Lagrangian description of transport equations for shock waves in three-dimensional elastic solids

A set of transport equations for the growth or decay of theamplitudes of shock waves along an arbitrary propagation directionin three-dimensional 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 tran-sport 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.     

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

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.     

Indentation of a compressible soft electroactive half-space: Some theoretical aspects

We theoretically study the indentation response of a compressible soft electroactive material by a rigid punch. The half-space material is assumed to be initially subjected to a finite deformation and an electric biasing field. By adopting the linearized theory for incremental fields, which is established on the basis of a general nonlinear theory for electroelasticity, the appropriate equations governing the perturbed infinitesimal elastic and electric fields are derived particularly when the material is subjected to a uniform equibiaxial stretch and a uniform electric displacement. A general solution to the governing equations is presented, which is concisely expressed in terms of four quasi-harmonic functions. By adopting the potential theory method, exact contact solutions for three common perfectly conducting rigid indenters of flat-ended circular, conical and spherical geometries can be derived, and some explicit relations that are of practical importance are outlined.     

Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical cavity

The thermoelastic interaction for the three-phase-lag (TPL) heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory (2TT). The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order 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 vector-matrix differential equation, which is solved by a state-space 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 ramp-type 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 two-temperature Green-Naghdi theory with energy dissipation (2TGN-III) and two-temperature TPL model (2T3phase)) are shown graphically. The effects of two-temperature and ramping parameters are also studied.     

Stability analyses of the mass abrasive projectile high-speed penetrating into concrete target. Part Ⅰ： Engineering model for the mass loss and nose-blunting of ogive-nosed projectiles

The mass loss and nose blunting of a projectile during high-speed 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 nose-blunting of the ogive-nosed 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     

Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock

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 stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix 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 thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.     

INFLUENCE OF GLASS CULLET IN CEMENT PASTES

1. Introduction The necessity for glass cullet recycling is becoming more and more imperative not only due to the general need of solid waste volume reduction, but also due to the strict European legislation, which defines the levels of re- cycling packaging materials including glass cullet. Accord- ing to valid estimates, the total consumption of packaging materials was 58 million tones for 1997 in Europe, 25% of which comprised glass. The present target for recycling is a minimum of 25% for…     

DYNAMICS OF MULTI—DEFORMABLE BODIES

The Gibbs-Appell equations provide what is the powerful tool to formulate equations of motion not only for rigid-body, but also for deformable body. The application of the Gibbs-Appell equations in formulating equations of motion of multi-deformable boodies is developed and exploited in this paper. The advantages of using Gibbs-Appell equation are shown herein. Equations of motion of multi-deformable bodies with explicit form have been obtained and their physical meaning is apparent. In addition, recently developed new ideas are also employed. These ideas include the use of Euler parameters, quasi-coordinates, and relative coordinates.     

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

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 strain-hardening material undergoes serious local deformation but is not perforated during the impact.The theoretical analysis is based on an energy approach, in which the Cowper-Symonds 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.     

Generalized passivity-based chaos synchronization

In this paper, a new passivity-based synchronization method for a general class of chaotic systems is proposed. Based on the Lyapunov theory and the linear matrix inequality （LMI） approach, the passivity-based controller is presented to make the synchronization error system not only passive but also asymptotically stable. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation studies for the Genesio-Tesi chaotic system and the Qi chaotic system are presented to demonstrate the effectiveness of the proposed scheme.     

高强低合金钢甲弧形弹侵彻速度与深度的计算

给出了弧形弹头侵入３０ＭｎＣｒＮｉＭｏＢ高强低合金钢过程中弹头的侵彻深度与速度的关系式。阐明了弹头初速度只有超过某临界值才能侵入钢甲。指出弹头侵入钢甲一定深度后，空穴膨胀理论才能适用，此时弹头与钢甲之间的摩擦系数取０．０２更符合实际。     

球形弹丸正撞击薄板防护屏碎片云特性研究

以质量、动量和能量守恒为基础,结合平面激波理论和热力学理论,对球形铝弹丸正撞击薄板铝防护屏形成的碎片云特性进行了建模,模型计算结果与实验结果吻合较好。利用该模型对多种工况下碎片云特性进行了计算,结果表明:(1)碎片云质心速度和膨胀速度随撞击速度和弹丸直径的增加而增大,随防护屏厚度增大而减小;膨胀半角随撞击速度和防护屏厚度的增大而增大,随弹丸直径的增大而减小;(2)速度和膨胀半角变化曲线具有相似性;(3)对于给定的弹丸和防护屏材料,碎片云中受到激波加载部分的材料各相态质量分数只与弹丸撞击速度有关。这些规律与实验规律吻合。     

考虑头形磨损变化的动能弹侵彻深度研究

质量损失主要发生在弹体头部,讨论残余弹头形状因子的主要影响因素,给出了更为一般化的残余弹头形状因子与初始撞击速度之间的关系.假设在整个侵彻过程中弹体头部形状因子及质量保持瞬时速度平方的线性关系,得到了能够考虑弹体头部质量磨损的侵彻深度计算方法.弹体质量损失将导致其侵彻深度存在上限,该修正模型可以找出达到侵彻深度上限的弹体初始撞击速度.     

弹体垂直侵彻深度工程计算模型

利用空腔膨胀理论计算各种形状弹头的法向侵彻阻力，并考虑作用在弹体头部的库仑摩擦阻力和作用在弹体侧壁粘滞摩擦阻力的影响，根据牛顿定律确定弹体在靶体介质中的运动微分方程，由运动边界条件确定弹体的侵入深度，最后与试验结果进行了比较，表明结果是可靠的。     

穿甲机理的数值研究

为了深入开展穿甲机理的研究,本文对三组穿甲问题——钨弹以1000m/s打钢靶,钢弹以1000m/s打钢靶,钢弹以1000m/s打铝靶,作了数值研究,应用流体弹塑性力学模型,二维不定常欧拉型编码CPG-LTDL code进行计算,计算结果与试验对比符合良好。 对计算结果的分析指出:(1)弹丸侵彻能力不是取决于它的整体动能,而是取决于弹靶接触面上的压力,当靶板参数和弹材固定时,可用弹丸初始面积比动能来标志,(2)铝靶在抗侵彻过程中呈流体性态,高强度铝钣的抗侵彻性能不如普通的A3钢钣,因此应致力于研制具有抗高压、耐高温的新型铝材,而不是单纯追求提高铝材的常规强度。     

Numerical simulation of flow fields induced by a supersonic projectile moving in tubes

Numerical study of the shocked flows generated by a supersonic projectile released from a launch tube into a big chamber has been performed in this paper. Based on fixed Cartesian grids, the two-dimensional axisymmetric Euler equations are solved by the fifth-order WENO scheme implemented with moving boundary conditions. Both the level set technique and ghost fluid method are used for capturing the moving interface of the projectile implicitly. The numerical results show that complex shock phenomena exist in the transient shock flow, resulting from shock-wave reflection, shock-wave focusing, shock-wave/projectile interaction and shock-wave/contact surface interactions. The relationships between the acceleration of the projectile and the transient shock flow are also discussed in detail.     

弹体高速入水特性实验研究

进行了速度在35～160 m/s的平头、卵形和截卵形弹体入水实验,利用高速相机记录了弹体入水和空泡扩展的详细过程,得到了3种弹体在入水初期的水中弹道轨迹和空泡形状,并比较分析了弹体头部形状对入水弹道稳定性的影响.结果表明,平头弹体在水中飞行有良好的弹道稳定性,截卵形弹体往往由于受力不均衡在入水后期发生偏转,卵形弹体则在...     

SIMILARITY LAWS AND SCALING OF PENETRATION TESTS

利用球形空腔膨胀理论的响应函数对靶板在弹体撞击下的侵彻进行分析，并基于量纲理论建立了侵彻相似律的一般形式.通过对侵彻混凝土靶的已有实验数据进行分析，得到了不同缩比因子下，无量纲侵彻深度曲线随侵彻速度不同而发生偏转和偏移.考虑到材料的应变率效应和损伤演化，认为几何相似律对混凝土等脆性材料在抗侵彻时不成立，有必要引入材料应变率效应和损伤演化对几何相似律的修正.     

细长薄壁弹体的屈曲和靶体等效分析

利用金属靶开展动能深侵彻弹的穿甲屈曲实验研究。实验观察到长/短型弹体动塑性屈曲破坏分别表现为轴向皱褶型和轴向外翻撕裂型2种基本模式。不同的屈曲破坏模式与弹体几何、撞击初条件以及靶材等密切相关。区别于刚性尖头弹穿甲金属靶的韧性隧道开孔,尖头弹因屈曲破坏易变形为钝头形,导致弹体穿透靶板表现为挤凿穿甲。利用薄壁中空柱壳的弹性欧拉屈曲分析和弹体塑性屈服的极限分析给出弹体动塑性屈曲的临界条件。同时给出屈曲实验中混凝土靶和金属靶的等效条件。