级数展开

Methods Conformal mapping and series expansion are used.

利用复变保角变换和级数展开法。

The constant term and non-singular terms, which are called general T-stress here, play a significant role in determining the stress and strain fields around a crack tip which in turn can affect the calculation of stress intensity factor of the crack.

裂纹尖端的奇异应力场可以表达为Williams级数展开的形式，其中常数项和非奇异项对裂纹尖端的应力应变场有着很大的影响，这些影响反过来作用于裂纹应力强度因子的计算。

Based on the series expansion technology in complex potential theory established by Muskhelishvili the complex stress functions can be estabished. By utilizing the continuity principle of the boundary condition and the characteristics of far field and according to the comparison of the coefficients of the terms on both sides of the equation with the same exponent the present problem can be transformed into solving of linear equation set.

根据Muskhelishvili复势理论的级数展开技术，构造了合适的各区复应力函数；然后，利用边界上位移、力的连续性条件和远场的性态，通过等式两边同次幂指数的系数比较，将问题转化为线性方程组的求解；结合叠加原理，获得混凝土在此情况下环向应力的解析解答。

As a result, it shows thatthe static or dynamic subsystem optimum alone is not equal to the system optimum. Three initial value problems met in the optimal design of flying vehicle are studied andconclusions are derived that: orthogonal test method can be adopted to decide the initial valueof static optimization problem, some mathematical techniques can be used to deal with thecostate variables of Maximum Principle and decide the initial value of the costate variable,the indirect method can be used to get the analytical solution under ideal case to guide thechoice of the initial control curve in the direct method. With some numerical examples oftrajectory optimization, it shows that all these methods are useful not only in accelerating theconvergence but also in converging to the global optimum.

针对飞行器优化设计中的三种初始值问题进行了研究，以远程弹道导弹弹道的工程优化为例说明，对于静态优化问题，采用正交试验法选取初始值，不仅可以大大加快收敛的速度，而且更有可能收敛到全局最优解；以气动力辅助变轨问题为例说明，用共态变量的一阶泰勒级数展开可以解决极大值原理中共态变量初值难于确定的问题；以二级弹道导弹的主动段弹道优化为例说明，利用间接法在理想情况下得到的解析解来指导直接法初始控制曲线的选择，将大大有利于提高直接法的收敛速度。

The paper presents a linear transient solution for the solitary wave generated by a piston-type paddle in a finite flume based on the boundary condition derived by Dean and Dalrymple (1991). The wavemaker problem is simplified by decomposing the wave potential into two parts. One is the evanescent wave and the other is progressive wave. The possible solution for the evanescent wave is expressed in form of the Fourier series.

本文根据Dean与Dalrymple（1991）描述造波水槽内部之线性边界条件，将水槽内部之流速势分为振荡波与前进波以简化问题，再以Fourier级数展开，可将问题化为二非齐次常微分方程式，在给定造波初始条件的情况下即可解析有限长度造波水槽自静止开始造波一段时间后停止之线性暂态解。

The analytic expression of a probability current is derived by using the power series expansion method and used to generate the curve characteristics of the current varying with other parameters.

采用幂级数展开的方法得到了几率流的解析式，给出几率流随外参数变化的特性曲线。

The main research aspects are as following. 1. The zero-order differential operator is constructed, based on the inside interpolation collocation method.

一、在内延拓配点的基础之上，构造了0阶导算子去对函数进行相应的级数展开和插值，证明了它对边缘效应和Gibbs现象的抑制作用。

Based on Reddy higher-order shear deformation plate theory and general von Kármán-type equations, the analytical solutions for free vibration and dynamic response of simply supported functionally graded plates with piezoelectric layers in thermal environments are described with double Fourier series, where temperature-dependent material properties are taken into account.

基于Reddy高阶剪切变形理论和广义Kármán 型方程，用双重Fourier级数展开法求得了热环境下带压电层的功能梯度复合材料混合层合板的自由振动及动力响应的解析解，分析中考虑了材料热物参数对温度变化的依赖性，讨论了环境温度和控制电压对固有频率及动力响应的影响。

Firstly, according to the Laplace equation of ellipsoidal coordinates and the ellipsoidal harmonic functions in common use, the ellipsoidal series expansion of harmonic functions outside the referential ellipsoidal is introduced.

论文首先从椭球坐标的Laplace方程和常用的椭球谐函数出发，介绍了参考椭球面外调和函数的椭球谐级数展开。

We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion in this paper.

我们提出了一种基于Dini级数展开的准离散汉克尔变换算法。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。