The Richtmyer–Meshkov instability of a 'V' shaped air/helium interface subjected to a weak shock

The Richtmyer–Meshkov instability of a ‘V' shaped air/helium gaseous interface subjected to a weak shock wave is experimentally studied.A soap film technique is adopted to create a ‘V' shaped interface with accurate initial conditions.Five kinds of ‘V' shaped interfaces with different vertex angles are formed to highlight the effects of initial conditions on the flow characteristics.The results show that a spike is generated after the shock impact,and grows constantly with time.As the vertex angle increases,vortices generated on the interface become less noticeable,and the spike develops less pronouncedly.The linear growth rate of interface width after compression phase is estimated by a linear model and a revised linear model,and the latter is proven to be more effective for the interface with high initial amplitudes.The linear growth rate of interface width is,for the first time in a heavy/light interface configuration,found to be a non-monotonous function of the initial perturbation amplitude–wavelength ratio.     

Numerical simulations of the process of multiple shock–flame interactions

Based on a weighted essentially nonoscillatory scheme, the multiple interactions of a flame interface with an incident shock wave and its reshock waves are numerically simulated by solving the compressible reactive Navier–Stokes equations with a single-step Arrhenius chemical reaction. The two-dimensional sinusoidally perturbed premixed flames with different initial perturbed amplitudes are used to investigate the effect of the initial perturbation on the flame evolutions. The results show that the development of the flame interface is directly affected by the initial perturbed amplitudes before the passages of reshock waves, and the perturbation development is mainly controlled by the Richtmyer–Meshkov instability(RMI). After the successive impacts of multiple reshock waves, the chemical reaction accelerates the consumption of reactants and leads to a gradual disappearance of the initial perturbed information. The perturbation developments in frozen flows with the same initial interface as those in reactive flows are also demonstrated.Comparisons of results between the reactive and frozen flows show that a chemical reaction changes the perturbation pattern of the flame interface by decreasing the density gradient,thereby weakening the baroclinic torque in the flame mixing region, and therefore plays a dominant role after the passage of reshock waves.     

Approximate solutions of the Alekseevskii–Tate model of long-rod penetration

The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.     

Finite deformation analysis of crack tip fields in plastically compressible hardening–softening–hardening solids

Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic–viscoplastic constitutive relation with various hardening–softening–hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The initial crack is taken to be a semi-circular notch and symmetry about the crack plane is imposed. Plastic compressibility is found to give an increased crack opening displacement for a given value of the applied loading. The plastic zone size and shape are found to depend on the plastic compressibility, but not much on whether material softening occurs near the crack tip.On the other hand, the near crack tip stress and deformation fields depend sensitively on whether or not material softening occurs. The combination of plastic compressibility and softening(or softening–hardening) has a particularly strong effect on the near crack tip stress and deformation fields.     

VIBRATION AND ACOUSTIC RADIATION FROM SUBMERGED STIFFENED SPHERICAL SHELL WITH DECK-TYPE INTERNAL PLATE

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic spherical shell with an elastic plate attached to its internal surface, in which Dirac-δ functions are employed to introduce the moments and forces applied by the attachment on the surface of shell, by means of expanding field quantities as Legendre series, a semi-analytic solution is derived for the vibration and acoustic radiation from a submerged stiffened spherical shell with a deck-type internal plate, which has a satisfactory computational effectiveness and precision for an arbitrary frequency range. It is easy to analyze the effect of the internal plate on the acoustic radiation field by using the formulas obtained by the method proposed. It is concluded that the internal plate can significantly change the mechanical and acoustic characteristics of shell, and give the coupling system a very rich resonance frequency spectrum. Moreover, the method can be used to study the acoustic radiation mechanism in similar structures as the one studied here.     

STOCHASTIC ELASTO-PLASTIC FRACTURE ANALYSIS OF ALUMINUM FOAMS

Model I quasi-static nonlinear fracture of aluminum foams is analyzed by considering the effect of microscopic heterogeneity. Firstly, a continuum constitutive model is adopted to account for the plastic compressibility of the metallic foams. The yield strain modeled by a two- parameter Weibull-type function is adopted in the constitutive model. Then, a modified cohesive zone model is established to characterize the fracture behavior of aluminum foams with a cohesive zone ahead of the initial crack. The tensile traction versus local crack opening displacement relation is employed to describe the softening characteristics of the material. And a Weibull statistical model for peak bridging stress within the fracture process zone is used for considering microscopic heterogeneity of aluminum foams. Lastly, the influence of stochastic parameters on the curve of stress-strain is given. Numerical examples are given to illustrate the numerical model presented in this paper and the effects of Weibull parameters and material properties on J-integral are discussed.     

SOLUTION OF NONLINEAR HEAT CONDUCTION EQUATION AND IMAGE METHOD

In this paper,the author proves that, for a nonlinear heat conduction equation, there is no discontinuous solution. Some methods of solution for a nonlinear conduction equation are depicted. For a plane interface, the reflection and transmission of a heat wave are given by the method of images. The 1st order of approximation of this method is proved. Lastly, the prevention of superheated electrons is laser implosion of deuterium tritium gas sphere with a shell made of high Z material is interpreted.     

THE METHOD OF MIXED BOUNDARY CONDITION FOR A KION OF LINEAR AND NONLINEAR COMPOSITE STRUCTURE

This paper deals with the axisymmetrical deformation of shallow shells in largedeflection,which are in conjunction with linear elastic structures at the boundary.A methodof mixed boundary condition for this problem is introduced.then the problem of a compositestructure is transformed into a problem of a single structure and the integral equations aregiven.The perturbation method is used to obtain the solutions and an example of compositestructure consisting of a shallow spherical and a cylindrical shell is presented.     

Non-linear characteristics of Rayleigh–Taylor instable perturbations

The direct numerical simulation method is adopted to study the non-linear characteristics of Rayleigh-Taylor instable perturbations at the ablation front of a 200 μm planar CH ablation target. In the simulation, the classical electrical thermal conductivity is included, and NND difference scheme is used. The linear growth rates obtained from the simulation agree with the Takabe formula. The ampli- tude distribution of the density perturbation at the ablation front is obtained for the linear growth case. The non-linear characteristics of Rayleigh-Taylor instable perturbations are analyzed and the numerical results show that the amplitude distributions of the compulsive harmonics are very different from that of the fundamental perturbation. The characteristics of the amplitude distributions of the harmonics and their fast growth explain why spikes occur at the ablation front. The numerical results also show that non-linear effects have relations with the phase differences of double mode initial perturbations, and different phase differences lead to varied spikes.     

SURFACE EFFECT ON NANOSIZED VOID GROWTH IN A RIGID-PERFECTLY PLASTIC MATERIAL

The influence of the surface effect on the nanosized spherical void growth in a rigidperfectly plastic material is analyzed and the mechanism of the nanosized void growth with high triaxiality is given. Based on the Rice and Tracey model for a macro void growth, the present model is proposed to account for the nanosized void growth under a uniform remote strain rate field with consideration on the surface effect. It is concluded that the surface effect yields an evident resistant influence on the nanosized void growth. That is, this influence decays as the void radius increases. With high triaxiality, the nanosized void growth is divided into two stages： the initial stage and the mature stage. At the first stage, the void grows slowly and the influence of surface effect is relatively weak, whereas at the second stage, the influence is significant and the void grows drastically.     

Dislocation stability in three-phase nanocomposites with imperfect interface

Interface imperfection can significantly affect the mechanical properties and failure mechanisms as well as the strength and toughness of nanocomposites. The elastic behavior of a screw dislocation in nanoscale coating with imperfect interface is studied in the three-phase composite cylinder model. The interface between inner nanoin- homogeneity and intermediate coating is assumed as perfectly bonded. The bonding between intermediate coating and outer matrix is considered to be imperfect with the assumption that interface imperfection is uniform, and a linear spring model is adopted to describe the weakness of imperfect interface. The explicit expression for image force acting on dislocation is obtained by means of a complex variable method. The analytic results indicate that inner interface effect and outer interface imperfection, simultaneously taken into account, would influence greatly image force, equilibrium position and stability of dislocation, and various critical parameters that would change dislocation stability. The weaker interface is a very strong trap for glide dislocation and, thus, a more effective barrier for slip transmission.     

Adaptive nonlinear model predictive control design of a flexible-link manipulator with uncertain parameters

This paper presents a novel adaptive nonlinear model predictive control design for trajectory tracking of flexible-link manipulators consisting of feedback lineariza-tion, linear model predictive control, and unscented Kalman filtering. Reducing the nonlinear system to a linear system by feedback linearization simplifies the optimization prob-lem of the model predictive controller significantly, which, however, is no longer linear in the presence of parame-ter uncertainties and can potentially lead to an undesired dynamical behaviour. An unscented Kalman filter is used to approximate the dynamics of the prediction model by an online parameter estimation, which leads to an adaptation of the optimization problem in each time step and thus to a better prediction and an improved input action. Finally, a detailed fuzzy-arithmetic analysis is performed in order to quantify the effect of the uncertainties on the control structure and to derive robustness assessments. The control structure is applied to a serial manipulator with two flexible links containing uncertain model parameters and acting in three-dimensional space.     

Theoretical study of void closure in nonlinear plastic materials

Void closing from a spherical shape to a crack is investigated quantitatively in the present study. The constitutive relation of the Void-free matrix is assumed to obey the Norton power law. A representative volume element （RVE） which includes matrix and void is employed and a Rayleigh-Ritz procedure is developed to study the deformation-rates of a spherical void and a penny-shaped crack. Based on an approximate interpolation scheme, an analytical model for void closure in nonlinear plastic materials is established. It is found that the local plastic flows of the matrix material are the main mechanism of void deformation. It is also shown that the relative void volume during the deformation depends on the Norton exponent, on the far-field stress triaxiality, as well as on the far-field effective strain. The predictions of void closure using the present model are compared with the corresponding results in the literature, showing good agreement. The model for void closure provides a novel way for process design and optimization in terms of elimination of voids in billets because the model for void closure can easily be applied in the CAE analysis.     

Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures

The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.     

DEFORMATIONS AND STABILITY OF SPHERICAL CAPS UNDER CENTRALLY DISTRIBUTED PRESSURES

In this paper the deformations and stability in large axisymmetric deflection of spherical caps under centrally distributed pressures are investigated. The Newton-apline method for solving the nonlinear equations governing large axisymmetric deflection of spherical caps is presented. The buckling behavior is studied for a cap with fixed geometry when the size of the loaded radius is allowed to vary, and for a fixed loaded radius when the shell geometry is allowed to vary. The influence of the buckling modes on the criticalloads is analysed. Numerical results are given for v=0.3.     

Investigation of temperature effect on stress of flexspline

The effect of temperature loading on the stress of a flexspline is investigated. Based on the geometric and mechanical characteristics of the harmonic gear flexspline, a circular thin shell model is presented in this paper. The theoretical solution for the flexspline under different displacement loads and different temperature fields is derived. Meanwhile, an impact factor formula, which reflects the effect of the temperatures of the inner and outer surfaces of the flexspline on the stress of the flexspline, is presented. Finally, numerical calculations by the finite element method （FEM） are adopted to verify the corresponding conclusions.     

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.     

BUCKLING OF COOLING TOWER SHELLS WITH RING-STIFFENERS

With the stability analysis of hyperbolic cooling tower shells with ring-stiffeners,ourpaper proposes the linear pre-buckling consistent theory.The numerical result shows thatthis linear analysis method is very effective and practical in engineering,for its precision ofcomputation is up to the level of the nonlinear analysis when it is used for the study of criticalloads of the hyperbolic cooling tower which is mainly governed by wind pressure and for thestudy of the effect of some other factors concerned in design on the buckling of shells.Basedon that.we have obtained a series of conclusions which will greatly benefits the engineeringdesign when discussing the effect on the critical wind loading of the shell which is caused bythe following factors such as the position of rings,the number of rings and the dead weight.     

Electrohydrodynamic instability of two superposed Walters B´ viscoelastic fluids in relative motion through porous medium

Summary  The electrohydrodynamic Kelvin–Helmholtz instability of the interface between two uniform superposed viscoelastic (B′ model) dielectric fluids streaming through a porous medium is investigated. The considered system is influenced by applied electric fields acting normally to the interface between the two media, at which there are no surface charges present. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by either streaming and applied electric fields for the potentially unstable configuration, or streaming only for the potentially stable configuration, as long as perturbations in the direction of streaming are ignored. For perturbations in all other directions, there exists instability for a certain wavenumber range. The instability of this system can be enhanced (increased) by normal electric fields. In the presence of surface tension, it is found also that the normal electric fields have destabilizing effects, and that the surface tension is able to suppress the Kelvin–Helmholtz instability for small wavelength perturbations, and the medium porosity reduces the stability range given in terms of the velocities difference and the electric fields effect. Finally, it is shown that the presence of surface tension enhances the stabilizing effect played by the fluid velocities, and that the kinematic viscoelasticity has a stabilizing as well as a destabilizing effect on the considered system under certain conditions. Graphics have been plotted by giving numerical values to the parameters, to depict the stability characteristics. Received 27 March 2000; accepted for publication 3 May 2001     

The axisymmetric long-wave interfacial stability of core-annular flow of power-law fluid with surfactant

The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable.