A rigorous analytical method for doubly periodic cylindrical inclusions under longitudinal shear and its application

An infinite elastic solid containing a doubly periodic parallelogrammic array of cylindrical inclusions under longitudinal shear is studied. A rigorous and effective analytical method for exact solution is developed by using Eshelby's equivalent inclusion concept integrated with the new results from the doubly quasi-periodic Riemann boundary value problems. Numerical results show the dependence of the stress concentrations in such heterogeneous materials on the periodic microstructure parameters. The overall longitudinal shear modulus of composites with periodic distributed fibers is also studied. Several problems of practical importance, such as those of doubly periodic holes or rigid inclusions, singly periodic inclusions and single inclusion, are solved or resolved as special cases. The present method can provide benchmark results for other numerical and approximate methods. (C) 2003 Elsevier Ltd. All rights reserved.

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.

Excretion pattern investigation of urinary normal and modified nucleosides of breast cancer patients by RP-HPLC and factor analysis method

Modified nucleosides, formed post-transcriptionally in RNA by a number of modification enzymes, are excreted in abnormal levels in the urine of patients with malignant tumors. To test their usefulness as tumor markers, and to compare them with the conventional tumor markers, a reversed-phase high-performance liquid chromatographic (RP-HPLC) method and a factor analysis method have been used to study the excretion pattern of nucleosides of breast cancer patients. A clear cut differentiation of the breast cancer group and the healthy individuals in two clusters without overlapping was obtained. Copyright (C) 2000 John Wiley & Sons, Ltd.

Total analytical method for Radix astragali extract using two-binary multi-segment gradient elution liquid chromatography

There is an urgent need for thorough analysis of Radix astragali, a widely used Chinese herb, for quality control purposes. This paper describes the development of a total analytical method for Radix astragali extract, a multi-component complex mixture. Twenty-four components were separated step by step from the extract using a series of isocratic isopropanol-methanol elutions, and then 42 components were separated similarly using methanol-water elutions. Based on the log k(w) and -S of the 66 components obtained from the above procedure and the optimization software developed in our laboratory, an optimum elution program consisting of seven methanol-water segments and four isopropanol-methanol segments was developed to finish the task of analyzing the total components in a single run. Under optimized gradient conditions, the sample of Radix astragali extract was analyzed. As expected, most of the components were well separated and the experimental chromatogram was in a good agreement with the predicted one.

Interaction of linear waves with infinitely long horizontal cylinders studied by boundary element method

The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the Boundary Integral Equation method (BIEM). Simpler new expressions for the Green functions are derived, and verified by comparison of results obtained by BIEM with these by an analytical method. Examined are the radiation and scattering of linear waves by two typical configurations of cylinders in two-layer deep water. Hydrodynamic behaviors including hydrodynamic coefficients, wave forces, reflection and transmission coefficients and energies are analyzed in detail, and some interesting physical phenomena are observed.

地震采集观测系统的共聚焦分析

Focal beam analysis is a method for assessment of acquisition geometries that is directly linked to pre-stack migration. About dealing with the complex subsurface structures, the conventional survey design methods which do not take into account the subsurface are no longer valid. Based on the Fourier finite-difference (FFD) large-step wave field extrapolation and Born-Kirchhoff (BK) small-step wavefield interpolation, the thesis presents a rapid resolution analysis of 3D seismic survey design by focal beams in complicated media. Subsequently, The SEG/EAEG salt model is used to illustrate the method. Based on the focal beam resolution definition, each kind of influence factor is discussed. The focal beam analysis usually is carried out in a single frequency, but the actual seismic waves always contain a frequency bandwidth. In this thesis, theoretical relationship between focal beam analysis and frequency is derived. Since the effects of focal beam analysis are linear with frequency simply, the multi-frequency focal beam analysis using interpolation is developed. At the same time, the resolution of different frequency bandwidth is interconvertible in accordance with Signal uncertainty principle. The resolution of all frequency bands can be calculated by using only a few focal beam analysis for a seismic survey. In the last section of this thesis, I propose a new approach to predicting acquisition footprint, based on the assumption of Common-Middle-Point stack without constructing a special velocity model. The approach is a simplistic analytical method in which the acquisition footprint pattern is a weighted, linear summation of limited-offset fold-of-stack plots. Because the value of acquisition can be got by quantificational and rapidly calculating, we can exactly do a comparative analysis among different plans of seismic survey by this method.

软土亚塑性模型与一维非线性固结理论研究

With the great development of Tianjing New Coastal District economy, people need more land to build and live. Land subsidence, which is caused by its special engineering geological conditions, has restricted the further development in the district. Soft soil consolidation is main factor of land subsidence ;thus , on the basis of consolidation theory, the paper make further study on soft soils one-dimension nonlinear consolidation which contains two parts:(1) the nonlinear consolidation of permeability coefficient and compressibility coefficient changing with time and depth, which means real one-dimension nonlinear consolidation;(2) the non-homogeneous consolidation of permeability coefficient and compressibility coefficient only changing with depth. Firstly, nonlinear characteristics of soft soils are elaborated. Hypoplastic theory is introduced to establish a modified soft soils nonlinear constitutive model; the nonlinear governing equation of compressibility coefficient is built, and the nonlinear characteristics of compressibility coefficient are analyzed. Secondly, Considering Load Fluctuation and soil thickness changing ,the consolidation characteristics of single layer is discussed in the paper; meanwhile, on the basis of the Davis and Raymond’s hypothesis and single layer nonlinear consolidation equation, the doubled-layer one-dimension nonlinear consolidation equation is also derived. The solution of the equation is obtained by analytical method, and the consolidation characteristics of doubled-layer soft soil nonlinear theory is also analyzed. Finally, based on assumption that permeability coefficient and compressibility coefficient is varying along depth, single layer soil one-dimension non-homogeneous consolidation differential equation is derived; and the approximate solution is obtained. Furthermore, the single layer non-homogeneous consolidation is extended to double layer non-homogeneous consolidation theory. By using parabolic differential scheme, the matrix equation is established; and the solution of the matrix equation is obtained by chase method. Consolidation characteristics of soil soft single (double) layer non-homogeneous consolidation theory and Terzaghi’s theory are also discussed.

Numerical Analysis of Theoretical Model of the Rf MEMs Switches

An improved electromechanical model of the RF MEMS (radio frequency microelectromechanical systems) switches is introduced, in which the effects of intrinsic residual stress from fabrication processes, axial stress due to stretching of beam, and fringing field are taken into account. Four dimensionless numbers are derived from the governing equation of the developed model. A semi-analytical method is developed to calculate the behavior of the RF MEMS switches. Subsequently the influence of the material and geometry parameters on the behavior of the structure is analyzed and compared, and the corresponding analysis with the dimensionless numbers is conducted too. The quantitative relationship between the presented parameters and the critical pull-in voltage is obtained, and the relative importance of those parameters is given.

Vaporization of heated materials into discharge plasmas

The vaporization of condensed materials in contact with high-current discharge plasmas is considered. A kinetic numerical method named direct simulation Monte Carlo (DSMC) and analytical kinetic approaches based on the bimodal distribution function approximation are employed. The solution of the kinetic layer problem depends upon the velocity at the outer boundary of the kinetic layer which varies from very small, corresponding to the high-density plasma near the evaporated surface, up to the sound speed, corresponding to evaporation into vacuum. The heavy particles density and temperature at the kinetic and hydrodynamic layer interface were obtained by the analytical method while DSMC calculation makes it possible to obtain the evolution of the particle distribution function within the kinetic layer and the layer thickness.

抗滑桩阻力上下限解法

基于工程上常用的Janbu普遍条分法(GPS)和剩余推力法，提出了确定单排或多排抗滑桩抗滑阻力的上、下限计算方法。该法假定桩前、桩后滑动土体具有不同的稳定性系数，或假定桩前、桩后滑动土体具有不同的剩余推力，并且抗滑桩承受的下滑力是水平距离的函数。对于单排桩，借助于下限法可以通过试算确定其设桩范围；对于多排桩，借助于上限法可以通过有限的组合枚举确定其最佳的配置。上、下限法的结合可以巨大降低计算量，同时又能满足工程精度要求。运用该方法还可以确定不宜设置抗滑桩的位置范围。文中的算例展示了该方法的具体运用过程。

Theoretical analysis for mechanical erosion of carbon-base materials in ablation

This article derives and provides a theoretical analysis for the mechanical erosion of carbon-base materials in ablation. The theory of mechanical erosion based on a nondimensional critical roughness parameter is proposed, The important parameters in this analytical method are independent of the test, The analysis accounts for the heating, pressure, and shear forces acting on material particles exposed to the boundary-layer flow. For the validity of a theoretical analytical method a computational example is given. The theoretical results agree fairly with the experimental data.

Extremum principle of crystal plasticity

An analytical method for determining slip shear rate under prescribed stress rate or prescribed strain rate has been presented on the basis of the incremental theory of crystal plasticity. The problem has been reduced to a quadric convex programming.In order to analyse the plastic response of crystals subjected to external load, two new extremum principles are proposed. They are equivalent to the boundary-value problem of crystal plasticity. By the new extremum principles, the slip shear rates are independent function which can be obtained from the variational equation.

High-order asymptotic field of tensile plane-strain nonlinear crack problems

In this paper, the governing equations and the analytical method of the secondorder asymptotic field for the plane-straln crack problems of mode I have been presented. The numerical calculation has been carried out. The amplitude coefficients k2 of the second term of the asymptotic field have been determined after comparing the present results with some fine results of the finite element calculation. The variation of coefficients k2 with changes of specimen geometry and developments of plastic zone have been analysed. It is shown that the second term of the asymptotic field has significant influence on the near-crack-tip field. Therefore, we may reasonably argue that both the J-integral and the coefficient k2 can beeome two characterizing parameters for crack initiation.