequency far-field elastic waves scattered by the crack is investigated. The results show that desired information on a crack can be obtained from the first arriving scattered longitudinal waves only. It is shown that an approximate high-frequency solution to the direct problem, based on physical elastodynamics, yields an expression for the scattered far-field of longitudinal motion which suggests a solution to the inverse problem by application of Fourier-type inversion integrals to scattering data. Two kinds of inversion integrals are examined. The inversion problem becomes relatively simple if some a-priori information is available, either on the orientation of the plane of the crack or on a plane of symmetry. The method of inversion is verified for a flat crack of elliptical shape. Some computational technicalities are discussed, and the method is also applied to experimental scattering data.     

Elastodynamic inversion for shape reconstruction and type classification of flaws

Two linearized inverse scattering methods are investigated to reconstruct the shape of flaws in the elastic solid. One is based on the Born approximation and the other is based on the Kirchhoff approximation. The Born inversion is sensitive to the volumetric flaw but not to a crack-like flaw. On the other hand, the Kirchhoff inversion reacts to both boundaries of volumetric and crack-like flaws. The combined use of Born and Kirchhoff inversions leads to the classification method of flaw type. The performance of the proposed classification procedure is demonstrated by the numerical simulations and then by the experimental measurements for the two-dimensional models of flaws. An example for the three-dimensional shape reconstruction is also shown by using the numerically calculated backscattering amplitudes.     

Interacting cracks and ellipsoidal inhomogeneities by the equivalent inclusion method

Based on the Eshelby's equivalent inclusion method (EIM) and Hill's theorem on discontinuities of elastic fields across the interfaces, a theory for the determination of the stress intensity factors (SIFs) of arbitrarily oriented interacting cracks under non-uniform far-field applied stress (strain) is developed. As shown in this investigation the EIM proposed by Moschovidis and Mura can be extended for treatment of such problems, but their formulations are quite cumbersome and computationally inefficient. An alternative analytical approach is proposed that is computationally more efficient, and unlike the method of Moschovidis and Mura can easily handle complex problems of interacting inhomogeneities and cracks. It is seen that as the interaction between the inhomogeneities becomes stronger, this method yields results that are closer to the solutions reported in the literature than the solutions obtained using the extended EIM of Moschovidis and Mura, which is developed herein. Problems involving combinations of interacting elliptic and penny shape cracks and inhomogeneities are excellent candidates for demonstration of the accuracy and robustness of the present theory, for which the previous EIM produces less accurate results. Due to the limitations imposed on the existing methods, every reported treatment has been tailored for a certain category of problems, and only uniform far-field loadings have been remedied. In contrast, the present theory is more general than the previously reported theories and it encompasses interacting cracks having a variety of geometries subjected to non-uniform far-field applied stress (strain); moreover, it is applicable to modes, I, II, III, and mixed mode fracture.     

Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping flaws under uniaxial compression

Failure of rock mass that is subjected to compres-sive loads occurs from initiation, propagation, and linkage of new cracks from preexisting fissures. Our research inves-tigates the cracking behaviour and coalescence process in a brittle material with two non-parallel overlapping flaws using a high-speed camera. The coalescence tensile crack and tensile wing cracks were the first cracks to occur from the pre-existing flaws. The initiation stresses of the primary cracks at the two tips of each flaw were simultaneous and decreased with reduced flaw inclination angle. The following types of coalescence cracks were identified between the flaws: pri-mary tensile coalescence crack, tensile crack linkage, shear crack linkage, mixed tensile-shear crack, and indirect crack coalescence. Coalescence through tensile linkage occurred mostly at pre-peak stress. In contrast, coalescence through shear or mixed tensile-shear cracks occurred at higher stress. Overall, this study indicates that the geometry of preexisting flaws affect crack initiation and coalescence behaviour.     

An investigation of partial cone cracks in silicon nitride balls

Hybrid silicon nitride ball/steel raceway bearings are used in advanced aircraft engines and space propulsion systems. Silicon nitride is a brittle material and partial cone cracks, or c-cracks, originate from contact interactions during manufacturing. These cracks limit the Rolling Contact Fatigue (RCF) life of the balls. Here the authors examine subsurface Hertzian stresses between contacting spheres, using an analytical stress solution, to investigate their applicability to predicting and characterizing crack size and shape. The authors also incrementally develop these cracks through an iterative crack growth procedure using a 3D finite element analysis. Comparisons are then made to experimental images of the flaws in silicon nitride. By varying the initial conditions during the contact interaction of the balls we demonstrate that a wide range of cone and partial cone cracks, observed in practice, can be generated using both the analytical and numerical fracture mechanics approaches. Furthermore, an expression is presented for the impact velocity that induces a cone crack from a maximum radial stress criterion at the contact periphery.     

An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression

This study presents crack initiation, propagation and coalescence at or near pre-existing open cracks or flaws in a specimen under uniaxial compression. The flaw geometry in the specimen was a combination of a horizontal flaw and an inclined flaw underneath. This flaw geometry is different from those reported in the previous studies, where a pair of parallel flaws was used. Three materials were used, PMMA (Poly Methyl MethAcrylate), Diastone (types of molded gypsum), and Hwangdeung granite. Crack initiation and propagation showed similar and different patterns depending on the material. In PMMA, tensile cracks initiated at the flaw tips and propagated to the tip of the other flaw in the bridge area. The cracks then coalesced at a point of the inclined flaw, which is affected by the flaw inclination angle. For Diastone and Hwangdeung granite, tensile cracks were observed followed by the initiation of shear cracks. Coalescence occurred mainly through the tensile cracks or tensile and shear cracks. Crack coalescence was classified according to the crack coalescence types of parallel flaws for overlapping flaw geometry in the past works. In addition, crack initiation and coalescence stresses in the double-flawed specimens were analyzed and compared with those in the single-flawed specimen. Numerical simulations using PFC^2D (Particle Flow Code in two dimensions) based on the DEM (Discrete Element Method) were carried out and showed a good agreement with the experimental results in the coalescence characteristics in Hwangdeung granite. These experimental and numerical results are expected to improve the understanding of the characteristics of cracking and crack coalescence and can be used to analyze the stability of rock and rock structures, such as the excavated underground openings or slopes, tunneling construction, where pre-existing cracks or fractures play a crucial role in the overall integrity of such structures.     

基于频率和模态保证准则的结构内部多缺陷反演

静响应(位移、应变等)在实际问题的反演分析中很难由安装在结构上的一组传感器记录得到,而结构的动力特性(频率、振型)和 动力响应(加速度、速度、动位移)在实际问题中较易通过传感器采集得到. 文中基于频率残差和模态保证准则构建了反演分析模型的目标函数,并结合频域内动力扩展有限元法和人工蜂群智能优化算法 的优点,扩展有限元法通过引入非连续位移模式在不重新划分网格的情况下通过改变水平集函数反映缺陷的数量、位置及大小, 避免了反演分析每次迭代过程中的网格重剖分,人工蜂群智能优化算法在每次迭代中都采用全局和局部搜索,找到最优解的概 率大幅增大并可很好地避免局部最优,同时,通过引入拓扑变量,将缺陷的数量纳入到反演分析过程中,迭代过程中可智能反演出缺陷的数目,建立了结构内部多缺陷(孔洞、裂纹)的反演分析模型. 通过若干算例的分析表明:建立的反演分析模型能够较为准确地探测出结构内部圆形、椭圆形以及裂纹状缺陷的数量、位置及大小,且算法具有较好的鲁棒性.      

Inverse electromagnetic scattering for a locally perturbed perfectly conducting plate

We consider a simple but fully three-dimensional inverse problem to determine the shape of a local perturbation of a perfectly conducting plate from far-field measurements of time harmonic electromagnetic fields. For this purpose we reformulate the model problem as an exterior Maxwell problem for a symmetric domain, and prove an equivalence between the model problem and its reformulation. Then, linear sampling method is applied to solve the reformulated problem. We illustrate the feasibility of this method by some numerical examples.