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 projectiles on rigid targets was first introduced by G. I. Taylor(1948)^[1]. The importance of this theory lies in the fact that the dynamic yield strength of the materials can be determined from the measurement of the plastic deformation of flat-ended cylindrical projectiles. From the experimental results^[2] we find that the dynamic yield strength is independent of impact velocity, and that it is higher than the static yield strength in general, and several times higher than the static yield strength in certain cases. This gives an important foundation for the study of elastoplastic impact problems in general. However, it is well known that the complexity of differential equations in Taylor’s theory compelled us to use the troublesome numerical solution. In this paper, the analytical solution of all the equations in Taylor’s theory is given in parametrical form and the results are discussed in detail.In the latter part of this paper, the method of calculation of impulse of impact is improved by considering the processes of radial’ movement of materials. The analytical solution of the improved theory shows that it gives better agreement with the experimental results than that of original Taylor’s theory.     

Normal perforation of a thin infinite plate by a flat-headed cylindrical projectile

Analytical formulae for calculating the stress acting on the contact surface between projectile and target and for calculating the moving velocity of this contact surface under impact are both suggested in this paper. These formulae can be thought of as a generalization of the well-known Hopkins and Kolsky’s theory in plastic domain. And then, an analytical formula for calculating ballistic limit is also suggested. It is also proved in this paper that the shear stress acting on the cylindrical surface of the plug is distributed uniformly.     

A PERTURBATION SOLUTION OF FREE VIBRATION OF CYLINDRICAL SHELLS WITH RING-STIFFENERS

In this paper,the free vibration of cylindrical sheel with ring-stiffeners is studied indetail by using the PLK method in singular perturbation and the general Hale’s law, and theformulas calculating natural frequencies of cylindrical sheel with ring-stiffeners areexpressed.Finally,the FEM solution is also given to prove the perturbation solution to beseemly,and this comparison shows that the method yields very good results.     

NORMAL PERFORATION OF A THIN INFINITE PLATE BY A FLAT-HEADED CYLINDRICAL PROJECTILE

Analytical formulae for calculating the stress acting on the contact surface between projectile and target and for calculating the moving velocity of this contact surface under impact are both suggested in this paper. These formulae can be thought of as a generalization of the well-known Hopkins and Kolsky's theory in plastic domain. And then, an analytical formula for calculating ballistic limit is also suggested. It is also proved in this paper that the shear stress acting on the cylindrical surface of the plug is distributed uniformly.     

Analysis of postbuckling strength of stringer stiffened cylindrical shells under axial compression

An analysis of the postbuckling strength of stringer stiffened cylindrical shells, subject to axial compression is described. The method used in this paper is based on plastic analysis extending Murray’s method which was used to analyse postbuckling behaviour of stiffened plates loaded axially and in bending. The mechanism tripping of stringer and crumpling of shell plate is described based on how the test specimens are deformed after buckling.Finally the theoretical analyses are compared with the experimental results of steel specimens. The theoretical results coincide quite well with the experimental data. It should therefore be possible to use the method described here to analyse postbuckling strength of stringer stiffened cylindrical shells and to estimate energy absorption capabilities in relation to collision studies.     

General solution for large deflection problems of nonhomogeneous circular plates on elastic foundation

In this paper, a new method is presented based on [1]. It can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients. By this method, the general solution for large deformation of nonhomogeneous circular plates resting on an elastic foundation is derived. The convergence of the solution is proved. Finally, it is only necessary to solve a set of nonlinear algebraic equations with three unknowns. The solution obtained by the present method has large convergence range and the computation is simpler and more rapid than other numerical methods.Numerical examples given at the end of this paper indicate that satisfactory results of stress resullants and displacements can be obtained by the present method. The correctness of the theory in this paper is, confirmed.     

Structure dependent elastic properties of supergraphene

Complete replacement of aromatic carbon bonds in graphene by carbyne chains gives rise to supergraphene whose mechanical properties are expected to depend on its structure. However, this dependence is to date unclear. In this paper, explicit expressions for the in-plane stiffness and Poisson’s ratio of supergraphene are obtained using a mole-cular mechanics model. The theoretical results show that the in-plane stiffness of supergraphene is drastically (at least one order) smaller than that of graphene, whereas its Pois-son’s ratio is higher than 0.5. As the index number increases (i.e., the length of carbyne chains increases and the bond density decreases), the in-plane stiffness of supergraphene decreases while the Poisson’s ratio increases. By analyzing the relation among the layer modulus, in-plane stiffness and Poisson’s ratio, it is revealed that the mechanism of the faster decrease in the in-plane stiffness than the bond density is due to the increase of Poisson’s ratio. These findings are useful for future applications of supergraphene in nanomechanical systems.     

ANALYSIS OF COMPOSITE LAMINATED PLATES

In the static and dynamic analysis of composite laminates, a theory for the laminated plates is presented in this paper. Because the deflection W_b which is caused by the classical bending deformation and the deflection W_s which is caused by the shear deformation are divided from the total deflection W in the theory, this makes it easy to solve the governing equations. In addition, this theory is convenient for the discussion and analysis of the effects of transverse shear deformations on bendings, vibrations and stabilities of laminated plates.     

PROGRESSING STEP BY STEP AND INTEGRATING CALCULATION OF OVERCRITICAL DEFORMATION OF SPHERICAL SHALLOW SHELLS

In this paper,the problem of second buckling of the spherical shallow shell is calculatedby use of the method of progressing step by step and in integating.The result is more exactthan that of first approximate analyis for over-critical deformation of spherical shallowshell It has been solved that the solution of second appoximate analysis in this problemcan’t befound.The calculating example in this paper shows that the solution of progressingstep by step and integrating converges to second approximate solution.     

EXTENSION OF POINCARE’S NONLINEAR OSCILLATION THEORY TO CONTINUUM MECHANICS (I)-BASIC THEORY AND METHOD

In this paper we extend Poincare’s nonlinear oscillation theory of discrete system to continuum mechanics. First we investigate the existence conditions of periodic solution for linear continuum system in the states of resonance and non-resonance. By applying the results of linear theory, we prove that the main conclusion of Poincare’s nonlinear oscillation theory can be extended to continuum mechanics. Besides, in this paper a new method is suggested to calculate the periodic solution in the states of both resonance and nonresonance by means of the direct perturbation of partial differential equation and weighted integration.     

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

Based on the theory of porous media,a general Gurtin variational principle for theinitial boundary value problem of dynamical response of fluid-saturated elastic porous media isdeveloped by assuming infinitesimal deformation and incompressible constituents of the solid andfluid phase.The finite element formulation based on this variational principle is also derived.Asthe functional of the variational principle is a spatial integral of the convolution formulation,thegeneral finite element discretization in space results in symmetrical differential-integral equationsin the time domain.In some situations,the differential-integral equations can be reduced to sym-metrical differential equations and,as a numerical example,it is employed to analyze the reflectionof one-dimensional longitudinal wave in a fluid-saturated porous solid.The numerical results canprovide further understanding of the wave propagation in porous media.     

SPACE VARIABLE TRANSFORM METHOD FOR FREE VIBRATION ANALYSIS OF THICK CYLINDRICAL SHELL WITH ARBITRARY BOUNDARY CONDITIONS

In this paper, a general analytical method—space variable transform method is presented for solving free vibration problems of thick cylindrical shell with arbitrary boundary conditions. Free vibration characteristics of cantilever thick cylindrical shell are cvaluated by the presented method, and the numerical results are compared with the corresponding results of thin shell theory and experimental values. Theoretical analysis and calculating results show that the method presented in this paper has good convergence and aecuracy and can be extended to analyze free vibration of beams, plates and shells.     

THE SOLUTION OF LARGE DEFLECTION PROBLEM OF THIN CIRCULAR PLATE BY THE METHOD OF COMPOSITE EXPANSION

In this paper, the method of composite expansion in perturbation theory is used for the solution of large deflection problem of thin circular plate. In this method. the outer field solution and the inner boundary layer solution are combined together to satisfy all the boundary conditions. In this paper, Hencky's membrane solution is used for the first approximation in outer field solution, and then the second approximate solution is obtained. The inner boundary layer solution is found on the bases of boundary layer coondinate. In this paper, the reciprocal ratio of maximum deflection and thickness of the plate is used as the small parameter. The results of this paper improves quite a bit in comparison with the results obtained in 1948 by Chien Wei-zang.     

AN ANALYSIS OF THE EFFECTS OF THE PROSTATIC HYPERTROPY ON HE URINARY FLOW IN LOWER-URINARY-TRACT

In this paper an analytic model corresponding to the collapsible tube for analysing theurinary flow in lower-urinary-tract is set up from physiologic background.By analysing themodel it is found that the self-excited oscillations can both occur in the region of negativeand positive slope of P_n-Q_n characteristic. So this paper extends the results of ConradGriffiths,Conrad, Cohen and McQueen and others that the self-excited oscillationscan only occur in the region of negative slope of P_n-Q_n characteristic.The effects ofprostatic hypertropy on the flow parameters in lower-urinary-tract is discussed in detail bynumerical calculations.The results show that it is possible to know the conditions ofprostatic hypertropy according to the changes of bladder pressure, outlet urinary velocityand other parameters. From these results a theoretical method to detect and diagnoseprostatic hypertropy is provided.     

ELASTIC-PLASTIC DYNAMIC RESPONSE OF A CANTILEVER BEAM SUBJECTED TO OBLIQUE IMPACT AT ITS TIP

By employing large deformation governing equations expressed in the form of finite difference, the dynamic responses of an elastic, perfectly plastic cantilever subjected to an oblique impact at its tip was numerically studied. Through analyzing the instantaneous distribution of the yield function （φ = ｜M/Mo｜ ＋ （N/No）^2）, bending moment and axial force during the early stage of the response, the elastic-plastic deformation mechanism and the influence of axial component of an oblique impact on the dynamic response of a cantilever beam were discussed. The present analysis shows that the deformation mechanism of an elastic-plastic cantilever subjected to an oblique impact consists of four phases, i.e. ‘the expanding compressed plastic region＇ mode; the ‘generalized traveling plastic hinge＇ and ‘shrinking plastic region＇ mixed mode; the ‘stationary plastic hinge＇ mode and ‘elastic vibration＇ mode. Compared with the two-phase deformation mode obtained by using the rigid, perfectly plastic approach, the mode of shrinking plastic region that occurred instantly after the oblique impact and the mode of stationary hinge were both confirmed. The primary features of the deformation mechanism are captured by both analysis methods. It has also been found that the beam＇s deformation is mainly controlled by the axial component of the oblique impact in the early phase of the dynamic response, the deformation mechanism is obviously different from the case of a transverse impact. With further development of the response, the axial component attenuates rapidly and gives negligible contribution to the yielding of the beam cross-section. At the same time, the bending moments along the cantilever develop gradually and dominate the beam＇s deformation. The numerical results indicate that the mass, impact speed and oblique angle are the important factors that influence the elastic-plastic dynamic response of a cantilever beam.     

THE CONSTRUCTION OF LARGE ELEMENT IN FINITE ELEMENT METHOD

In the usual finite element method.the order of the inter-polation in an element is kept unchanged.and the accuracyis raised by subdividing the grid denser and denser.Alter-natively.in the large element method.the grid is kept un-changed.and the terms of approximate series in the elementare increased to raise the accuracy.In this paper,a method for constructing large elementsis presented.when using this method,two sets of variables.one set defined inside the element.and the other defined onthe boundary of the element.are adopted.Then,these twosets of variables are combined by the hybrid-penalty functionmethod.This method can be applied to any elliptic equationsin a domain With arbitrary shape and arbitrary complex boun-dary condition.It is proved with strict mathematical methodin this paper.that in general cases,the accuracy of this me-thod is much higher than that of the usual element and thelarge element method presented in[7].Therefore.the deqreesof freedom needed in this method are much fewer than t     

DISCUSSION ON BARENBLATT’S EQUATIONS OF MEAN MOVEMENT OF THE INHOMOGENEOUS FLUID

In this paper,it is proved that Barenblatt’s equation of mean movement of the inhomogeneous fluid is not cor-rect,because his equations are based on the assumption that the characteristics of inhomogeneity of fluid are only af-fected with respect to gravitational terms.The correct form of the equation of mean movement of the inhomogeneous fluid is derived in this paper.     

THE DYNAMIC COMPUTATION OF CLOSED CYLINDRICAL SHELL UNDER IMPACT LOAD

This article discusses the dynamic computation of the closed cylindrical shell underimpact load.In the text we analyse the changes of the momenta and the energy on eachstage in the impact process,take into account the effect of the mass of impact object and thesystem of the closed cylindrical shell by impact,and transform the distributed mass of thewhole cylindrical shell into an only concentrated“equivalent mass”by the method ofreduced mass.Consequently we derive the dynamic factor of the closed cylindrical shell dueto impact load.The method proposed in this paper is of practical worth and is more convenient incalculations.     

ANALYSIS OF POSTBUCKLING STRENGTH OF STRINGER STIPFENED CYLINDRICAL SHELLS UNDER AXIAL COMPRESSION

An analysis of the postbuckling strength of stringer stiffened cylindrical shells, subject to axial compres-sion is described. The method used in this paper is based on plastic analysis extending Murray's method which was used to analyse postbuckling behaviour of stiffened plates loaded axially and in bendin9. The mechanism tripping of stringer and crumpling of shell plate is described based on how the test specimens are deformed after buckling. Finally the theoretical analyses are compared with the experimental results of steel specimens. The theoretical results coincide quite well with the experimental data. It should therefore be possible to use the method described here to analyse postbuckling strength of stringer stiffened cylindrical shells and to estimate energy absorption capabilities in relation to collision studies.     

COMPLETELY EXPONENTIALLY FINITE DIFFERENCE METHODS FOR PROBLEMS OF TURNING POINT

In this paper we construct a completely exponentially fitted finite difference schemefor the boundary value problem of differential equation with turning points,extendingMiller’s method and simplifying the method of the proof,We prove the first order uniformconvergence of the scheme.The numerical results show that it is better than(?)in’sscheme.