Equidistribution of Random Walks on Spheres

We study the equidistribution on spheres of the n-step transition probabilities of random walks on graphs. We give sufficient conditions for this property being satisfied and for the weaker property of asymptotical equidistribution. We analyze the asymptotical behaviour of the Green function of the simple random walk on ² and we provide a class of random walks on Cayley graphs of groups, whose transition probabilities are not even asymptotically equidistributed.     

Electro-optic response of cubic liquid crystal compounds in Kerr cell geometry

We present the results of our investigations on the electro-optic response of the cubic phase liquid crystal compounds 1,2-bis-[4-n-octyloxy-benzoyl]-hydrazine (BABH8) and 4'-n-hexadecyloxy-3'-nitrobiphenyl-4-carboxylic acid (ANBC16) in Kerr cell geometry. The AC electric field response in the BABH8 cubic phase was found to be as small as that of the isotropic phase, even though there was a response in the adjacent smectic C (SmC) phase. The response in the SmC phase means that the BABH8 molecule itself has an electric field coupling ability, but this ability is strongly inactivated in the cubic phase. This inactivity to the AC fields was also found in the cubic phase of ANBC16. This behaviour could be explained by the small structural unit size of the cubic phase.     

Surface instability of orthotropic laminated materials under compression

The piecewise-homogeneous material model and the three-dimensional linearized theory of stability with the assumption of small subcritical strains are used to study the surface buckling of orthotropic and transtropic laminates. A plane problem is formulated, and characteristic equations are derived. A solution is found for a specific transtropic material with different orientations of the isotropy axis __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 64–72, July 2006.     

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

In the present paper a finite layer method is studied for the elastodynamics 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 series of layers in the direction of depth, the material functions 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. This paper is based on a portion of the author's dissertation submitted in partial fulfillment of the requirements of degree of Ph. D. at the Shanghai Institute of Appl. Math. & Mech., Shanghai.     

横观各向同性圆柱体自由振动的弹性力学解

本文由横观各向同性的弹性力学方程出发，研究有限长圆柱体的自由振动问题。利用文献「１」的通解，将位移分量和应力分量分别表达成傅里叶－塞尔级数和双曲－贝塞尔级数的形式。通过边界条件和级数的正交关系，得到关于有限长圆柱自由振动频率的特征方程。利用数值方法求解特征根，从而得到圆柱体三维振动的自振频率。     

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

In the present paper a finite layer method is studied for the elastodynamics 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 series of layers in the direction of depth the material fimetioms in each layer are simulated by exponential fumctions Consequently, the fundamental equations to be solved can be simplified if the fouricr 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.     

Structure of the constitutive relations for hereditarily elastic materials reinforced by hard fibers

The problem of simplifying the nonlinear hereditary elasticity relations is considered for strongly anisotropic materials such as fiber-reinforced composites. This is done using their property that the material stiffness is high along the reinforcement and is low in the cross-sectional direction. The material is considered transversally isotropic. The simplification is performed by analyzing asymptotic representations of creep relations. Relations of various degrees of accuracy for various types of composites and stress states are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 120–127, May–June, 2005.     

Stress Concentration at Interacting Spherical Inclusions in a Transversely Isotropic Body

An elastic-equilibrium problem is rigorously solved for a transversely isotropic body containing a finite number of arbitrarily arranged and oriented transversely isotropic spherical inclusions or an infinite periodic array of such inclusions. The solution is found based on the superposition principle for general solutions of single-particle problems and the addition theorems for partial vector solutions of the elastic equilibrium equations. The numerical results presented allow assessing the influence of matrix anisotropy on the stress concentration between inclusions     

Spatial Estimates for the Constrained Anisotropic Elastic Cylinder

This paper establishes spatial estimates in a prismatic (semi-infinite) cylinder occupied by an anisotropic homogeneous linear elastic material, whose elasticity tensor is strongly elliptic. The cylinder is maintained in equilibrium under zero body force, zero displacement on the lateral boundary and pointwise specified displacement over the base. The other plane end is subject to zero displacement (when the cylinder is finite, say). The limiting case of a semi-infinite cylinder is also considered and zero displacement on the remote end (at large distance) is not assumed in this case. A first approach is developed by considering two mean-square cross-sectional measures of the displacement vector whose spatial evolution with respect to the axial variable is studied by means of a technique based on a second-order differential inequality. Conditions on the elastic constants are derived that show the cross-sectional measures exhibit alternative behaviour and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay. A second approach considers cross-sectional integrals involving the displacement and its gradient and furnishes information upon the spatial evolution, without restricting the range of strongly elliptic elastic constants. Such models are principally based upon a first-order differential inequality as well as on one of second order. The general results are explicitly presented for transversely isotropic materials and graphically illustrated for a cortical bone.     

Two-Phase Filtration in a Transversally Isotropic Porous Medium: Experiment and Theory

The results of an experimental determination of the relative phase permeabilities during flow of two immiscible fluids in stratified sandstone with transversally isotropic characteristics are presented. The measurements were performed on samples oriented in three directions: along, perpendicular to and at an angle of 45° to the stratification plane. An approximate solution of the problem of steady two-phase flow toward a finite gallery in an anisotropic porous medium for arbitrary relative orientation of the gallery and the principal axes of the absolute permeability tensor is given. This solution was tested against the experimental results. The good agreement between the theoretical and experimental results makes it possible to recommend for engineering calculations both the relations between the absolute and phase permeabilities for transversally isotropic and orthotropic porous media and the approximate solution obtained.