1.

Stability analyses of the mass abrasive projectile highspeed penetrating into concrete target. Part Ⅱ： Structural stability analyses





Hao Wu ;XiaoWei Chen ;Qin Fang ;LiLin He《Acta Mechanica Sinica》,2014年第6期


The initial oblique and attacking angles as well as the asymmetrical nose abrasion may lead to bending or even fracture of a projectile,and the penetration efficiency decreases distinctly.The structural stability of a highspeed projectile nonnormally penetrating into concrete and the parametric influences involved are analyzed with the mass abrasion taken into account.By considering the symmetrical or asymmetrical nose abrasion as well as the initial oblique and attacking angles,both the axial and the transverse drag forces acting on the projectile are derived.Based on the ideal elasticplastic yield criterion,an approach is proposed for predicting the limit striking velocity（LSV）that is the highest velocity at which no yielding failure has occurred and the projectile can still maintain its integral structural stability.Furthermore,some particular penetration scenarios are separately discussed in detail.Based on the engineering model for the mass loss and noseblunting of ogivenose projectiles established in Part I of this study,the above approach is validated by several highspeed penetration tests.The analysis on parametric influences indicates that the LSV is reduced with an increase in the asymmetrical nose abrasion,thelengthdiameterratio,and the concrete strength,as well as the oblique and attacking angles.Also,the LSV raises with an increase in the initial caliberradiushead（CRH）and the dimensionless cartridge thickness of a projectile.

2.

Stability analyses of the mass abrasive projectile highspeed penetrating into concrete target. Part Ⅰ： Engineering model for the mass loss and noseblunting of ogivenosed projectiles





Hao Wu ;XiaoWei Chen ;LiLin He ;Qin Fang《Acta Mechanica Sinica》,2014年第6期


The mass loss and nose blunting of a projectile during highspeed deep penetration into concrete target may cause structural destruction and ballistic trajectory instability of the penetrator,obviously reducing the penetration efficiency of penetrator.Provided that the work of friction between projectile and target is totally transformed into the heat to melt penetrator material at its nose surface,an engineering model is established for the mass loss and noseblunting of the ogivenosed projectile.A dimensionless formula for the relative mass loss of projectile is obtained by introducing the dimensionless impact function I and geometry function N of the projectile.The critical value V c0of the initial striking velocity is formulated,and the mass loss of projectile tends to increase weakly nonlinearly with I/N when V0〉V c0,whilst the mass loss is proportional to the initial kinetic energy of projectile when V0

3.

LAGRANGIAN DESCRIPTION OF TRANSPORT EQUATIONS FOR SHOCK WAVES IN THREEDIMENSIONAL ELASTIC SOLIDS 被引次数：1





李永池 T. C. T. Ting《应用数学和力学(英文版)》,1982年第3卷第4期


A set of transport equations for the growth or decay of theamplitudes of shock waves along an arbitrary propagation directionin threedimensional nonlinear elastic solids is derived using theLagrangian coordinates.The transport equations obtained showthat the time derivative of the amplitude of a shock wave alongany propagation ray depends on (i) an unknown quantity immediatelybehind the shock wave,(ii) the two principal curvatures of theshock surface,(iii) the gradient taken on the shock surface ofthe normal shock wave speed and (iv) the inhomogeneous term.whichis related to the motion ahead of the shock surface.vanisheswhen the motion ahead of the shock surface is uniform.Severalchoices of the propagation vector are given for which the transport equations can be simplified.Some universal relations,which relate the time derivatives of various jump quantities toeach other but which do not depend on the constitutive equationsof the material,are also presented.

4.

Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock 被引次数：1





M. K. Ghosh M. Kanoria《应用数学和力学(英文版)》,2008年第29卷第10期


This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stressfree and is subjected to a timedependent thermal shock. The basic equations have been written in the form of a vectormatrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermophysical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.

5.

Effects of threephaselag on twotemperature generalized thermoelasticity for infinite medium with spherical cavity





S. BANIK M. KANORIA《应用数学和力学(英文版)》,2012年第33卷第4期


The thermoelastic interaction for the threephaselag (TPL) heat equation in an isotropic infinite elastic body with a spherical cavity is studied by twotemperature generalized thermoelasticity theory (2TT). The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourthorder derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace transformation, the fundamental equations are expressed in the form of a vectormatrix differential equation, which is solved by a statespace approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the thermal loading (the thermal shock and the ramptype heating) and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion techniques. The numerical values of the physical quantity are computed for the copper like material. Significant dissimilarities between two models (the twotemperature GreenNaghdi theory with energy dissipation (2TGNIII) and twotemperature TPL model (2T3phase)) are shown graphically. The effects of twotemperature and ramping parameters are also studied.

6.

ANALYSIS OF SURFACE EXCITATION OF ELASTIC WAVE FIELD IN A HALF SPACE OF PIEZOELECTRIC CRYSTAL——GENERAL FORMULAE OF SURFACE EXCITATION OF ELASTIC WAVE FIELD





汪承灏 陈东培《Chinese Journal of Acoustics》,1985年第3期


This paper developes the general theory of the surface excitation of elastic wave field in a halfspace of piezoelectric crystal for both free and metallized surfaces.It is shown that the general elastic wave field U is equal to the convolution of the generalized Green's functions G and the generalized forces T, U = G Twhere symbol,expresses dotproductconvolution. The generalized Green's functions are independent of excitation conditions and only dependenton material parameters and orientation. For the piezoelectric crystal,not only a mechanical source distribution at the surface,but anelectrical source distribution can also excite the elastic wave fields.Complete expressions of thegeneralized forces representing mechanical and electrical source distribution respectively are given.Especially for the free surface,the surface electrical sources can be composed of the discontinuityof normal electric displacement at the surface,and of the discontinuity of the tangential electric fieldas well.

7.

THE MECHANICAL QUADRATURE METHODS AND THEIR EXTRAPOLATION FOR SOLVING BIE OF STEKLOV EIGENVALUE PROBLEMS





《计算数学(英文版)》,2004年第22卷第5期


By means of the potential theory Steklov eigenvalue problems are transformed into general eigenvalue problems of boundary integral equations (BIE) with the logarithmic singularity.Using the quadrature rules, the paper presents quadrature methods for BIE of Steklov eigenvalue problem, which possess high accuracies O(h^3) and low computing complexities. Moreover, an asymptotic expansion of the errors with odd powers is shown. Using h^3Richardson extrapolation, we can not only improve the accuracy order of approximations, but also derive a posterior estimate as adaptive algorithms. The efficiency of the algorithm is illustrated by some examples.

8.

A spherical cavity expansion model for penetration of ogivalnosed projectiles into concrete targets with sheardilatancy 被引次数：1





Tao He HeMing Wen XiaoJun Guo《Acta Mechanica Sinica》,2011年第27卷第6期


A dynamic spherical cavityexpansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed projectiles.Shear dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatantkinematic relation.A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into account.The influences of various target parameters such as shear strength,bulk modulus,density,Poisson’s ratio and tensile strength on the depth of penetration are delineated.It is shown that the model predictions are in good agreement with available experimental data.It is also shown that the shear strength plays a dominant role in the target resistance to penetration.

9.

Experimental investigation of penetration performance of shaped charge into concrete targets 被引次数：2





Cheng Wang Tianbao Ma Jianguo Ning《Acta Mechanica Sinica》,2008年第24卷第3期


In order to develop a tandem warhead that can effectively destroy concrete targets, this paper explores the penetration performance of shaped charges with different cone angles and liner materials into concrete targets by means of experiments. The penetration process and the destruction mechanism of concrete targets by shaped charges and kinetic energy projectiles are analyzed and compared. Experimental results suggest that both kinetic energetic projectile and shaped charge are capable of destroying concrete targets, but the magnitudes of damage are different. Compared with a kinetic energy projectile, a shaped charge has more significant effect of penetration into the target, and causes very large spalling area. Hence, a shaped charge is quite suitable for firststage charge of tandem warhead. It is also found that, with the increase of shaped charge liner cone angle, the depth of penetration decreases gradually while the hole diameter becomes larger. Penetration depth with copper liner is larger than of aluminum liner but hole diameter is relatively smaller, and the shaped charge with steel liner is between the above two cases. The shaped charge with a cone angle of 100° can form a jet projectile charge （JPC）. With JPC, a hole with optimum depth and diameter on concrete targets can be formed, which guarantees that the secondstage warhead smoothly penetrates into the hole and explodes at the optimum depth to achieve the desired level of destruction in concrete targets.

10.

Topological aspect of vortex lines in twodimensional Gross—Pitaevskii theory





赵力 杨捷 谢群英 田苗《中国物理 B》,2012年第21卷第9期


Using the mapping topological theory, we study the topological structure of vortex lines in a twodimensional generalized GrossPitaevskii theory in (3+1)dimensional spacetime. We obtain the reduced dynamic equation in the framework of the twodimensional GrossPitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss BoseEinstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the δ function indicates that the vortices can only be generated from the zero points of Φ and are quantized in terms of the Hopf indices and Brouwer degrees. The mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the twodimensional GrossPitaevskii theory.

11.

Molecular dynamics study of thermal stress and heat propagation in tungsten under thermal shock





付宝勤 赖文生 袁悦 徐海燕 李纯 贾玉振 刘伟《中国物理 B》,2013年第12期


Using molecular dynamics （MD） simulation, we study the thermal shock behavior of tungsten （W）, which has been used for the plasma facing material （PFM） of tokamaks. The thermoelastic stress wave, corresponding to the collective displacement of atoms, is analyzed with the Lagrangian atomic stress method, of which the reliability is also analyzed. The stress wave velocity corresponds to the speed of sound in the material, which is not dependent on the thermal shock energy. The peak pressure of a normal stress wave increases with the increase of thermal shock energy. We analyze the temperature evolution of the thermal shock region according to the Fourier transformation. It can be seen that the “obvious” velocity of heat propagation is less than the velocity of the stress wave; further, that the thermoelastic stress wave may contribute little to the transport of kinetic energy. The heat propagation can be described properly by the heat conduction equation. These results may be useful for understanding the process of the thermal shock of tungsten.

12.

PROGRESSIVE FRAGMENT MODELING OF FAILURE WAVE IN CERAMICS UNDER PLANAR IMPACT LOADING





姚国文 刘占芳 黄培彦《应用数学和力学(英文版)》,2006年第27卷第2期


Polycrystalline ceramics have heterogeneous mesostructures which result in high singularity in stress distribution. Based on this, a progressive fragment model was proposed which describes the failure wave formation and propagation in shocked ceramics. The governing equation of the failure wave was characterized by inelastic bulk strain with material damage and fracture. And the inelastic bulk strain consists of dilatant strain from nucleation and expansion of microcracks and condensed strain from collapse of original pores. Numerical simulation of the free surface velocity was performed in good agreement with planar impact experiments on 92.93％ aluminas at China Academy of Engineering Physics. And the longitudinal, lateral and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.

13.

ADAPTIVE DELAUNAY TRIANGULATION WITH MULTIDIMENSIONAL DISSIPATION SCHEME FOR HIGHSPEED COMPRESSIBLE FLOW ANALYSIS 被引次数：1





P. Dechaumphai S. Phongthanapanich《应用数学和力学(英文版)》,2005年第26卷第10期


IntroductionHighspeed compressible flows normally involve many complex flow phenomena,suchas shock waves,flow expansions,and shockshock interactions[1].Effects of thesephenomena are critical in the design of highspeed structures.These flows are charact…

14.

曲边多角形域上第一类边界积分方程的机械求积算法与分裂外推 被引次数：4





黄晋 吕涛《计算数学》,2004年第26卷第1期


This paper presents mechanical quadrature methods for solving firstkind boundary integral equations on polygonal regions, which possesses high accuracy O(h0^3)and low computing complexities. Moreover, the multivariate asymptotic expansion of the error with hi^3(i = 1,…,d) power is shown. Using the multiparameter asymptotic expansion, we not only get a high precisioin approximation solution by means of the splitting extrapolation, but also derive a posteriori estimation.

15.

A general solution for Stokes flow and its application to the problem of a rigid plate translating in a fluid





XiangYu Li SiCong Ren QiChang He《Acta Mechanica Sinica》,2015年第31卷第1期


A general solution for 3D Stokes flow is given which is different from, and more compact than the existing ones and more compact than them in that it involves only two scalar harmonic functions. The general solution deduced is combined with the potential theory method to study the Stokes flow induced by a rigid plate of arbitrary shape translating along the direction normal to it in an unbounded fluid.The boundary integral equation governing this problem is derived. When the plate is elliptic, exact analytical results are obtained not only for the drag force but also for the velocity distributions. These results include and complete the ones available for a circular plate. Numerical examples are provided to illustrate the main results for circular and elliptic plates. In particular, the elliptic eccentricity of a plate is shown to exhibit significant influences.

16.

INSTABILITY THEORY OF SHOCK WAVE IN A CHANNEL





徐复 陈乐山《应用数学和力学(英文版)》,1993年第14卷第12期


The instability theory of shock wave was extended from the case with an infinitefront to the case of a channel with a rectangular cross section.First,themathematical formulation of the problem was given which included a system ofdisturbed equations and three kinds of boundary conditions.Then,the general solutionsof the equations upstream and downstream were given and each contained fiveconstants to be determined.Thirdly,under one boundary condition and oneassumption,it was proved that all of the disturbances in front of the shock front andone of the two acoustic disturbances behind the shock front should be zero.Theboundary condition was that all of the disturbed physical quantities should approach tozero at infinity.The assumption was that only the unstable shock wave was concernedhere.So it was reasonable to assumeω=iγ,γwas the instability growth rate andwas a positive real number.Another kind of boundary conditions was that the normaldisturbed velocities should be zero at the solid wall of the cha

17.

Theory of sound field in a room





MAADahYou《Chinese Journal of Acoustics》,2003年第22卷第4期


In the normalmode theory of Morse, it gives a series of normal modes as the solution of forced vibration in a room. But actually there is always the direct radiation besides the normal modes which represent the reverbrant sound field only. The reason is that the normal modes were assumed only in the source, and naturally normal modes only are obtained in the solution. A theory of double source is proposed, that the sound source is both the source of the direct radiation as if in free space before the boundary surfaces were reached by the direct radiation, and after the first reflection from the boundary surfaces, the source of the reflected wavelets, randomly distributed both in space an in time on the boundary surfaces that build up the normal modes after further reflections. The wave equation is formed accordingly, and the solution of the wave equation, the sound field in a room, contains explicitly both the direct radiation and the reverberant sound formed of normal modes. The approximate mean square sound pressure is found to be the dircet sound determined by the sound power of the source,and reverberant sound determined by the sound power reduced by a factor of π/2, different slightly from the result obtained from energy consideration, if the source is pure tone. There is essentially no difference for a source of band noise.

18.

Green Function and Perturbation Method for Dissipative Systems Based on Biorthogonal Basis





ZHANG Li GAO YiBo WANG Cheng《理论物理通讯》,2009年第51卷第6期


Based on the approach of biorthogonal basis, we carry out the quasinormal modes （QNMs） expansions for a class of open systems described by the wave equation with outgoing wave boundary conditions. For such a nonHermitian system, the eigenfunction perturbation expansions and Green function method, which are based on the orthogonal eigenvectors of the Hermitian Hamiltonian for the dosed quantum system, can be generalized in terms of the biorthogonal basis, the two sets of eigenfunctions of H and its adjointness H . The timeindependent perturbation theory for the complex frequencies can be also developed.

19.

ANALYTICAL EVALUATION OF PERMANENT DEFLECTION OF A THIN CIRCULAR PLATE STRUCK NORMALLY AT ITS CENTER BY A PROJECTILE





Chen Liebin Yang Jialing《Acta Mechanica Solida Sinica》,2007年第20卷第2期


The permanent deflection of a thin circular plate struck normally at its center by a projectile is studied by an approximate theoretical analysis,FEM simulation and experiment.The plate made of rate sensitive and strainhardening material undergoes serious local deformation but is not perforated during the impact.The theoretical analysis is based on an energy approach, in which the CowperSymonds equation is used for the consideration of strain rate sensitive effects and the parameters involved are determined with the aid of experimental data.The maximum permanent deflections predicted by the theoretical model are compared with those of FEM sim ulation and published papers obtained both by theory and experiment,and good agreement is achieved for a wide range of thickness of the plates and initial impact velocities.

20.

The （w/g）expansion method and its application to Vakhnenko equation





李文安 陈浩 张国才《中国物理 B》,2009年第18卷第2期


This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the (ω/g)expansion method, which can be thought of as the generalization of (G /G)expansion given by Wang et al recently. As an application of this new method, we study the wellknown Vakhnenko equation which describes the propagation of highfrequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko equation are obtained.
