级数解

Moreover compared with the Taylor series solution, the frequency shifts in our solutions appear in the expression of oscillations of all orders in both classical and quantum cases, so multiple-scale perturbation method is more suitable for solving the weak-coupling anharmonic oscillation than the Taylor series approach.

与Taylor级数解相比较，无论是在经典还是在量子解中频率移动都出现在各阶振动表达式中，所以多尺度微扰解是弱耦合非简谐振动的较好解法。

Based on the complex potential method about the plane theory of the elasticity of an anisotropic body,stress distributions in the plate with multiple cracks are obtained by using the conformal mapping and the Faber series expansion.

采用各向异性体平面弹性理论中的复势方法，应用保角映射技术和F aber级数展开，导出在任意载荷作用下多裂纹板应力场的级数解，引入当量屈服应力修正裂尖塑性区，并利用Sw ift韧带屈服准则建立含共线分布多裂纹结构的剩余强度分析模型，计算结果与试验结果吻合较好。

Based on the laminate theory, a laminate weakened by damage is treated as an anisotropic thin plate. Using the complex potential method in the plane theory of elasticity of an anisotropic body, the series solution of finite anisotropic thin plate containing an elliptical inclusion is proposed with the help of Faber series. A hybrid element with an elliptical inclusion for anisotropic materials is obtained by using the hybrid variable principle, and the element efficiency is verified by numerical examples. The state of the damage is modeled by an elliptical soft inclusion, and using the point stress criterion based on characteristic curve and Yamada-Sun etc. criteria, the prediction of the strength of a composite laminate with damage is set up. The effects of various parameters on the stress distribution and the residual strength of a composite laminate weakened by damage are detailedly studied.

首先基于经典层板理论，将复合材料层板的弹性问题化归为均匀各向异性板来求解；采用各向异性体平面弹性理论中的复势方法，以Faber级数为工具，给出了有限大含椭圆核各向异性板弹性问题的级数解形式；利用杂交变分原理，成功导出含椭圆核各向异性板杂交应力有限元，并用算例验证了该单元的可行性和有效性；采用含刚度折减椭圆形弹性核的冲击损伤模型，引入基于特征曲线和Yamada-Sun破坏准则的点应力判据，建立了含损伤复合材料层板剩余强度的分析方法；通过数值计算详细讨论了各种几何参数对损伤层板应力分布、剩余强度的影响，得到了一系列对工程应用具有实用价值的结论。

Based on the complex potential method about the plane theory of the elasticity of an anisotropic body, stress distributions in the plate with multiple cracks are obtained by using the conformal mapping and the Faber series expansion. The equivalence yield stress considers the effect on plastic zones. The Swift strip yield criteria is used to predict the residual strength of plate containing multiple collinear cracks.

采用各向异性体平面弹性理论中的复势方法，应用保角映射技术和Faber级数展开，导出在任意载荷作用下多裂纹板应力场的级数解，引入当量屈服应力修正裂尖塑性区，并利用Swift韧带屈服准则建立含共线分布多裂纹结构的剩余强度分析模型，计算结果与试验结果吻合较好。

However, the second associated Legendre function is too complicated to compute, so a simple and practical ellipsoidal harmonic series expansion is introduced, and the series solution and integral solution of the Dirichlet boundary value problem and the Neumann boundary value problem under ellipsoidal boundary are given.

鉴于展开式中第二类缔合勒让德函数的计算较为复杂，接着引入一种形式简单、实用的椭球谐级数展开，介绍了椭球界面下Dirichlet边值问题和Neumann边值问题的级数解和积分解。

Combining the precise exponential matrix calculation with the basic assumptions of constant average acceleration method of the Newmark family, explicit integral method with Taylor series and its algorithm are put forward.

将Newmark-β法中常平均加速度法的基本假定与精细指数算法结合，根据指数矩阵的Taylor级数展开式，提出了动力方程的显式级数解，并设计了相应的时程积分算法。

In this paper, the analysis model of crustal vertical movement is established based on the hypothesis of the global flux isostatic datum, and its harmonic function series solution is proposed.

根据全球通量均衡假说建立了地壳垂直形变场的分析模型，在球面近似下求得了该模型的球谐函数级数解并拟合了两个不同区域的地壳垂直形变场，编绘了等值线图，继而在密切平面坐标系下导出了该模型的Fourier级数解。

Now by using Dai's exact solution formula and studying the asymptotical behavior controlcondition and using the series expression of the famous Riemann Zeta-function in number theory,after introducing and proving a new representation theory of inverse Laplace transformation wedirectly obtained Chen's solution formulae and their unique existence condition without usingLaplace transformation and〓 inverse formula.

本文从带消发散参数的严格解出发，通过研究渐近行为控制条件，利用数论中著名的Riemann-Zeta函数的级数表示，引入并证明一个逆Laplace变换的新的表示定理，直接导出了陈等发展的级数解，并得到了级数解的存在、唯一性条件。

Secondly, the effectiveness and limitation of the classical perturbation, such as the method of multiple scales and the Poincare-Lindstedt method, are discussed in detail through a Duffing oscillator with delayed velocity feedback. It is shown that the two perturbation methods are effective only in solving the approximate solution of the first two orders. An ambiguity or paradox will be encountered when they are used to seeking for the third or higher order approximation of solution.

其次，以一具有时滞速度反馈的Duffing系统为例，研究了经典摄动法如多尺度法，Poincaré-Lindstedt法等在求解时滞微分方程级数解时的适用性和局限性问题，指出利用这些方法只能有效求得系统的前两阶近似解，而在求系统的三次以上近似解时会出现矛盾或二义性。

The construction of the solution space for shallow-water equations on the equatorialβ?plane and the equations about the tropical circulation to heating are mainly studied. The solution method of exact solution in the analytic function class and the computational procedure to the series solution are expressed for the well-posed problem.

平面近似的浅水方程组和热源强迫的热带环流方程组，重点研究了它们的解空间构造，并给出了各种适定的定解问题在解析函数类空间中准确解的具体的求解方法，并编制程序去计算其级数解。

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。