解析法

The ATF method is also applied to develop singular element in the V-notch analysis and an element with notch named ATF-VN is formulated.

采用解析试函数法构造了含切口单元ATF-VN。用此单元分析切口问题也非常有效。

In the past, there exists difficulty for calculating nearly singular integrals arising from boundary element analysis of the problems of thin body. However, by now, the difficulty of nearly singular integrals has been resolved by analytical integral algorithm, which has been put into uses in analyzing the conventional structures and thin body structures in the potential problems.

过去边界元法求解薄体结构存在着几乎奇异积分的困难，目前几乎奇异积分问题已得到成功解决，解析积分算法也已成功应用于分析二维位势问题常规结构和薄体结构。

A practicable analytic solusion is obtained for any sector by means of Fourier series with singular items.

从位移场带奇性分离的Fourier级数表达式着手，得到扇形问题可实际操作的解析解，可以证明此级数解法与Wiliams分离变量法等价。

Finally, it should be mentioned here that the singular solution of single layer and multilayer saturated porous media axisymmetric and non-axisymmetric Biot's consolidation problems may be set up, according to present solution.

以本文提出的解答作为基础，可建立单层和多层饱和多孔介质轴对称和非轴对称问题的奇异解，为边界元法提供层状地基Biot固结问题的基本解的解析表达式。

Furthermore,the stability behavior and accuracy characteristics of the algorithmare proven by a spectral decomposition method.

在前人工作的基础上，提出了一种新的用于解决结构动力分析问题的时间积分方法——Taylor级数方法；建立了求解线性问题和非线性项可以表示为多元多项式形式的非线性问题的Taylor级数方法的理论，并给出递归求解通式；阐述了该方法的程序实施过程，给出了计算流程图，并在非线性有限元分析平台NFAP中嵌入了Taylor级数方法的计算模块；利用谱分解的方法分析了该方法的稳定性和精度特性，以封闭的解析形式给出了描述积分法特性的周期延长率和振幅衰减率的表达式；通过对该方法的理论分析和特性研究，阐述了该方法的可行性和高效性。

It means to recognize periodicity by analyzing the spectral density of periodically variable sequence, then to judge the measured period true or false through the statistical examination of Fisher's Kappa and Bartlett's Kolmogorovsmirnov.

第三节"波动周期的模型测定法"以"收入—支出"结构和"需求导向"为基本构架，通过建立中国宏观经济波动模型来测定宏观经济内生变量波动的周期长度，这种通过解析思路测定经济变量波动周期的方法，具有理论支撑，其科学性、可信性是显而易见的。

The first stage is screen experiment. A 24-1 Fractional Factorial Design and resolution IV experiment is used to find out which main effect and interaction effect have obvious influence on the precision positioning of feeding table by these four factors. The Minitab program including Half Normal Plot, Pareto Chart, and ANOVA is applied to diagnose obvious effects. The second stage is optimization experiment. The fitness of regression model is obtained by using CCD of RSM with statistical hypothesis testing, regression analysis, lack-of-fit testing, and residual analysis. The optimum values can be found out by using response surface plot and contour plot.

在第一阶段为筛选实验采用24-1部分因子实验，解析度为IV，求出这4个因子主效应及交互作用哪些会对进给平台定位精度有显著的影响，在分析方面使用统计软体Minitab做初步分析，应用了半常态机率图、柏拉图与变异数分析来判断出显著因子与交互效应显著，第二阶段优化实验采用反应曲面法的中央合成设计，搭配统计检定、回归分析、缺适性检定(Lack-of-Fit)、残差分析来取决回归模式之合适性，最后根据反应曲面图及等高线图求出最佳值做验证实验。

Then the problem is reduced to less degrees of freedom to solve nonlinear equations by the modal synthesis method.To verify the successfulness of this method,an example is given.

利用非线性振动理论的平均方法，求得经模态综合法降维后系统方程的近似解析解。

What's more, this solution technique is available to obtain the potential subharmonic resonance and it overcame difficulties of traditional analytic Harmonic Balance Method based on the describing functions in resolving superharmonic and subharmonic response.

克服了传统的解析谐波平衡法基于描述函数进行而难以求解一般周期响应和次谐波响应的缺点。

The Fourier transfermation about the azimuthal angle and Hankeltransfermation about the radial dirction have been used to turn the basic dis-placement equatioons and constitutive equations under cylindrical coordinatesystem into a system of second order ordinary differential equations in thewavenumber domain,by use of the initial prarameter method to solve differ-ential equations.

利用关于方位角的Fourier变换及关于径向的Hankel变换，将柱坐标系下位移基本方程和本构方程转化为波数域内二阶常微分方程组，利用求解微分方程的初参数法，建立了介质层的传递矩阵，导出了层状弹性半空间在地表作用任意静荷载情形下的解析解。

The reasons of iron ions content overproof in grade Ⅱ desalting water system,such as variation water quality,contamination of regenerant , operation adjustment of pretreatment system and switching operation of bed were discussed.

对二级脱盐水系统中铁离子含量超标的原因，如来水水质发生波动、再生剂受到污染、预处理系统操作调整、床体运行切换等进行了论述。

You were hired to drum up new business, so go and do it.

公司雇你招徕新业务，你就做你的事好了。