FINITE LAYER ANALYSIS FOR SEMI-INFINITE SOILS (Ⅰ)——GENERAL THEORY

In the present paper a finite layer method is studied for the flastodynarnics of transverse isotropic bodies. With this method, semi-infinite soils can be considered as an transverse isotropic half-space, its material functions varying with depth. Dividing the half-space into a scries of layers in the direction of depth, the material junctions in each layer are simulated by exponential functions Consequently, the fundamental equations to be solved can be simplified if the Fourier transform with repsect to coordinates is used. We have obtained the relationship between the 'layer forces' and 'layer displacements'. This finite layer method, in fact, can also be called a semi-analytical method. It possesses those advantages as the usual semi-analytical methods do, and can be used to analyse the problem of the interaction between soils and structures.

FINITE LAYER ANALYSIS FOR SEMI-INFINITE SOILS (Ⅱ)——SPECIAL CASES AND NUMERICAL EXAMPLES

In the present paper reductions of the finite layer mathod once studied in detail by the authors for the elastodvnamics of transverse isotropic bodies are given to several special cases. Two-dimensional problems, axisymmetric problems and static problems are discussed, respectively, and this finite layer method is also generalized to the problems in which materials possess viscous properties. Two numerical examples have been presented for the axisymmetric case. From these two examples it can be concluded that the finite layer method can be used to analyse semi-infinite layered soils and to deal with the problem of the interaction between soils and structures.

Effects of layer interactions on instantaneous stability of finite Stokes flows

The stability analysis of a finite Stokes layer is of practical importance in flow control. In the present work, the instantaneous stability of a finite Stokes layer with layer interactions is studied via a linear stability analysis of the frozen phases of the base flow. The oscillations of two plates can have different velocity amplitudes, initial phases, and frequencies. The effects of the Stokes-layer interactions on the stability when two plates oscillate synchronously are analyzed. The growth rates of two most unstable modes when δ < 0.12 are almost equal, and δ = δ*/h*, where δ*and h*are the Stokes-layer thickness and the half height of the channel, respectively. However, their vorticities are different. The vorticity of the most unstable mode is symmetric, while the other is asymmetric. The Stokes-layer interactions have a destabilizing effect on the most unstable mode when δ < 0.68, and have a stabilizing effect when δ > 0.68. However, the interactions always have a stabilizing effect on the other unstable mode. It is explained that one of the two unstable modes has much higher dissipation than the other one when the Stokes-layer interactions are strong. We also find that the stability of the Stokes layer is closely related to the inflectional points of the base-flow velocity profile. The effects of inconsistent velocity-amplitude, initial phase, and frequency of the oscillations on the stability are analyzed. The energy of the most unstable eigenvector is mainly distributed near the plate of higher velocity amplitude or higher oscillation frequency. The effects of the initial phase difference are complicated because the base-flow velocity is extremely sensitive to the initial phase.

A new method for solving Biot's consolidation of a finite soil layer in the cylindrical coordinate system

A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface （z = 0） and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.

A new analytical solution to axisymmetric Biot's consolidation of a finite soil layer

A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface （z= 0） and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.

Three-Dimensional Simulations of RESET Operation in Phase-Change Random Access Memory with Blade-Type Like Phase Change Layer by Finite Element Modeling

An optimized device structure for reducing the RESET current of phase-change random access memory （PCRAM） with blade-type like （BTL） phase change layer is proposed. The electrical thermal analysis of the BTL cell and the blade heater contactor structure by three-dimensional finite element modeling are compared with each other during RESET operation. The simulation results show that the programming region of the phase change layer in the BTL cell is much smaller, and thermal electrical distributions of the BTL cell are more concentrated on the TiN/GST interface. The results indicate that the BTL cell has the superiorities of increasing the heating efficiency, decreasing the power consumption and reducing the RESET current from 0.67mA to 0.32mA. Therefore, the BTL cell will be appropriate for high performance PCRAM device with lower power consumption and lower RESET current.

Plane strain consolidation of soil layer with anisotropic permeability

This paper presents an alternative analytical technique to study a plane strain consolidation of a poroelastic soil by taking into account the anisotropy of permeability. From the governing equations of a saturated poroelastic soil, the relationship of basic variables for a point of a soil layer is established between the ground surface （z=0） and the depth z in the Laplace-Fourier transform domain. Combined with the boundary conditions, an exact solution is derived for plane strain Biot＇s consolidation of a finite soil layer with anisotropic permeability in the transform domain. Numerical inversions of the Laplace transform and the Fourier transform are adopted to obtain the actual solution in the physical domain. Numerical results of plane strain Biot＇s consolidation for a single soil layer show that the anisotropic of permeability has a great influence on the consolidation behavior of the soils.

Numerical investigations of asymmetric flow of a micropolar fluid between two porous disks

Numerical solution is presented for the two- dimensional flow of a micropolar fluid between two porous coaxial disks of different permeability for a range of Reynolds number Re （-300≤ Re 〈 0） and permeability parameter A （1.0≤A ≤2.0）. The main flow is superimposed by the injection at the surfaces of the two disks. Von Karman＇s similarity transformations are used to reduce the governing equations of motion to a set of non-linear coupled ordinary differential equations （ODEs） in dimensionless form. An algorithm based on the finite difference method is employed to solve these ODEs and Richardson＇s extrapolation is used to obtain higher order accuracy. The results indicate that the parameters Re and A have a strong influence on the velocity and microrotation profiles, shear stresses at the disks and the position of the viscous/shear layer. The micropolar material constants cl, c2, c3 have profound effect on microrotation as compared to their effect on streamwise and axial velocity profiles. The results of micropolar fluids are compared with the results for Newtonian fluids.

ON THE FINITE DIFFERENCE METHODS FOR TWO DIMENSIONAL TURBULENCE BOUNDARY LAYER

In this paper,the author first establishes the general finite difference formula for the governing equations of the turbulent average velocities in a steady two dimensional incompressible fluid boundary layer-inner layer.Next, three key parameters of the difference scheme are determined respectively by several simple flow models with known analytical solutions.Finally a special five points difference system is given and its application value is showed by a numerical example for the vertical velocity distribution in an Ekman's layer.

VARIABLE MESH FINITE DIFFERENCE METHOD FOR SELF-ADJOINT SINGULARLY PERTURBED TWO-POINT BOUNDARY VALUE PROBLEMS

A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter- uniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by finite difference method taking variable mesh. To support the efficiency of the method, several numerical examples have been considered.