粘弹性厚壁筒问题的辛本征解方法

将哈密顿体系引进到粘弹性力学厚壁筒问题中,在辛体系下重新描述了基本问题,即建立了正则方程组。借助于积分变换,得到了拉伸、扭转和弯曲等问题的解以及有边界局部效应的解。将原问题归结为辛几何空间中的零本征值本征解和非零本征值本征解问题,从而建立了一种有效的分析问题方法和数值方法。为解决同类问题提供了一条可行的路径。     

当前环境工程地质领域的几个主要问题及研究对策

本文总结了当前环境工程地质领域几个急待研究解决的主要问题, 分析了这些问题的研究现状, 主要科学问题及研究对策。最后, 提出了研究解决这些问题的基本技术路线。     

按位移推导平面轴对称问题的一般性解答

根据平面轴对称问题的物理概念, 将平面轴对称问题分为轴对称应力问题和轴对称位移问题, 给出了这两种轴对称问题的基本方程, 并指出平面轴对称位移问题是平面轴对称应力问题的特例. 在此基础上, 分别按位移推导了平面轴对称应力问题和平面轴对称位移问题的一般性解答. 按位移推导平面轴对称问题, 可以考虑体力分量, 从而可避免按应力函数推导平面轴对称应力问题时不能考虑体力分量的局限性.     

关于平面问题分类的再探讨

关于平面问题分类的再探讨张雷顺（郑州工学院,郑州４５０００２）由于平面问题比较简单,所以在弹性力学教材中,对平面问题给出了较多的篇幅,也列举了较多的例题．在工程中,相当多的问题也都近似为平面问题处理．但在认定平面问题和进行平面问题分类方面,作者发现时...     

农业工程中的某些力学问题

随着农业生产发展和农产品商品化程度提高,农业工程中提出了许多新的力学问题.本文对这些问题作了初步调研,并对其中部份问题作了简要介绍,例如土壤压实、水果和蔬菜的机械损伤、谷物的应力裂纹、蛋壳强度、粮仓问题、灌溉问题、农业生产建筑中的环境问题等.     

辛体系下平面热黏弹性圣维南问题的解析解

借助积分变换,将辛体系引入平面热黏弹性问题,建立了基本问题的对偶方程,并将全 部圣维南问题归结为满足共轭辛正交关系的零本征值本征解问题. 同时,利用变量代换和本 征解展开等技术给出了一套求解边界条件问题的具体方法. 算例讨论了几种典型边界条件问 题,描述了热黏弹性材料的蠕变和松弛特征,体现了这种辛方法的有效性.     

龙子湖水文工程地质条件分析与渗漏控制

在详细分析了龙子湖地区水文地质条件和工程地质条件的基础上,根据龙子湖的设计方案,指出龙子湖建成后可能存在渗漏量过大的问题,从而影响该区的生态环境等环境地质问题。本文建立了三维渗流数值模型,通过数值模拟证实了龙子湖建成后确实存在渗漏量过大的问题,并为解决这些环境地质问题提供参考方案,还预测分析了环境水文地质条件改变后可能进一步出现的问题并提出了相应的解决方案。     

非线性弹性力学平面应变的一个稳定性问题及其一些应用

本文研究了和谐材料在大弹性变形下的稳定问题,并考虑了第一第二第三边值问题的稳定问题,获得了平面弹性问题的特征值的求法。     

纵横荷载共同作用下基础板弯曲问题样条边界元分析

本文从计入中面力的薄板控制微分方程出发,导出了求解纵横荷载共同作用下基础板弯曲问题和稳定问题的计算格式,耦合片平面问题和板弯曲问题,有效地解决了复杂荷载作用下板弯曲问题和临界荷载的计算。     

问题链教学模式在流体力学教学中的应用

简要介绍了问题链教学模式,分析了该教学模式的内涵和关键要素,以流体力学课程中教学实例说明问题链教学模式的应用方法. 培养了学生问题意识,提高了学生独立思考和创新能力.     

获得热传导问题“拟解析解”的精细积分算法

研究并讨论了用于热传导分析有限元解的精细积分算法，算法很好地克服了传统方法求解时的单调性问题，且对空间离散后所获得方程的解是解析的，因而算法的解将具有“拟解析解”的意义，论文证明了算法单调性．     

KdV-Burgers方程的级数解

给出ＫｄＶ－Ｂｕｒｇｅｒｓ方程的有界行波解的精确级数解,采用Ａｄｏｍｉａｎ算子分解法分别求行二个区域ζ〈０和ζ〉０的级数解,然后利用对接连续条件构成整体级数解。所得级数解能精确满足对接连续条件,并由此得到确定级数的系数递推公式,无需解非红性高阶代数方程组。与某些精确解及其它方法比较,计算简捷具在对接点处是收剑的。对某些非线性波动现象的研究,可作为计算和分析的数学依据。     

Transient conduction in a plate cooled by free convection

An approximate analytical solution of the one-dimensional conduction equation with a natural convection boundary condition is presented. The solution is based on the heat balance integral technique and possesses considerable utility. The accuracy of the solution is tested by comparison with an exact solution for a range of linear forced convection problems and with a Crank-Nicolson solution for a range of nonlinear free convection problems. It is demonstrated that significant differences can occur between the temperature responses of a solid cooled by either free of forced convective flow at similar Biot numbers.     

A theoretical solution for axially symmetric problems in elastodynamics

This paper presents a theoretical solution for the basic equation of axisymmetric problems in elastodynamics. The solution is composed of a quasi-static solution which satisfies inhomogeneous boundary conditions and a dynamic solution which satisfies homogeneous boundary conditions. After the quasi-static solution has been obtained an inhomogeneous equation for dynamic solution is found from the basic equation. By making use of eigenvalue problem of a corresponding homogeneous equation, a finite Hankel transform is defined. A dynamic solution satisfying homogeneous boundary conditions is obtained by means of the finite Hankel transform and Laplace transform. Thus, an exact solution is obtained. Through an example of hollow cylinders under dynamic load, it is seen that the method, and the process of computing are simple, effective and accurate.     

弹性动力学轴对称问题的理论解

本文给出了弹性动力学轴对称问题基本方程的一种理论解。它由满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加构成。在求得准静态解后,代入基本方程,得到动态解所需满足的非齐次方程。由相应的齐次方程的特征值问题,定义了有限Hankel变换。通过这种变换及Laplace变换,求得动态解,从而得到了一个完整的理论解。文中通过对一个实例求解,表明该方法求解过程简便,实用,求解结果精确。     

多阶变截面杆的弹性稳定计算

本文研究单阶和多阶截面杆在集中和分布轴向荷载作用下的弹性稳定计算方法,首次给出了其整体稳定和局部稳定的解析解.     

Modelling of the moisture concentration field due to cyclical hygrothermal conditions in thick laminated pipes

The paper presents a new method to calculate the moisture concentration field induced by cyclical environmental conditions in thick laminated pipes. The solution which is obtained is composed of a transient solution over the interior of the pipe wall and a fluctuating solution within two thin regions, close to the inner and outer lateral surfaces of the pipe wall. The thickness of these two regions is depending on both materials and frequency conditions. The transient solution is determined by using an analytical method based on the solving in average of the field equation. The fluctuating solution is derived from a finite difference scheme. It is shown that after some period of time the transient solution tends towards a permanent time independent solution. In that case, the fluctuating solution becomes a periodic solution which is conditioned by the cyclical boundary conditions. Finally, the effect of particular cyclical conditions on the moisture concentration in thick wall pipes will be tackled.     

SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

IntroductionInthispaper,westudiedakindofboundaryvalueproblems (BVPs)forsemi_linearretardeddifferentialequationwithnonlinearboundarycondition :　　　　εx″(t) =f(t,x(t) ,x(t-ε) ,ε) ,　　t∈(0 ,1 ) ,(1 )　　　　x(t) =φ(t,ε) ,　t∈[-ε0 ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,(2 )whereε>0isasmallparameterandε0 isasufficientlysmallpositiveconstant.ThereweremanyresultsofstudyingonsingularlyperturbedboundaryvalueproblemforretardeddifferentialequationinRefs.[1～5] .Butthosestudiespossessedanesse…     

Elastodynamic wave scattering by an incompressible elastic inclusion

The problem of scattering of time-harmonic elastodynamic waves by an incompressible elastic inclusion is solved by means of the null field approach. The solution is obtained both directly and as a limit of the solution to the corresponding problem for a compressible inclusion. It is also demonstrated that the null field solution to the problem of scattering by a rigid movable scatterer can be obtained from a null field solution for the incompressible scatterer by taking the limit of infinite shear modulus. Some numerical results for spherical and spheroidal inclusions are given.     

A combinatorial algorithm for the discrete optimization of structures

The definition of local optimum solution of the discrete optimization is first given, and then a comprehensive combinatorial algorithm is proposed in this paper. Two-level optimum method is used in the algorithm. In the first level optimization, an approximate local optimum solution is found by using the heuristic algorithm, relative difference quotient algorithm, with high computational efficiency and high performance demonstrated by the performance test of random samples. In the second level, a mathematical model of (-1, 0, 1) programming is established first, and then it is changed into (0, 1) programming model. The local optimum solution X^* will be from the (0, 1) programming by using the delimitative and combinatorial algorithm or the relative difference quotient algorithm. By this algorithm, the local optimum solution can be obtained certainly, and a method is provided to judge whether or not the approximate optimum solution obtained by heuristic algorithm is an optimum solution. The above comprehensive combinatorial algorithm has higher computational efficiency.Project supported by Natural Science Foundation of Shandong Province