Construction of the refractive index profiles for few-mode planar optical waveguides

We present a nondestructive technique to predict the refractive index profiles of isotropic planar waveguides, on which a thin gold film is deposited to as the cladding. The negative dielectric constant of the metal results in significant differences of effective indices between TE and TM modes. The two polarized modes and a surface plasmon resonance (SPR) with abundant information of the surface index can be used to construct the refractive index profiles of single-mode and two-mode waveguides at a fixed wavelength.     

Calculation of the Thermoelastoplastic Nonaxisymmetric Stress-Strain State of Layered Orthotropic Shells of Revolution

The methods for determining the nonaxisymmetric thermoelastoplastic stress-strain state of layered orthotropic shells of revolution are developed. It is assumed that the layered package deforms without mutual slippage or separation of layers. The problem is solved using the geometrically nonlinear theory of shells based on the Kirchhoff-Love hypotheses. In the isotropic layers, plastic deformations may appear, whereas the orthotropic layers deform in the elastic region. It is assumed that the mechanical properties of the materials are temperature-dependent. The thermoplasticity equations are presented in a form corresponding to the method of additional deformations. The order of the system of partial differential equations obtained is reduced with the help of trigonometric series in the circumferential coordinate. The resulting systems of ordinary differential equations are solved by the Godunov technique of discrete orthogonalization. The nonaxisymmetric thermoelastoplastic stress-strain states of layered shells of revolution are considered as examples.     

Non-linear radial oscillations of a transversely isotropic hyperelastic incompressible tube

The constitutive equation for a transversely isotropic incompressible hyperelastic material is written in a covariant form for arbitrary orientation of the anisotropic director. Three non-linear differential equations are derived for radial oscillations in radial, tangential and longitudinal transversely isotropic thin-walled cylindrical tubes of generalised Mooney-Rivlin material. A Lie point symmetry analysis is performed. The conditions on the strain-energy function and on the net applied surface pressure for Lie point symmetries to exist are determined. For radial and tangential transversely isotropic tubes the differential equations are reduced to Abel equations of the second kind. Radial oscillations in a longitudinal transversely isotropic tube and in an isotropic tube are described by the Ermakov-Pinney equation.     

三维各向同性谐振子的代数解法

用带角动量的玻色算子统一构成三维各向同性谐振子的能量本征函数，并讨论了它们和直接求解微分方程得到的本征解之间的关系．这种方法快捷优美，而且有统一的表达式和简单的李代数关系。     

An axisymmetrical quasi-Kirchhoff-type shell element for large plastic deformations

Summary An axisymmetrical shell element for large plastic strains is developed. The theory is based on the multiplicative decomposition of the material deformation gradient into an elastic and a plastic part. For quasi-Kirchhoff-type axisymmetric shells this leads to a product of the elastic and plastic stretches. By introduction of logarithmic strains the decomposition becomes additive. Plastic incompressibility is fulfilled in an exact manner.Support for this work was provided by the Deutsche Forschungsgemeinschaft (DFG) under contract Wr 19/7-1. The financial aid for the first and second author is gratefully acknowledged.     

Elementary solution of contact problems for a transversely isotropic elastic layer bonded to a rigid foundation

The contact problem for an arbitrary punch acting on a transversely isotropic elastic layer bonded to a rigid foundation is solved by the generalized images method developed by the author earlier. The problem is reduced to that of an electrostatic problem of infinite row of coaxial charged disks in the shape of the domain of contact. The solution can be obtained by the method of iteration, collocations or any other standard procedure for solving integral equations. Exact inversion can be obtained in the case of a circular domain of contact. The mean value theorem can be used for estimation of the resultant force and tilting moment acting on a punch of arbitrary shape and circular domain of contact. A limiting case of general solution gives the solution for an isotropic layer. (Received: August 11, 2003)     

杭州 市 区环境工程地质及软土地基稳定性评价

本文着重 对杭 州市环 境工程地 质特 点及其软土 地基稳定性 作出指导性评 价.对加强地下工程建设,城市 总体规划布局,城市详细 规划,单体 建筑设计和 施工,工程地 质勘 察等的宏观控制与微观指导,具有重要意 义     

Implications and Constraints of Time-Independent Poisson Ratios in Linear Isotropic and Anisotropic Viscoelasticity

It is proven that time-independent viscoelastic Poisson ratios (PR) can only exist under separation of variable solutions which severely limits the class of applicable problems to quasi-static ones with incompressible homogeneous materials and non-moving boundaries under separable stress or displacement boundary conditions without any thermal expansions. Therefore, composites which are inherently anisotropic and sandwich structures which are nonhomogeneous and anisotropic are generally precluded from having time-independent PRs. Equal time variations for material properties in all directions are shown to be another simultaneous requirement instead of the incompressibility condition for achieving time-independent PRs. However, such restricted models lead to physically unrealistic bulk moduli responses when compared to experimentally determined relaxation moduli and are not generally achievable in current real materials. Consequently, viscoelastic materials are best characterized in terms of relaxation or creep functions, moduli or compliances rather than combinations of the latter with Poisson's ratios. Additionally, the assumption of constant PRs in problems involving thermal and chemical expansions, such as curing and manufacture of viscoelastic composites, is shown to be unjustified and insupportable. The distinct viscoelastic PR definitions, as found in the literature, are examined and classified into five categories. It is further shown that each is inherently unrelated to the others and all are always time-dependent, unless the above extremely limiting conditions are imposed. An extensive literature review indicates that experimental results overwhelmingly confirm the time dependent nature of viscoelastic PRs as no constant experimentally observed PRs were reported.     

Free Vibrations of Transversely Isotropic Hollow Cylinders

An asymptotic process for evaluating the frequencies of free axisymmetric vibrations of transversely isotropic hollow cylinders is proposed. This process is developed in detail for a cylinder with hinge-supported ends and free lateral surfaces. The approaches which make it possible to construct algorithms for identifying their natural frequencies within the given interval are tested on model problems. The results from the Kirchhoff-Love and Ambartsumyan theories are compared with those from the 3D elasticity theory. In the first term of an asymptotic expansion, two frequencies coinciding with those obtained using the applied shell theory are found and a countable set of frequencies absent in this theory is determined.     

INTERFACIAL CRACK ANALYSIS IN THREE-DIMENSIONAL TRANSVERSELY ISOTROPIC BI-MATERIALS BY BOUNDARY INTEGRAL EQUATION METHOD

The integral-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions, in which the displacement discontinuities across the crack faces are the unknowns to be determined. The interface is parallel to both the planes of isotropy. The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method. The stress intensity factors were expressed in terms of the displacement discontinuities. In the non-oscillatory case, the hyper-singular boundary integral-differential equations were reduced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials.