反对称角铺设层合矩形板在不同边界条件下的后屈曲问题

本文以板的无量纲最大挠度为摄动参数,应用摄动法研究了在几种支承情况下,反对称角铺设层合矩形板的后屈曲问题,并以梁的特征函数所构成的广义付里叶级数作为高阶摄动偏微分方程的近似解,本文方法简捷,计算收敛性好、数据可靠。     

摄动DQ法分析板的大挠度热弯曲

本文给出了求解板的大挠度热弯曲问题的摄动DQ法。该方法由二阶摄动得到板的大挠度热弯曲问题的一组线性摄动方程后运用DQ法进行求解,具有良好的计算精度和计算效率。     

Reissner板弯曲问题的渐近解

本文从分析Ｒｅｉｓｓｎｅｒ板理论与Ｋｉｒｃｈｈｏｆｆ板理论的关系入手，导出了对Ｒｅｉｓｓｎｅｒ板问题的求解，可用摄动技术转化为相应边界条件下求解一系列Ｋｉｒｃｈｏｆｆ板问题，最后给出了算例也证明了本文方法具有简单，精度高的特点。     

四边固支梯形板大挠度问题摄动解法

本文采用Voh—Karman薄板大挠度方程,以板中点挠度值作小参数求得了均布荷载下中面边界条件为Nn=o,Vs=o的固支梯形板的摄动解,本文特例与现有梯形板小挠度和矩形板大挠度结果比较吻合较好。文末还讨论了倾角对板挠度和内力的影响,所给图表对工程设计有实用价值     

板壳结构非线性随机有限元法研究

采用摄动随机有限元法研究了具有随机参数的板壳结构大挠度动力响应问题。基于Mindlin-Reissner板理论,采用全量Lagrangian法推导了具有板壳结构的大变形、大转动的动力响应有限元列式;通过基于等参变换的局部模型对随机场进行离散,结合摄动技术,建立了基于摄动技术的增量形式的随机有限元列式,计算结果与Monte-Carlo法相比较表明了该方法的有效性和精确性。通过该方法,为进一步进行结构可靠性分析提供了依据和方便。     

弹性基础上矩形板热后屈曲分析

本文给出双参数弹性基础上矩形板在均匀和非均匀（抛物型）热分布作用下后屈曲分析。采用摄动－Ｇａｌｅｒｋｉｎ混合法给出完善和非完善矩形板热屈曲载荷和热后屈曲平衡路径。本文同时给出数值算例并讨论各种参数变化的影响。     

正交各向异性矩形板后屈曲行为分析

本文以板最大变形为摄动参数,用摄动法分析了中面双向均压和周边受剪的四边简支的正交各向异性矩形板的后屈曲问题.先将用力函数和挠曲函数表示的von KOrman大变形耦合形式的非线性偏微分方程组简化为一组去偶形式的线性偏微分方程组:再将力函数和挠曲函数表示为双傅氏级数,把线性偏微分方程组化为线性代数方程组,从而获得问题的渐过解.文中对玻璃纤维增强环氧的复合材料矩形板给出了数值结果和图表,讨论了边长比、载荷参数等因素对后屈曲行为的影响.数值结果表明本文级数解有很好的收敛性,并与参考文献进行了比较,很吻合.      

基于改进区间摄动分析的统计能量分析法

为高效定量地度量系统参数的不确定性对其高频动响应的影响规律,在参数可用数据不足条件下首先建立区间参数系统的统计能量分析模型。通过保留部分高阶摄动项而提出改进区间摄动分析法,在不损失计算效率前提下提高已有区间摄动分析法的计算精度,进一步提出基于改进区间摄动分析的统计能量分析法。以板腔系统为对象,通过与不同区间分析法的比较验证了所提方法的有效性。     

变厚度夹层环形板的非线性弯曲

本文对具有变厚度的夹层环形板大挠度弯曲问题进行研究。利用变分原理导出表层和夹心均为变厚度的夹层环形板大挠度弯曲问题的控制方程和边界条件,进一步给出表层和夹心均为双曲型变厚度的夹层环形板大挠度方程,采用摄动法求得了具有双曲型变厚度夹层环形板在外边缘为可移夹紧固定、内边缘与一刚性中心固结情况下非线性弯曲问题的渐近解,得到内边缘处无量纲挠度与无量纲载荷和无量纲应力的解析表达式,并讨论几何参数和物理参数对夹层环板弯曲的影响。     

初始缺陷对板钢结构极限承载力的影响分析

从含初始弯曲的大挠度方程出发,以薄板厚度的折减量为摄动参数,将残余应力考虑成等效荷载,并通过参数分析的方法修正残余应力等效荷载,根据实用板与理想板的比拟,得出板的厚度折减量和板的极限承载力方程。非线性有限元分析和试验数据的对比表明:该文提出的方法实用、精度高,是分析板钢结构极限承载力的通用方法,可作为非线性有限元分析方法的补充,大大简化了结构极限承载力分析的复杂性。     

Analytical solution of groundwater waves in unconfined aquifers with sloping boundary

A new analytical solution is derived for tide-driven groundwater waves in coastal aquifers using higher-order Boussinesq equation. The homotopy perturbation solution is derived using a virtual perturbation approach without any pre-defined physical parameters. The secular term removal is performed using a combination of parameter expansion and auxiliary term. This approach is unique compared with existing perturbation solutions. The present first-order solution compares well with the previous analytical solutions and a 2D FEFLOW solution for a steep beach slope. This is due to the fact that the higher-order Boussinesq equation captures the streamlines better than ordinary Boussinesq equation based on Dupuit’s assumption. The slope of the beach emerges as an implicit physical parameter from the solution process.     

An Iterative Finite Element Perturbation Method for Computing Electrostatic Field Distortions

A finite element perturbation method is developed for computing electrostatic field distortions and the ensuing charges and forces on moving conductive regions subjected to fixed potentials. It is based on the subsequent solution of an unperturbed problem in a complete domain, where conductive regions have been extracted, and of perturbation problems in subdomains restricted to the surroundings of the added conductive regions. The solution of the unperturbed problem serves as source (with a very reduced support) for the perturbation subproblems. For every new position of the conductors, the solution of the unperturbed problem does not vary and is thus reused; only the perturbation subproblems have to be solved. Further, this approach allows for the use of independent and well-adapted meshes. An iterative procedure is required if the conductive regions are close to the sources.     

楔形杆轴纵、扭固有振动的修正摄动解

将含大参数的二阶线性方程的修正摄动解应用于楔型杆轴的固有纵振和扭振的研究,得到了其作固有纵振、扭振时的修正摄动解。并通过实例计算,比较了这种方法得出的解与Bessel方法一级近似解之间的误差。可以证明该修正摄动解具有相当高的精度。     

A perturbation solution for the Laminar boundary layer on a continuous moving surface

Summary A perturbation solution is presented for the nonsimilar boundary layer flow past a moving surface with constant wall velocity. A zero pressure gradiant is assumed and the tangential velocity and stagnation enthalpy profiles are prescribed at the initial station. The eigen values obtained for the first order perturbation solution are integers and the eigen functions are the derivatives of the error function. The same Green's function is obtained for all the higher order perturbation equations, and the higher order perturbation solutions are given in integral form in terms of the Green's function. The analyses include both the momentum equation and the energy equation which is uncoupled with the momentum equation, and which is subjected to a nonsimilar velocity flow field.     

Summation of perturbation solutions to nonlinear oscillations

Summary By coupling the Lindstedt-Poincaré perturbation technique with a rational approximation, we propose a method for summing up the perturbation solutions of the nonlinear oscillation of a conservative single-degree-of-freedom system. The equation of motion contains a parameter. This method can represent the singularities of the period at certain values of the oscillation amplitude and extend the range of validity of the perturbation solution. For constructing the summation, all is needed are the coefficients of the pertubation expansion of the periodic solution. Approximate formulas for the period and the corresponding periodic solution of the nonlinear oscillation are established. Two examples are used to illustrate the effectiveness of the method.     

Multiple coordinate perturbations for secular problems with two small parameters

In order to study equations of the form $\text{? (u) = ??(u) ? ηg(u)}$, a perturbation method is proposed that allows to construct a parametric solution in multiple variables. This solution is obtained by applying the Poincaré-Lighthill method to the perturbation in η and that of multiple scales to the perturbation in ?.The method is then applied to two examples: a damped oscillator with a nonlinear restoring force and a progressive wave in a gas in presence of gravity. A criterium for shock formation is given in the last problem.Finally a derivation is given, which provides sufficient conditions to obtain the proposed parametric solution.     

强非线性自激振子同宿轨道的摄动分析方法

在双曲函数摄动法的基础上,推广双曲函数Lindstedt-Poincaré (L-P)法的适用范围,使之适用于定量分析一类含五次强非线性项的自激振子的同宿分岔和同宿解问题。以双曲函数系为基础推导出适用于高次非线性系统的摄动步骤,对极限环的同宿分岔参数进行摄动展开,给出同宿摄动解奇异项的定义,以消除同宿摄动解奇异项作为确定极限环同宿分岔点的条件,给出能够严格满足同宿条件的同宿轨道摄动解。算例表明,在相平面内该方法的结果与Runge-Kutta法数值周期轨道的逼近结果比较吻合。     

非牛顿润滑流的Maxwell模型的摄动解

对各种形式的Maxwell模型已有一些研究结果。Tichy讨论了粘弹性流体的Maxwell模型并对二维润滑流应用这一模型，使用以Deborah数为摄动量的正则摄动法，得到了模型的解。本文用双重正则摄动求解模型，得到了相应的解。顺便指出，所得速度的粘弹性修正项与Tichy的相应结果不同。     

五次非线性自激系统的同宿解及其分岔

推广了双曲函数Lindstedt-Poincaré (L-P)法摄动步骤,定量求解一类派生系统含五次强非线性项的自激振子的同宿解及其分岔值。对极限环的同宿分岔参数进行摄动展开,给出同宿摄动解奇异项的定义,以消除同宿摄动解奇异项作为确定极限环同宿分岔点的条件,给出能够严格满足同宿条件的同宿轨道显式摄动解,推导出任意阶解和同宿分岔点判别的一般表达式。应用该法具体分析了一类推广的Liénard振子的同宿解和同宿分岔问题,指出方法的优点和存在的问题。算例表明,在相平面内该方法的结果与Runge-Kutta法数值周期轨道的逼近结果较吻合,相应的同宿分岔点判定值也具备较好的精度。该方法可以进一步研究推广应用于分析其它形式更一般的系统的同(异)宿解和同(异)宿分岔问题。