含任意椭圆核各向异性板杂交应力有限元

基于含椭圆核有限大各向异性板弹性问题的复变函数级数解,应用杂交变分原理建立了一种与常规有限元相协调的含任意椭圆核各向异性板杂交应力有限元.单元内的应力场和位移场采用满足平衡方程、几何方程与物理方程的复变函数级数解,假设的复变函数级数解精确满足椭圆核边界处的位移协调条件和应力连续条件,单元外边界上的位移场按常规有限元位移场假设,单元内椭圆核的长轴可以与材料主轴不重合.单元刚度矩阵采用Gauss积分求得,并给出了建立刚度矩阵的主要公式和推倒过程.数值计算结果表明该单元具有计算精度高、计算工作量小等优点.     

压电材料平面裂纹尖端场的杂交应力有限元分析

基于复势理论和杂交变分原理建立了一种适用于力电耦合分析的杂交应力有限元模 型. 给出了建立刚度矩阵的主要公式和推导过程，单元内的位移场和应力场采用满足平 衡方程的复变函数级数解，假设的复变函数级数解事先精确满足裂纹的无应力和电位移法向 分量为零的条件，单元外边界的位移场假设按抛物线变化, 单元的刚度矩阵采用Gauss积分的方法得出. 通过对力电耦合裂尖场的数值计算验证了程序 的正确性和单元的有效性，同时也用所得结果校验了理论解.     

用离散速度方法计算浅水长波方程

用离散速度法计算浅水波方程，将空气动力学方程和浅水波方程作了比较，用Nadiga提出的近平衡流动方法模拟浅水波方程的连续和间断解。计算了一维的溃坝波问题和Thacker提出的连续解问题，结果与精确解作了比较，并且计算了水流跃过障碍物的问题。     

只有尖点的平面曲边多角形缺陷的应力分析

本文讨论了无限平面内含有多角形缺陷的平面问题;讨论了K-M函数φ(ζ)Ψ(ζ)的结构;在作一些补充说明后,证明了公式同样适用于多角形缺陷;求得了工程上遇到的翼形和唇形等只有尖点的曲边多角形缺陷的精确解;还讨论了弹性夹渣问题.     

细环壳钱伟长方程的精确解

1979年钱伟长对细环壳进行了非常系统的研究,推导出一个细环壳复变量方程,并给出了一个用连分式表达的级数精确解,但没有提及这个级数解是否可以化成为已知的特殊函数.本文利用一个线性变换,把细环壳的钱伟长方程变换成Mathieu方程,用Mathieu函数表示了问题的解,这样就把钱伟长的连分式解与Mathieu函数联系了起来.由于Mathieu函数是已知的特殊函数,这里的工作可为今后有关的细环壳具体计算带来方便.     

含边裂纹矩形截面偏心柱最大挠度的一个解析解

本文采用Rayleigh-Ritz能量变分法，计算分析了两端铰支含边裂纹矩形截面偏心柱的弹性挠度。首先选取三角函数级数作为柱挠度的试函数；然后分别计算弹性体系弯曲变形能和裂纹引起的变形能增量以及外边势能，进而得到体系的总势能；最终根据势能驻值条件确定挠度系数，从而得到一个在裂纹截面满足变形协调条件的挠度方程级数解。在假设裂纹位于柱中间截面的基础上，进一步分析推出了最大挠度的解析公式。文中还就本文解与相应的Okamura解进行了对比分析，指出了Okamura解存在的缺点和适用范围。     

一种寻求层状流动新解的方法

复杂层状流动是流体力学中的一类典型的流动。一般而言，流体力学中有两种特殊的流动：一种是Beltrami流动，另一种就是层状流动。对于前者，已经讨论过很多；但是后者的精确解却很难获得，这是因为很难解这种流动的Navier-Stokes方程或Euler方程。从不可压缩条件出发，如果让速度的形式满足一些特殊的条件，可以得到关于这种流动的某些新的精确解，例如发现一种间歇流精确解。     

轴对称圆环壳复变量方程的逼近——渐近解法

求解轴对称圆环壳的复变量方程,一般用级数方法和渐近方法。众所周知,级数解仅对μ=12(1-V~2)~(1/2)(a~2/r_0h)较小的圆环壳才有很好的收敛性;相反,渐近解却对μ值较大的圆环壳才得到很好的近似。本文是在过去工作的基础上,采用逼近——渐近方法,求出了对μ值一致有效的解。计算表明,对于μ=0.5的细环壳,逼近——渐近方法给出的结果和级数解的结果是一致的,而渐近解的误差较大;对于μ=15,逼近——渐近方法给出的结果和渐近解的结果一致。     

用改进的模态综合法计算空间双层框架的模态特性

本文用作者在资料[2]中论证的改进模态综合技术,计算了空间双层框架的固有振动特性,并将所获得的数值结果与精确解、Benfield 法的结果[3]以及实测数据[4]作了比较,证明这方法不仅对于部件间简单对接的情况,而且对于高度赘余对接的情况也有良好的精度。     

Curle边界层的一个新的级数解

本文以文献[4]所给出的变换为基础,导出了Curle边界层摩擦应力的一个新的级数解,和Blasius级数解相比,新级数有着较好的规律性和较快的收敛速度。本文根据已知项所提供的信息和分离点的特性,得出了级数通项的表达式。以这一通项估计余项,所得结果与Curle的准确解相当吻合。本文实际上以一个简明的实例,说明文献[4]所提出的变换将会给边界层的研究和计算带来一定的好处。     

Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term简

This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.     

Exact traveling wave solutions to 2D-generalized Benney-Luke equation

By using the dynamical system method to study the 2D-generalized Benney- Luke equation, the existence of kink wave solutions and uncountably infinite many smooth periodic wave solutions is shown. Explicit exact parametric representations for solutions of kink wave, periodic wave and unbounded traveling wave are obtained.     

Traveling Waves in Diffusive Random Media

The current paper is devoted to the study of traveling waves in diffusive random media, including time and/or space recurrent, almost periodic, quasiperiodic, periodic ones as special cases. It first introduces a notion of traveling waves in general random media, which is a natural extension of the classical notion of traveling waves. Roughly speaking, a solution to a diffusive random equation is a traveling wave solution if both its propagating profile and its propagating speed are random variables. Then by adopting such a point of view that traveling wave solutions are limits of certain wave-like solutions, a general existence theory of traveling waves is established. It shows that the existence of a wave-like solution implies the existence of a critical traveling wave solution, which is the traveling wave solution with minimal propagating speed in many cases. When the media is ergodic, some deterministic \hbox{properties} of average propagating profile and average propagating speed of a traveling wave solution are derived. When the media is compact, certain continuity of the propagating profile of a critical traveling wave solution is obtained. Moreover, if the media is almost periodic, then a critical traveling wave solution is almost automorphic and if the media is periodic, then so is a critical traveling wave solution. Applications of the general theory to a bistable media are discussed. The results obtained in the paper generalize many existing ones on traveling waves. AMS Subject Classification: 35K55, 35K57, 35B50     

THE DYNAMIC BUCKLING OF ELASTIC-PLASTIC COLUMN SUBJECTED TO AXIAL IMPACT BY A RIGID BODY

I. INTRODUCTIONSince the 1960s the investigation on the dynamic buckling of elastic-plastic structures under impactload has been a very active subject of study in solid mechanics. In this respect the research advanceswere summarized and reviewed from di?erent aspects by some famous scholars[1??4]. The column is themost important structural element in practical engineering. So the dynamic buckling of the column hasattracted much more attention of many researchers. Lindberg H.E. carried ou…     

THE BOUNDARY ELEMENT METHOD (BEM) FOR WAVE EQUATION

The formula of BEM suited to solve the problems of wave propagation in boundlessmedium is obtained from numerical treatment of Kirchhoff integral equation.Afer quotingthe coefficients of refraction and reflection of wave at surface or interface,the expression ofBEM which is suitable for the problems of wave propagation in multi-isotropic mediums isalso given.     

刚性块轴向撞击杆的弹塑性动力屈曲

用特征线法分析了刚性块轴向撞击弹塑性直杆时应力波传播的全过程,得到了杆冲击端与固定端应力的变化规律及刚性块与杆首次分离的时间．基于能量原理,考虑了弹塑性应力波的传播与反射,建立了弹塑性杆在刚性块轴向撞击下的横向扰动方程,给出了问题的级数解,由解的稳定性得到了发生屈曲时的临界条件;通过数值计算和分析,给出了临界速度与冲击质量、线性强化模量及临界时间间的关系．     

The concave or convex peaked and smooth soliton solutions of Camassa-Holm equation

ＩｎｔｒｏｄｕｃｔｉｏｎＣａｍａｓｓａ ,Ｈｏｌｍ[1]ｏｂｔａｉｎｅｄａｃｌａｓｓｏｆｎｅｗｃｏｍｐｌｅｔｅｌｙｉｎｔｅｇｒａｂｌｅｓｈａｌｌｏｗｗａｔｅｒｅｑｕａｔｉｏｎ ,ｉ.ｅ.,Ｃａｍａｓｓａ＿Ｈｏｌｍｅｑｕａｔｉｏｎ2ｕｔ+ 2ｋｕｘ-12 ｕｘｘｔ+ 6ｕｕｘ =ｕｘｕｘｘｘ+ 12 ｕｕｘｘｘ. ( 1 )Ｆｏｒｅｖｅｒｙｋ,ｔｈｅＥｑ .( 1 )ｉｓａｃｌａｓｓｏｆｃｏｍｐｌｅｔｅｌｙｉｎｔｅｇｒａｂｌｅｓｙｓｔｅｍ .Ｔｈｉｓｃｌａｓｓｏｆｅｑｕａｔｉｏｎｉｓａｃｌａｓｓｏｆｎｏｔｏｎｌｙｓｔｒａｎｇｅｂｕｔａｌｓｏ…     

Bifurcations of traveling wave solutions and exact solutions to generalized Zakharov equation and Ginzburg-Landau equation

This paper studies the dynamic behaviors of some exact traveling wave solutions to the generalized Zakharov equation and the Ginzburg-Landau equation. The effects of the behaviors on the parameters of the systems are also studied by using a dynamical system method. Six exact explicit parametric representations of the traveling wave solutions to the two equations are given.     

Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects

In this paper, we study the existence, uniqueness and stability of traveling wave fronts in the following nonlocal reaction–diffusion equation with delay

WAVE INTERACTIONS IN SULICIU MODEL FOR DYNAMIC PHASE TRANSITIONS

Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis.For any given initial data with two pieces of constant states,the Riemann solutions are constructed as a combination of elementary waves. When the initial profile contains three pieces of constant states,the solution may be constructed from the Riemann solutions,with each two adjacent states connected by elementary waves.A new Riemann problem forms when these two waves collide.Through the exploration of these Riemann problems,the outcome of wave interactions may be classified in a suitable parametric space.