EVANS FUNCTIONS AND INSTABILITY OF A STANDING PULSE SOLUTION OF A NONLINEAR SYSTEM OF REACTION DIFFUSION EQUATIONS

In this paper, we consider a nonlinear system of reaction diffusion equations arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients. The main purpose is to couple together linearized stability criterion (the equivalence of the nonlinear stability, the linear stability and the spectral stability of the standing pulse solutions) and Evans functions to accomplish the existence and instability of standing pulse solutions of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equations. The Evans functions for the standing pulse solutions are constructed explicitly.     

动力应变局部化传播及尺寸效应数值模拟

采用 FLAC-3 D模拟了应变软化岩土材料局部化剪切带的发展、扩容对剪切带倾角的影响及试件的宽度效应。随着加载时步的增加 ,彼此孤立的两个应变场逐渐靠近、叠加 ,最终形成了剪切带网络。无论端面约束强或弱 ,剪切带的倾角的数值模拟结果都与罗斯科倾角比较接近。增加试样宽度 ,剪切带的宽度增加 ,剪切带变得不平直 ;宽度越大 ,岩样上端面中点的压应力 -加载时步曲线的峰值强度越大 ,宽度对弹性阶段没有大的影响     

显含阻尼项的二阶非线性中立型Emden-Fowler微分方程的振动性和渐近性

本文研究一类带有更广泛而又不失物理意义阻尼项的二阶非线性中立型Emden-Fowler时滞微分方程的振动性和渐近性.利用指数变换、Riccati变换和不等式技巧,获得该类方程几个新的振动准则,推广、改进和统一已有文献中的研究成果,并逐一给出例子说明了相应定理的实用效果.     

具有交易费用和马氏调制的均值-方差组合选择

研究了均值-方差准则下,最优投资组合选择问题.投资者为了增加财富它可以在金融市场上投资.金融市场由一个无风险资产和n个带跳的风险资产组成,并假设金融市场具有马氏调制,买卖风险资产时,考虑交易费用.目标是,在终值财富的均值等于d的限制下,使终值财富的方差最小,即均值-方差组合选择问题.应用随机控制的理论解决该问题,获得了最优的投资策略和有效边界.     

利用欧拉-拉格朗日方法预测层流泡状流的含气率分布

利用欧拉-拉格朗日方法，提出了用于预测竖直管道内绝热层流泡状流中含气率分布的三维模型。该模型能够跟踪单独的气泡轨迹，从而获取更多的界面力信息；同时气泡尺寸可以作为参数之一引入模型，使含气率分布的计算更为方便。模型中分析了绝热层流泡状流中气泡的各项受力表达式，建立了两种描述方法下的气液两相间的耦合关系。利用现有实验数据对模型进行的检验表明，该模型能够预测一定尺寸范围内气泡的分布；气泡径向分布主要取决于气泡所受侧向提升力。对于更大尺寸的气泡，气泡变形和气泡尾迹与当地流场间相互作用将对侧向提升力产生很大影响。     

Influence of a thin isotropic coating on the edge effect zone in isotropic and transversely isotropic materials

The effect of a thin isotropic coating on the edge effect zone in a representative element of a coated material is examined. Isotropic and transversely isotropic materials are considered. The transversely isotropic material has the elastic properties of unidirectional glass-fiber-reinforced plastic. The decay of the edge effect in the directions perpendicular to the coating plane and to the plane of isotropy is studied. A boundary-value problem of elasticity for piecewise-homogeneouse orthotropic bodies and a quantitative edge effect decay criterion for normal stresses are used as a design model. The problem is solved using the finite-difference method and base schemes. The results of evaluation of the edge effect zone in homogeneous and inhomogeneous materials are presented. It is shown that the presence of a thin isotropic coating blocks the edge effect, that is, decreases the edge effect zone in both isotropic and transversely isotropic materials __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 61–67, December 2007.     

A multiscale approach of fatigue and shakedown for notched structures

The aim of this paper is to analyse the fatigue phenomena in the presence of stress gradients. It is well-known that most fatigue criteria fail to predict the lifetime of components in the presence of high stress concentrations or stress gradients, as it is the case in the neighbourhood of cracks, holes notches and encountered for example in riveted or threaded structures. Proposed is a numerical approach in the framework of the high cycle fatigue domain in order to give a qualitative answer. The work starts from the numerical computation of macroscopic loading corresponding to some fatigue experiments on specimens with an inclusion of metallic grains embedded in a macroscopic matrix. The computed fields are then analysed in terms of the HCF (high cycle fatigue) criterion [1], which is based on the estimation of the shakedown limit at the grain scale. The infinite lifetime prediction is based on the assumption that fatigue occurs if at least one grain fails, i.e. reaches plastic shakedown. The predictions at mesoscopic and macroscopic scales are close if the macroscopic stress distribution is homogeneous. However in the case of the stress gradient, lifetime predicted at the macroscopic scale is underestimated when compared to the predictions made at the mesoscopic scale. Another result is that the gap between microscopic and macroscopic predictions obtained from these numerical computations can roughly be estimated by a diminution of stress of the same order of magnitude as found in the experiments and phenomenological observations.     

杆系结构的几何非线性分析──Ⅱ．三维问题

以三维连续体的虚功增量方程为基础，采用平动、转角位移分别插值的方法，导出了空间Ｔｉｍｏｓｈｅｎｋｏ梁大位移、大转动问题内力分析的ＵＬ法（ＵｐｄａｔｅｄＬａｇｒａｎｇｉａｉ１Ｆｏｒｍｕｌａｔｉｏｎ）。本文考虑了轴向、剪切、弯曲和扭转效应，提出了新的几何刚度矩阵，并建立了描述大转动规律的坐标转换矩阵。算例表明，依本文方法编制的程序具有分析结构强几何非线性行为的能力；在满足本文假定（即每次加载增量中转角增量是小量）的条件下，可以描述任意大角度的刚体转动。     

Differentiation of Energy Functionals in Two-Dimensional Elasticity Theory for Solids with Curvilinear Cracks

This paper considers the equations of two-dimensional elasticity theory in nonsmooth domains. The domains contain curvilinear cracks of variable length. On the crack faces, conditions are specified in the form of inequalities describing mutual nonpenetration of the crack faces. It is proved that the solutions of equilibrium problems with a perturbed crack converge to the solution of the equilibrium problem with an unperturbed crack in the corresponding space. The derivative of the energy functional with respect to the length of a curvilinear crack is obtained.