Showing papers in "Acta Mechanica Sinica in 1995"

A unified energy approach to a class of micromechanics models for composite materials

Abstract: Several micromechanics models for the determination of composite moduli are investigated in this paper, including the dilute solution, self-consistent method, generalized self-consistent method, and Mori-Tanaka's method. These micromechanical models have been developed by following quite different approaches and physical interpretations. It is shown that all the micromechanics models share a common ground, the generalized Budiansky's energy-equivalence framework. The difference among the various models is shown to be the way in which the average strain of the inclusion phase is evaluated. As a bonus of this theoretical development, the asymmetry suffered in Mori-Tanaka's method can be circumvented and the applicability of the generalized self-consistent method can be extended to materials containing microcracks, multiphase inclusions, non-spherical inclusions, or non-cylindrical inclusions. The relevance to the differential method, double-inclusion model, and Hashin-Shtrikman bounds is also discussed. The application of these micromechanics models to particulate-reinforced composites and microcracked solids is reviewed and some new results are presented.

Controlling chaos of a periodically forced nonsmooth mechanical system

Abstract: This paper deals with the control of the chaotic motion of a periodically forced mechanical system having nonsmooth restoring force due to elastic stops or clearances, so as to regulate the chaotic motion to a desired periodic motion by means of small time-dependent perturbation of a control parameter. The study begins with a rigorous description of OGY scheme of controlling chaos, and then focuses on the validity of the control scheme through analyzing the smoothness of the Poincare mapping in the scheme with respect to the system state and the control parameter. To simplify the control experiments, the selection of delay coordinates is subsequently discussed. Presented finally is an experiment of controlling chaotic motion of a harmonically forced mass-beam system with an elastic stop.

Experimental and theoretical study on numerical density evolution of short fatigue cracks

Abstract: Fatigue testing was performed using a kind of triangular shaped specimen to obtain the characteristics of numerical density evolution for short cracks at the primary stage of fatigue damage. The material concerned is a structural alloy steel. The experimental results show that the numerical density of short cracks reaches the maximum value when crack length is slightly less than the average grain diameter, indicating grain boundary is the main barrier for short crack extension. Based on the experimental observations and related theory, the expressions for growth velocity and nucleation rate of short cracks have been proposed. With the solution to phase space conservation equation, the theoretical results of numerical density evolution for short cracks were obtained, which were in agreement with our experimental measurements.

A combined programming and iteration algorithm for finite element analysis of three-dimensional contact problems

Abstract: Comparing with two-dimensional contact problems, three-dimensional frictional contact problems are more difficult to deal with, because of the unknown slip direction of the tangential force and enormous computing time. In order to overcome these difficulties, a combined PQP (Parametric Quadratic Programming) and iteration method is derived in this paper. The iteration algorithm, which alleviates the difficulty of unknown slip direction, is used along with the PQP method to cut down computing costs. Numerical example is given to demonstrate the validity of the present algorithm.

Rigid finite element and its applications in engineering

Abstract: Rigid Finite Element Method (RFEM) was proposed to simulate the mechanical behavior of discontinuous structures such as rock and soil structures. The authors' work on the theory and applications of RFEM is summarized in this paper. Based on the theory of RFEM, the Elastic Body-Seams Model (EBSM) is proposed to take the deformation and damage of rock masses into account.

Bidirectional soliton street

Abstract: The bidirectional long-wave model introduced by Wu (1994)[1] and Yih & Wu (1995)[2] is applied to evaluate interactions between multiple solitary waves progressing in both directions in a uniform channel of rectangular cross-section and undergoing collisions of two classes, one being head-on and the other overtaking collisions between these solitons. For a binary head-on collision, the two interacting solitary waves are shown to merge during a phase-locking period from which they reemerge separated, each asymptotically recovering its own initial identity while both being retarded in phase from their original pathlines. For a binary overtaking collision between a soliton of height α1 overtaking a weaker one of height α1, the two solition peaks are shown to either pass through each other or remain separated throughout the encounter according as α1/α2 or <3, respectively. With no phase locking during the overtaking, the two solitary waves re-emerge afterwards with their initial forms recovered and with the stronger wave being advanced whereas the weaker one retarded in phase from their original pathlines. By extension, the theory is generalized to apply to uniform channels of arbitrary cross-sectional shape.

Navier-Stokes analysis of a circulation control airfoil

Abstract: The two-dimensional, compressible, mass-averaged Navier-Stokes equations are used to investigate flows about a typical circulation control airfoil The governing equations are solved using the implicit approximate-factorization algorithm of Beam-Warming with a modified algebraic eddy viscosity model Results are compared with experimental data, and excellent agreement is obtained The effects of different jet momentum coefficients and angles of attack on the flow are studied The mechanism of genenating large lift by circulation control is discussed

Global bifurcations and chaos in a Van der Pol-Duffing-Mathieu system with three-well potential oscillator

Abstract: Semi-analytical and semi-numerical method is used to investigate the global bifurcations and chaos in the nonlinear system of a Van der Pol-Duffing-Mathieu oscillator. Semi-analytical and semi-numerical method means that the autonomous system, called Van der Pol-Duffing system, is analytically studied to draw all global bifurcations diagrams in parameter space. These diagrams are called basic bifurcation diagrams. Then fixing parameter in every space and taking parametrically excited amplitude as a bifurcation parameter, we can observe the evolution from a basic bifurcation diagram to chaotic pattern by numerical methods.

Convective coupled map for simulating spatiotemporal chaos in flows

Abstract: A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid flows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid flows can be envisaged.

Mechanical-electric coupling behaviour of a penny-shape crack in piezoelectric ceramics subjected to lateral shearing force

Abstract: 以弹性位移分量和电势函数为基本未知量时，横观各向同性压电介质三维问题的场方程可化为四个联立的二阶线性偏微分方程组，本文导出了用四个调和函数表示位移分量及电势函数的表达式，即得到了该场方程的势函数通解，作为通解的应用举例，文中求解了圆币形裂纹受横向剪切作用的问题，得到了裂尖附近应力场及电位移场的解析表达式，结果表明，在横向剪切载荷下圆币形裂纹的尖端场及应力、电位移强度因子均具有明显的机－电耦合性质，而应力和电位移分量在裂尖仍具有－１／２的奇异性。

Stress-strain field near the notch tip of a rubber sheet

Abstract: Analized in this paper is the elastostatic field near a notch tip in a rubber-like thin sheet. The asymptotic equations for the notch tip field are derived based on the constitutive relation given by Ref. [1]. Near field solutions are obtained in regions that decreases and increases in size as the notch tip is approached. Their singular character depends on the constitutive parameters as well as the angle of notch that is evaluated numerically.

On laser-induced reverse plugging effect

Abstract: A new kind of failure induced by long pulsed laser, named as reverse plugging effect (RPE), was experimentally observed in thin foil of brass. The whole failure process can be divided into three stages, namely thermal reverse bulging, shear deformation localization and reverse perforation. In this paper, a description of experimental and theoretical study on this newly discovered phenomenon is presented in detail.

Molecular dynamics simulation of crack-tip processes in copper

Abstract: The crack tip processes in copper under mode II loading have been simulated by a molecular dynamics method. The nucleation, emission, dislocation free zone (DFZ) and pile-up of the dislocations are analyzed by using a suitable atom lattice configuration and Finnis & Sinclair potential. The simulated results show that the dislocation emitted always exhibits a dissociated fashion. The stress intensity factor for dislocation nucleation, DFZ and dissociated width of partial dislocations are strongly dependent on the loading rate. The stress distributions are in agreement with the elasticity solution before the dislocation emission, but are not in agreement after the emission. The dislocation can move at subsonic wave speed (less than the shear wave speed) or at transonic speed (greater than the shear wave speed but less than the longitudinal wave speed), but at the longitudinal wave speed the atom lattice breaks down.

Fractal effects of dynamic crack propagation

Abstract: 假设裂纹顶端沿着分形轨迹运动，建立了裂纹扩展的分形弯折（ｋｉｎｋｉｎｇ）模型来描述裂纹的动态扩展。根据这个模型，我们推导了分形裂纹扩展对劝态应力强度和裂纹速度的影响．动态应力强度因子与表观应力强度因子之比Ｋ（ｌ（ｔ），Ｖ）／Ｋ（Ｌ（ｔ），Ｏ）是表观裂纹速度Ｖ＿Ｏ，材料微结构参数（ｄ／Δａ），分维Ｄ和裂纹扩展路径的弯折角θ的函数。本文研究结果表明：在分形裂纹扩展中，表观（或量测）的裂纹速度Ｖ＿Ｏ很难接近Ｒａｙｌｅｉｇｈ波速Ｃ＿ｒ．动态断裂实验中Ｖ＿Ｏ明显低于Ｃ＿ｒ的原因可能是分形裂纹扩展效应所致。材料的微结构，裂纹扩展路径的分维和弯折角均很强地影响动态应力强度因子和裂纹扩展速度。

Interactions of three-dimensional vicous axisymmetric vortex rings with a free surface

Abstract: The unsteady nonlinear interaction of three-dimensional vortices with a free surface is a great challenge in fluid mechanics, which has deep theoretical significance and important practical background. Applying the three-dimensional VOF method, the interactions of three-dimensional axisymmetric vortex rings with a free surface in an incompressible viscous fluid are numerically simulated. The influence of the Froude number and the surface tension are studied and the evolution of the vorticity, the trajectories of the vortex rings and the baroclinic vorticity on the surface are obtained. The results agreed well with the experiments reported in the literature.

Self-excited vibration of the shell-liquid coupled system induced by dry friction: The vibration mechanism of the Chinese cultural relic dragon washbasin

Abstract: The nonlinear vibration theory and the experimental modal analysis are used in this paper to study the self-excited vibration of the shell-liquid coupled system induced by dry friction. The effect of dry friction stick-slip coefficients and rubbing velocity on self-excited vibration, and the limit cycle and Hopf bifurcation solution of the system are obtained. In particular, it is shown that the phenomenon of 4 point (or 6 point) water droplet spurting of the Chinese cultural relic Dragon Washbasin is the result of the perfect combination of the self-excited vibration induced by dry friction and its special modes, which indicates the significant scientific value of the Chinese cultural relic Dragon Washbasin.

On the identification of residual impact properties of materials by acousto-ultrasonics —A pattern recognition approach

Abstract: This paper deals with the application of Acousto-ultrasonics, in conjunction with Pattern Recognition and Classification techniques, to the identification of residual impact properties of a class of polymeric material, namely, Polyvinylchloride (PVC). PVC specimens of different low-energy repeated impact damage states are processed by Acousto-ultrasonics (AU) to retrieve AU signals in the form of digitalized records. These AU signals are grouped as distinct classes, each pertaining to a known level of repeated impact damage. Describing features of these AU signals are used to build Pattern Recognition (PR) Classifiers. These classifiers are used to identify unknown damage states in other PVC specimens by classifying the retrieved AU signals as belonging to one of the classes. The obtained results indicate that Acousto-ultrasonics in combination with Pattern Recognition and Classification techniques can be used for the quantitative non-destructive identification of damage states in PVC specimens of unknown low-energy repeated impact conditions.

A new ductile fracture theory and its applications

Abstract: This investigation discusses further the extent to which a new damage theory recently proposed by the author can serve as a unified theory to characterize various ductile failure problems. A general damage integral and corresponding criterion for ductile fracture are presented. A new parameter for ductile fracture is emphasized, which is experimentally verified as a material constant independent of stress state, has clear physical meaning, and can easily be determined. The applicability of this theory to evaluation of the ductility of welds and engineering materials under various conditions is examined. Also, it is used to predict the effect of residual stress on failure of welds, to predict sheetforming limits, and to correlate the variability of elasto-plastic fracture toughness valuesJ 1c and δ c with different specimen geometries. A new constraint correction method is proposed, and constraint corrected new toughness parameterJ dc and δ dc are recommended. Experiments have shown that the toughness variation with different specimen geometries can effectively be removed by use of the method. The general applicability of the theory to characterization of various ductile failures provides a new design tool for engineering components or structures.

Coaxial interactions of two vortex rings or of a ring with a body

Abstract: Inviscid coaxial interactions of two vortex rings, including head-on collisions and leapfrogging motions, are considered using a contour dynamics technique. Interactions of vortex rings with solid bodies are also investigated by combining the contour dynamics technique with a boundary integral equation method. Numerical results show that a clean, successful passage motion is possible for two vortex rings with not too thick cores. In both cases of head-on collisions and leapfrogging motions, very large core deformations are observed when two vortex rings get close to each other. A head-tail structure is formed in the later stage of a head-on collision of two fat vortices. Numerical results also show that a vortex ring will stretch and slow down when it moves toward a solid boundary, will shrink and speed up when it moves away from a solid boundary, and will either translate steadily or approach an oscillating asymptotic state when it is far away from any boundaries.

Some issues of turbulence statistics

Abstract: The issue of dropping the random forcef i and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and Kukharkin, are discussed. According to the mean-square estimation method, the random forcef i should be dropped in the error expression of the LFP (Langevin-Fokker-Planck) model. However,f i is not neglected, its effect has been taken into account by the variational approach. In order to optimize the perturbation solution of the Liouville equation, the LFP model requires that the basic variable is as near to Gaussian as possible. Hence, the velocity, instead of the vorticity, should be chosen as the basic variable in the three-dimensional turbulence. Although the LFP model and the zero-order Gaussian term of PDF (probability density function) imply whiteness assumption (zero correlation time off i ), the higher-order non-Gaussian terms of PDF correspond to the nonwhiteness of turbulence dynamics, the variational approach does calculate the nonwhiteness effect properly.

Numerical study of vortex reconnection for two anti-parallel vortex tubes

Abstract: By direct numerical simulation of the Navier-Stokes equations we investigate the reconnection of two antiparallel vortex tubes. A new type of perturbation of the initial vorticity field is given which is different from that presented in Refs. [8] and [9]. The formation and the evolution of the “curved vortex belts”, their mutual action with the “bridges” are found. These are important phenomena not studied by others.

Controlling robot manipulators by dynamic programming

Abstract: A certain number of considerations should be taken into account in the dynamic control of robot manipulators as highly complex non-linear systems. In this article, we provide a detailed presentation of the mechanical and electrical implications of robots equipped with DC motor actuators. This model takes into account all non-linear aspects of the system. Then, we develop computational algorithms for optimal control based on dynamic programming. The robot's trajectory must be predefined, but performance criteria and constraints applying to the system are not limited and we may adapt them freely to the robot and the task being studied. As an example, a manipulator arm with 3 degress of freedom is analyzed.

MELrING EFFECTS OF ALUMINUM BUAL-SHEET STRUCTURE IN HYPERVELOCITY IMPACT

Abstract: 对超高速冲击铝双层板的熔化效应进行了实验研究和数值模拟，用扫描电镜观察后板的弹坑发现：当弹丸碰撞速度超过５ｋｍ／ｓ时，后板出现熔坑；随着弹丸碰撞速度的增加，后板熔坑数目亦随之增加，碎片云对后板的破坏明显减弱。数值模拟表明，击波加热和塑性功加热是熔化的两种机制，有关熔化主要特征的数值模拟结果与实验结果基本吻合。

Geometrically non-linear generalized hybrid element and refined element method of non-conforming modes

Abstract: A generalized hybrid method of non-conforming modes based on a non-linear generalized variational principles with relaxed interelement continuity requirements, is developed, and the plane quadrilateral geometrically non-linear element is presented, furthermore, non-linear refined element method is devised by orthogonal approach. It is shown that the refined element can improve the computational accuracy for non-conforming modes.

A three dimensional convective-diffusive model for the transportation of macromolecules and water across the arterial wall

Abstract: A new three dimensional convective-diffusive mathematical model for the transportation of macromolecules and water across the arterial wall is proposed based on the hypothesis of leaky junction-cell turnover. In contrast to previous one or two dimensional model, the present model considers for the first time the shape of the cell, nonuniform subendothelial pressure field and the special role of the internal elastic lamina (IEL). The three dimensional analytical solution of filtration of water and steady transport are obtained. The new theory have led to important physiological predictions, such as the concentration is higher and the flux of macromolecules is stronger in the low shear region than that in high shear region, etc..

Three-dimensional isodyne stress analysis—Present state, trends, theoretical problems

Abstract: The paper presents and discusses theoretical bases and methodology of development of two- and three-dimensional analytical and optical isodynes. Attention is given to the theoretical admissibility of the major components of the physical and mathematical models which are taken as the theoretical basis of the isodynes, and of the related analytical and experimental procedures of stress analysis. Efficiency and reliability of the nondestructive isodyne stress analysis are discussed.

A class of explicit forward time-difference square conservative schemes

Abstract: In the present paper, a class of explicit forward time-difference schemes are established from a geometric view with strict analytical deductions. This class includes the schemes with a constant time interval and with adjustable time intervals, which is proved to be effective and remarkably time-saving in numerical tests and applications.