A Global Method for Relaxation

A new method for the identification of the integral representation of a class of functionals defined on (where represents the family of open subsets of Ω) is presented. Applications are derived, such as the integral representation of the relaxed energy in corresponding to a functional defined in with a discontinuous integrand with linear growth; relaxation and homogenization results in are recovered in the case where bulk and surface energies are present. (Accepted April 20, 1998)     

索网结构静力分析的动态松驰法

应用动态松弛法 ,计算索网结构的位移和拉力。根据理论分析 ,给出时间增量和阻尼系数的一个取值公式 ,从而解决了以往凭经验选取这两个重要参数的困难。典型算例和实验结果说明了该方法的有效性和验证了计算结果的准确性     

一类平面Hamilton系统的大范围非线性化近似方法

在非线性动力系统的研究已经进入了占主导地位的时期,对其提出大范围的非线性化近似方法具有特别重要的意义.在本文中,我们主要对于一类典型的Hamilton系统,根据等势线有两个,或者三个交点的不同情形,给出7种不同的大范围最低次非线性化近似系统,并通过积分近似系统给出近似解(轨道).结果表明,近似椭圆周期轨道可通过线性化近似系统得到,而同(异)宿轨道则可通过2、3次非线性化近似系统得到.最后,将近似方法应用于一个具体Hamilton系统的分析.     

基于插值与点映射相结合的全局分析方法

利用插值的基本思想并结合点映射，提出了一种插值与点映射相结合的全局分析。通过吸引子之间的比较，判断相胞的顶点是否在同一吸引子的吸引域之内，从而识别出边界胞与非边界胞，并重点对边界胞进行处理，进而确定出相胞内各个相点的初值特性。通过比较与分析，本算法可以克服插值胞映射所存在的不足，算法简单且容易在计算机上实现。文中分析了算法产生误差的原因，给出了相应的处理方法。     

A Quantitative In Situ SEM Bending Method for Stress Relaxation of Microscale Materials at Room Temperature

Experimental Mechanics - Although the time-dependent deformation behaviors of microscale materials have been investigated through experiments with uniaxial loading conditions, the influence of the...     

A Global Existence Result for the Compressible Navier–Stokes Equations in the Critical L p Framework

The present paper is dedicated to the global well-posedness issue for the barotropic compressible Navier–Stokes system in the whole space \mathbbR^d{\mathbb{R}^d} with d ≧ 2. We aim at extending the work by Danchin (Inventiones Mathematicae 141(3):579–614, 2000) to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L ^p -type Besov norms, we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true. In passing, we obtain new estimates for the linearized and the paralinearized systems which may be of interest for future works on compressible flows.     

Concerning the W k,p -Inviscid Limit for 3-D Flows Under a Slip Boundary Condition

We consider the 3-D evolutionary Navier–Stokes equations with a Navier slip-type boundary condition, see (1.2), and study the problem of the strong convergence of the solutions, as the viscosity goes to zero, to the solution of the Euler equations under the zero-flux boundary condition. We prove here, in the flat boundary case, convergence in Sobolev spaces W ^k, p (Ω), for arbitrarily large k and p (for previous results see Xiao and Xin in Comm Pure Appl Math 60:1027–1055, 2007 and Beir?o da Veiga and Crispo in J Math Fluid Mech, 2009, doi:). However this problem is still open for non-flat, arbitrarily smooth, boundaries. The main obstacle consists in some boundary integrals, which vanish on flat portions of the boundary. However, if we drop the convective terms (Stokes problem), the inviscid, strong limit result holds, as shown below. The cause of this different behavior is quite subtle. As a by-product, we set up a very elementary approach to the regularity theory, in L ^p -spaces, for solutions to the Navier–Stokes equations under slip type boundary conditions.     

金属基复合材料的蠕变与松弛

本文利用微观力学方法研究了金属基复合材料的常温蠕变和应力松弛,连续纤维在弹性粘塑性基体内单向铺设。本文的结果与实验结果符合较好。研究表明,纤维在轴向对基体的蠕变起到明显阻止作用,而在横向和剪切变形下的作用较小。在低应力水平下,复合材料的蠕变变形很小,在高应力水平时,蠕变变形明显甚至引起蠕变破坏。     

非线性系统全局动态特性分析的PCM法及其在转子轴承系统中的应用

本文将Ｐｏｉｎｃａｒｅ映射的思想与胞映射法相结合，提出了可用于高维非线性动力系统全局稳定性分析的新型数值方法：ＰＣＭ（Ｐｏｉｎｃａｒｅ－Ｃｅｌｌ－Ｍａｐｐｉｎｇ）法，和胞映射法相比，新方法在实用上具有明显的优点。为说明ＰＣＭ法的有效性，本文应用此方法对平衡转子轴承非线性动力系统进行了全局稳定性分析，同时给出了一确定状态空间中存在的所有周期解及其吸引域。     

Relaxation,propagation of sound,and transfer processes in molecular gases

Taking account of rotational and vibrational degrees of freedom of the molecules, a system of equations has been obtained for a molecular gas which describes slightly nonequilibrium states with a length and time on the order of magnitude of the length and time of the rotational and vibrational relaxation. By solving this system, which describes the propagation of sound and the transfer process, the absorption coefficient, the dispersion of the velocity of sound, the transfer coefficients (in particular, the thermal conductivity coefficient), and an expression for the total tensor of the pressures have been found and analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 53–67, September–October, 1970.The author thanks V. M. Zhdanov for his valuable advice and remarks, and also Yu, Ya. Polyak and B. M. Chistoserdov for their useful evaluations.     

A Mathematical Model for Short-Time Filtration in Poroelastic Media with Thermal Relaxation and Two Temperatures

In this work, we derive a set of governing equations for a mathematical model of generalized thermoelasticity in poroelastic materials. This model predicts finite speeds of propagation of waves contrary to the model of coupled thermoelasticity where an infinite speed of propagation is inherent. Next, we prove the uniqueness of solution of these equations under suitable conditions. We also obtain a reciprocity theorem for these equations. A thermal shock problem for a half-space composed of a poroelastic material saturated with a liquid is then considered. The surface of the half-space is assumed to be traction free, permeable, and subjected to heating. The Laplace transform technique is used to solve the problem. Numerical results for the temperature in the elastic body and fluid, displacement of the elastic body, velocity of the fluid, and stresses for both components are obtained and represented graphically.     

主动振动控制中传感／作动元件配置问题的全局优化方法研究

提出了一种主动振动控制中作动／传感元件位置的复合优化方法，它能有效地解决全局优化配置问题；通过对单点并置问题的优化，证明了该优化方法的有效性，并对多点配置问题也具有一定的参考价值。     

气体—颗粒激波松弛流动特性研究

提出了一种解气体－颗粒粘性流动方程组的方法。在此方法中，计算颗粒阻力时采用Ｈｅｎｄｅｒｓｏｎ阻力系数公式，得到两相激波松弛流动数值结果，并与实验结果作了比较，详细分析和讨论了计算结果，揭示了两相激波松弛流动特性随颗粒容积比分的变化规律     

A Global,Direct Algorithm for Path-Following and Active Static Control of Elastic Bar Structures*

ABSTRACT

A method is presented by means of which the equilibrium path of any elastic bar structure may be traced globally, without applying iteration techniques. The basic idea is that the bar structure is reduced to a set of Initial Value Problems (IVPs) with parameters, and the equilibrium path is piecewise linearly interpolated in the parameter space. The way in which this method is capable of handling problems of active static control is demonstrated. The mathematical basis of this type of method is described by Allgower and Georg [1] as the Piecewise Linear (PL) algorithm. Here it is shown how this algorithm can be applied to problems in structural mechanics.     

Relaxation and propagation of pulses in fluids

Mathematical bases for the diagnostics of relaxing fluids in probing by sound pulses based on recording these pulse shapes are developed. Analysis of the change in the pulse shape makes it possible to establish the type of relaxation and to determine its parameters: the relaxation time, the dispersion jump in the velocity, and others. To calculate the pulse shape, the creep kernels for the three main types of relaxation in fluids are found: Kneser relaxation, resonance relaxation, and relaxation associated with diffusive transfer. The shape of the pulse (initially square) near the front is calculated for these types of relaxation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 153–160, September–October, 1986.The authors are sincerely grateful to V. A. Borovikov for his valuable comments in the discussion of the present paper.     

Persistence,Permanence and Global Stability for an n-Dimensional Nicholson System

For a Nicholson’s blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is non-positive, then the population becomes extinct on each patch, whereas the total population uniformly persists if the spectral bound is positive. Explicit uniform lower and upper bounds for the asymptotic behavior of solutions are also given. When the population uniformly persists, the existence of a unique positive equilibrium is established, as well as a sharp criterion for its absolute global asymptotic stability, improving results in the recent literature. While our system is not cooperative, several sharp threshold-type results about its dynamics are proven, even when the community matrix is reducible, a case usually not treated in the literature.     

非线性动力系统全局分析的变胞胞映射法与转子／轴承系统的全局稳定性

在Ｐｏｉｎｃａｒｅ映射及胞映理论的基础上，提出了一种非线性动力系统全局分析的新方法－－变胞胞映射法，这种新方法改变了原胞映射法中胞在胞空间分布的不合理性及运算逻辑的不合理性，更适用于高维、大求解域非线性动力系统的求解。应用此方法，对具有非线性油膜力的Ｊｅｆｆｃｏｔ转子轴承系统进行了全局分析，绘制了系统分岔后的全局吸引域图，解释了一些工程中常见的非线性现象。     

Relaxation Methods for Measuring Residual Stresses: Techniques and Opportunities

Relaxation methods, also called “destructive” methods, are commonly used to evaluate residual stresses in a wide range of engineering components. While seemingly less attractive than non-destructive methods because of the specimen damage they cause, the relaxation methods are very frequently the preferred choice because of their versatility and reliability. Many different methods and variations of methods have been developed to suit various specimen geometries and measurement objectives. Previously, only specimens with simple geometries could be handled, but now the availability of sophisticated computational tools and of high-precision machining and measurement processes has greatly expanded the scope of the relaxation methods for residual stress evaluation. This paper reviews several prominent relaxation methods, describes recent advances, and indicates some promising directions for future developments.