压电材料椭圆切口的力学分析

在线性压电本构方程框架下，用复势函数方法对椭圆切口模型进行了精确的数值计算。完整地考虑了各向异性力电耦合效应以及切口内不同电介质的介电性质。给出了切口内部不同介电性质对压电材料内部应力的影响。指出了Sosa文章里的一些计算错误。由于现在文献中很小有关于电导通边界条件政府解的数值结果，所以本文同时提供了不同电边界条件下的理论解的数值结果。最后通过最小势能原理建立了8结点有限元模型，对椭圆切口问题进行了计算并与理论解进行了仔细比较。

A rational fraction polynomials model to study vertical dynamic wheel-rail interaction

This paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel-rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel-rail contact passing over a welding defect at different speeds.

The von Neumann-Morgenstern stable sets for 2x2 games

We analyze the von Neumann and Morgenstern stable sets for the mixed extension of 2 2 games when only single profitable deviations are allowed. We show that the games without a strict Nash equilibrium have a unique vN&M stable set and otherwise they have infinite sets.

Transient Flows in Low Permeability Porous Media with Composite Start-Up Pressure Gradient

A new mathematical model for the transient flow in the composite low permeability is established. It is solved by FEM with different boundary conditions such as infinite, circular closed and constant pressure boundary conditions. The typical curves for transient wellbore pressure have been presented. It is shown that the pressure and pressure derivative curves with composite start-up pressure gradients have different slopes which are depended on the start-up pressure gradients and the mobility radios in different regions. The boundary effects are the same as the normal reservoirs without start-up pressure gradients. The study provides a new tool to analyze the transient pressure test data in the low permeability reservoir.

The Displacement and Strain Field of Three-Dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

Numerical Analyses of Transonic Fluid/Structure interaction in Aircraft Engineering

Through the coupling between aerodynamic and structural governing equations, a fully implicit multiblock aeroelastic solver was developed for transonic fluid/stricture interaction. The Navier-Stokes fluid equations are solved based on LU-SGS (lower-upper symmetric Gauss-Seidel) Time-marching subiteration scheme and HLLEW (Harten-Lax-van Leer-Einfeldt-Wada) spacing discretization scheme and the same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Transfinite interpolation (TFI) is used for the grid deformation of blocks neighboring the flexible surfaces. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between fluid and structure. The developed code was fort validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. In the subsonic and transonic range, the calculated flutter speeds and frequencies agree well with experimental data, however, in the supersonic range, the present calculation overpredicts the experimental flutter points similar to other computations. Then the flutter character of a complete aircraft configuration is analyzed through the calculation of the change of structural stiffness. Finally, the phenomenon of aileron buzz is simulated for the weakened model of a supersonic transport wing/body model at Mach numbers of 0.98 and l.05. The calculated unsteady flow shows, on the upper surface, the shock wave becomes stronger as the aileron deflects downward, and the flow behaves just contrary on the lower surface of the wing. Corresponding to general theoretical analysis, the flow instability referred to as aileron buzz is induced by a stronger shock alternately moving on the upper and lower surfaces of wing. For the rigid structural model, the flow is stable at all calculated Mach numbers as observed in experiment

A Semi-Empirical Equation of Penetration Depth on Concrete Target Impacted by Ogive-Nose Projectiles

In this paper, the penetration process of ogive-nose projectiles into the semi-infinite concrete target is investigated by the dimensional analysis method and FEM simulation. With the dimensional analysis, main non-dimensional parameters which control the penetration depth are obtained with some reasonable hypothesis. Then, a new semi-empirical equation is present based on the original work of Forrestal et al., has only two non-dimensional combined variables with definite physical meanings. To verify this equation, prediction results are compared with experiments in a wide variation region of velocity. Then, a commercial FEM code, LS-DYNA, is used to simulate the complex penetration process, that also show the novel semi-empirical equation is reasonable for determining the penetration depth in a concrete target.

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.

Statistics of Turbulence in Benthal Boundary Layers

This paper deals with turbulence behavior inbenthalboundarylayers by means of large eddy simulation (LES). The flow is modeled by moving an infinite plate in an otherwise quiescent water with an oscillatory and a steady velocity components. The oscillatory one aims to simulate wave effect on the flow. A number of large-scale turbulence databases have been established, based on which we have obtained turbulencestatisticsof the boundarylayers, such as Reynolds stress, turbulence intensity, skewness and flatness ofturbulence, and temporal and spatial scales of turbulent bursts, etc. Particular attention is paid to the dependences of those statistics on two nondimensional parameters, namely the Reynolds number and the current-wave velocity ratio defined as the steady current velocity over the oscillatory velocity amplitude. It is found that the Reynolds stress and turbulence intensity profile differently from phase to phase, and exhibit two types of distributions in an oscillatory cycle. One is monotonic occurring during the time when current and wave-induced components are in the same direction, and the other inflectional occurring during the time when current and wave-induced components are in opposite directions. Current component makes an asymmetrical time series of Reynolds stress, as well as turbulence intensity, although the mean velocity series is symmetrical as a sine/cosine function. The skewness and flatness variations suggest that the turbulence distribution is not a normal function but approaches to a normal one with the increasing of Reynolds number and the current-wave velocity ratio as well. As for turbulent bursting, the dimensionless period and the mean area of all bursts per unit bed area tend to increase with Reynolds number and current-wave velocity ratio, rather than being constant as in steady channel flows.

Nonlinear Dynamic Responses of the Tensioned Tether under Parametric Excitations

The nonlinear dynamic responses of the tensioned tether subjected to combined surge and heave motions of floating platform are investigated using 2-D nonlinear beam model. It is shown that if the transverse-axial coupling of nonlinear beam model and the combined surge-heave motions of platform are considered, the governing equation is not Mathieu equation any more, it becomes nonlinear Hill equation. The Hill stability chart is obtained by using the Hill's infinite determinant and harmonic balance method. A parameter M, which is the function of tether length, the surge and heave amplitude of platform, is defined. The Hill stability chart is obviously different from Mathieu stability chart which is the specific case as M=0. Some case studies are performed by employing linear and nonlinear beam model respectively. It can be found that the results differences between nonlinear and linear model are apparent.

Subsonic interface crack with crack face contact

A steady-state subsonic interface crack propagating between an elastic solid and a rigid substrate with crack face contact is studied. Two cases with respective to the contact length are considered, i.e., semi-infinite and finite crack face contact. Different from a stationary or an open subsonic interface crack, stress singularity at the crack tip in the present paper is found to be non-oscillatory. Furthermore, in the semi-infinite contact case, the singularity of the stress field near the crack tip is less than 1/2. In the finite contact case, no singularity exists near the crack tip, but less than 1/2 singularity does at the end of the contact zone. In both cases, the singularity depends on the linear contact coefficient and the crack speed. Asymptotic solutions near the crack tip are given and analyzed. In order to satisfy the contact conditions, reasonable region of the linear contact coefficient is found. In addition, the solution predicts a non-zero-energy dissipation rate due to crack face contact.

Asymptotic Hyperstability of a Class of Linear Systems under Impulsive Controls Subject to an Integral Popovian Constraint

This paper is focused on the study of the important property of the asymptotic hyperstability of a class of continuous-time dynamic systems. The presence of a parallel connection of a strictly stable subsystem to an asymptotically hyperstable one in the feed-forward loop is allowed while it has also admitted the generation of a finite or infinite number of impulsive control actions which can be combined with a general form of nonimpulsive controls. The asymptotic hyperstability property is guaranteed under a set of sufficiency-type conditions for the impulsive controls.

Elastic deformation of soft membrane with finite thickness induced by a sessile liquid droplet

In this paper, the role of vertical component of Surface tension of a droplet on the elastic deformation of a finite-thickness flexible membrane was theoretically analyzed using Hankel transformation. The vertical displacement at the Surface was derived and can be reduced to Lester's or Rusanov's solutions when the thickness is infinite. Moreover, some Simulations of the effect of a liquid droplet on a membrane with a finite thickness were made. The numerical results showed that there exists a saturated membrane thickness of the order of millimeter, when the thickness of a membrane is larger than such a value, the membrane can be regarded as a half-infinite body. Further numerical calculations for soft membrane whose thickness is far below the saturated thickness were made. By comparison between the maximum vertical displacement of an ultrathin soft membrane and a half-infinite body, we found that Lester's or Rusanov's solutions for a half-infinite body cannot correctly describe Such cases. In other words, the thickness of a soft membrane has great effect on the surface deformation of the ultrathin membrane induced by a liquid droplet. (C) 2009 Elsevier Inc. All rights reserved.

Numerical Study On Transient Flow In The Deep Naturally Fractured Reservoir With High Pressure

According to the experimental results and the characteristics of the pressure-sensitive fractured formation, a transient flow model is developed for the deep naturally-fractured reservoirs with different outer boundary conditions. The finite element equations for the model are derived. After generating the unstructured grids in the solution regions, the finite element method is used to calculate the pressure type curves for the pressure-sensitive fractured reservoir with different outer boundaries, such as the infinite boundary, circle boundary and combined linear boundaries, and the characteristics of the type curves are comparatively analyzed. The effects on the pressure curves caused by pressure sensitivity module and the effective radius combined parameter are determined, and the method for calculating the pressure-sensitive reservoir parameters is introduced. By analyzing the real field case in the high temperature and pressure reservoir, the perfect results show that the transient flow model for the pressure-sensitive fractured reservoir in this paper is correct.

Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.