AN ANALYTICAL SOLUTION OF G.I.TAYLOR’S THEORY OF PLASTIC DEFORMATION IN IMPACT OF CYLINDRICAL PROJECTILES AND ITS IMPROVEMENT

The theory of plastic deformation in the impact of cylindrical projec-tiles on rigid targets was first introduced by G.I.Taylor(1948).The importance of this theorg lies in the fact that the dgnamic yieldstrength of the materials can be determined from the measurement ofthe plastic deformation of flat-ended cylindrical projectiles.Fromthe experimental results.we find that the dynamic gield strengthis independent of impact velocity.and that it is higher than the sta-tic yield strength in general,and several times higher than the sta-tic yield strength in certain cases.This gives an important founda-tion for the studg of elastoplastic impact problems in qeneral.How-ever,it is well known that the complexity of differential equationsin Taylor’s theory compelled us to use the troublesome numerical so-lution.In this paper,the analgtical solution of all the equationsin Taylor’s theory is given in parametrical form and the results arediscussed in detail.In the latter part of this paper,the method of calculatio     

THEORY OF THICK-WALLED SHELLS AND ITS APPLICATION IN CYLINDRICAL SHELL

In this paper, a theory of thick-walled shells is established by means of Hellinger-Reissner's variational principle, with displacement and stress assumptions. The displacements are expanded into power series of the thickness coordinate. Only the first four and the first three terms are used for the displacements parallel and normal to the middle surface respectively. The normal extruding and transverse shear stresses are assumed to bt, cubic polynomials and to satLyfy the boundary stress conditions on the outer and inner surfaces of the shell. The governing equations and boundary conditions are derived by means of variational principle. As an example, a thick-walled cylindrical.shell is disscussed with the theory proposed. Furthermore, a photoelastic experiment has been carried out, and the results are in fair agreement with the computations.     

ANALYTICAL SOLUTION OF FLOW IN INFINITE STRATIFIED OIL RESERVOIR AND ITS APPLICATION

This paper presents an analytical solution for the production function and pressuredistribution function of flow in infinite stratified oil reservoir with crossflow under thecondition of constant wellbore pressure(CWP condition)by Weber’s integraltransformation.The calculation results are shown in the form of curves and these resultscan be used to analyse unsteady flow test of production with CWP condition.     

QUASI－FLOW CORNER THEORY ON LARGE PLASTIC DEFORMATION OF DUCTILE METALS AND ITS APPLICATIONS

ＱＵＡＳＩ－ＦＬＯＷＣＯＲＮＥＲＴＨＥＯＲＹＯＮＬＡＲＧＥＰＬＡＳＴＩＣＤＥＦＯＲＭＡＴＩＯＮＯＦＤＵＣＴＩＬＥＭＥＴＡＬＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＳＨｕＰｉｎｇ（胡平）ＬｉｕＹｕｑｉ（柳玉启）ＧｕｏＷｅｉ（郭威）ＴａｉＦｅｎｇ（台风）（Ｒ...     

CHIEN’S SOLUTION AND ITS ASYMPTOTIC BEHAVIOR IN LARGE DEFLECTION OF CIRCULAR PLATES

A general treatment and residual values of Chien＇s solutionfor large deflection of circular plates are given.By means ofthe above results,the asymptotic behavior of Chien＇s solution isstudied.Two examples of uniform load and concentrated load arediscussed,respectively.     

CHIEN’S SOLUTION AND ITS ASYMPTOTIC BEHAVIOR IN LARGE DEFLECTION OF CIRCULAR PLATES

A general treatment and residual values of Chien’s solution for large deflection of circular plates are given. By means of the above results, the asymptotic behavior of Chien ’s solution is studied. Two examples of uniform load and concentrated load are discussed, respectively.     

NIELSEN’S AND EULER’S OPERATORS OF HIGHER ORDER IN ANALYTICAL MECHANICS

In this paper,the definitions of Nielsen＇s and Euler＇s operators of higher order arepresented These operators are concerned in analysis for systems with holonomicconstraints and non-holonomic constraints of higher order. Some theorems that indicatingrelation between the two operators are established Moreover.using the theorems,the newequations of mechanical systems with constraints of higher order are derived Finally,anexample is given.     

THE MEASUREMENT OF PLASTIC DEFORMATION AND CRACK GROWTH IN CRACKED SPECIMENS BY SAM

In this paper,scanning acoustic microscope(SAM) was used to obtainsome characteristic photographs which explain the mesoscopic information of severalcracked specimens.New results on subsurface information of steel,nickel andaluminium were presented.Plastic deformation and crack initiation were observed andanalysed.The length of crack propagation was measured.SAM is particularly suited tothe study of many mesoscopic phenomena in material science because it can imagemesoscopic subsurface feature without sectioning.It is revealed that SAM has a brightfuture in the field of mesomechanics.     

CONSTRUCTION OF MODIFIED TAYLOR－GALERKIN FINITE ELEMENTS AND ITS APPLICATION IN COMPRESSIBLE FLOW COMPUTATION

ＣＯＮＳＴＲＵＣＴＩＯＮＯＦＭＯＤＩＦＩＥＤＴＡＹＬＯＲ－ＧＡＬＥＲＫＩＮＦＩＮＩＴＥＥＬＥＭＥＮＴＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＩＮＣＯＭＰＲＥＳＳＩＢＬＥＦＬＯＷＣＯＭＰＵＴＡＴＩＯＮＣＯＮＳＴＲＵＣＴＩＯＮＯＦＭＯＤＩＦＩＥＤＴＡＹＬＯＲ...     

Plate impact and plastic deformation by projectiles

The problem of plastic deformation of thin plates struck by blunt projectiles but not perforated is considered. A streak camera and moiré technique were developed to measure the deflection as a function of time for the first few hundred microseconds after impact. The maximum radial strain is about three times the yield strain, the maximum tangential strain is very small. From these and other considerations it was found that there are three main regions of deformation. Since this is a traveling-wave problem, there is a radius beyond which there is no deformation. Inside of this is an annular region traversed by elastic bending waves of the Boussinesq type. Inside of this is an annular region whose dynamic behavior is governed by a membrane stress equal to the tensile yield stress and whose outer boundary travels at a wave velocity governed by the membrane equation. The inner region is a circular region of the diameter of the projectile and traveling with it. The projectile slows and comes to a stop after about 200 or 300 μsec. After this, the material unloads elastically; this elastic vibration behavior was not investigated. Both the time-displacement curve for the projectile and the displacement as a function of radius for specific times can be calculated numerically for dimensionless radius and dimensionless time for one parameter which is governed primarily by the projectile relative mass. The measured and predicted displacements agree within a few percent, except near the boundary between the plastic and the elastic region, for all times up to when elastic unloading commences.     

PERFORATION OF PLASTIC SPHERICAL SHELLS UNDER IMPACT BY CYLINDRICAL PROJECTILES

The objective is to study the perforation of a plastic spherical shell impacted by a cylindrical projectile. First, the deformation modes of the shell were given by introducing an isometric transformation. Then, the perforation mechanism of the shell was analyzed and an analytical model was advanced. Based on Hamilton principle, the governing equation was obtained and solved using Runge-Kuta method. Finally, some important theoretical predictions were given to describe the perforation mechanism of the shell. The results will play an important role in understanding the perforation mechanism of spherical shells impacted by a projectile.     

冲击载荷作用下柱壳链中的弹性波传播简化模型及其解析解

柱壳链能引起波形的弥散,具备操控波形的潜力。建立了柱壳链结构的等效连续介质模型和细观有限元模型,研究了质量块冲击作用下柱壳链中的弹性应力波传播过程及其几何弥散特性。基于考虑横向惯性修正的Rayleigh-Love波动方程,建立了柱壳链在质量块冲击下的控制方程,采用Laplace变换及其逆变换获得了位移场、速度场和应变场的解析解,所得结果与细观有限元模拟结果较好吻合。结果表明,在冲击过程中应变和速度峰值均逐渐减小,应变峰值、振荡幅度和波形前沿宽度与泊松比和惯性半径相关,泊松比和惯性半径越大,应变峰值越小,应变分布振荡越剧烈,波形前沿宽度越宽。     

An analytical solution of rectangular laminated plates by higher-order theory

I.IntroductionSincecompositematerialshavesuperiormechanicalproperties,theyarewidelyconcernedbytechnicians.Fromtheclassicallaminatetheorytothefirst-ordersheardeformationtheoryandfromthehigher-ordertheorytotheelasticitytheory,thetheoriesoflaminatedplatesofcompositemeterialsgetfastdevelopment.TheNaviersolutionofsimplysupportedrectangularplateswasdevelopedbyWhitneyandLeissalllforclassicallaminatetheory.TheNaviersolutionwasdevelopedbyWhitneyandPaganol'1forthefirst-ordersheardeformationtheory.Th…     

An approximate analytical solution of the cylindrical detonation wave generated by the linear explosion

The solution of the cylindrical detonation wave generated by the linear explosion was obtained by numerical method in ref.[1].In this paper,when the ratio of specific heatγ》1 by using the enlargement coordinate method,the first-order analytical solutions are obtained.The perturbation parameter isε=1/γ~2 .The correction of these solutions is checked at the end of this paper.     

The variational inequality formulation for the deformation theory in plasticity and its non-iterative solution

In this paper,the deformation theory in plasticity is formulated in the variational inequality,which can relax the constraint conditions of the constitutive equations.The new form makes the calculation more convenient than general energy forms and have reliable mathematical basis.Thus the plasticity theory may be solved by means of the quadratic programming instead of the iterative methods.And the solutions can be made in one step without any diversion of the load.     

The Okhotsimskii-Pontryagin method in control theory and analytical mechanics. Part I

The Okhotsimskii method for the differentiation of functionals in control theory is discussed on the basis of the Pontryagin formalism. The association of this method with other approaches to solving control problems and with methods of analytical mechanics is studied. Some typical cases of solving optimal control problems are considered.