级数展开

Shadow effect can not be neglected for thermal analysis of spacecraft,Accroding to the angle between solar light and antenna orbit plane and its orbit location,analytical geometry method was used for accurately calculating solar radiation heat flux distribution of reflector surfaces.To analyze the temperature field under heat flux,the formulations of net radiation flux density between two gray elements and the net flux density of gray surface under external thermal flux were deduced.Based on the characteristic of space environment,the nonlinear temperature distribution in transverse direction of reflector shell self radiation were considered,the finite element formulations were given for orthogonal material layered shell by Galerkin method.A layered element including a inner heat source layer was proposed,and the finite element formulation expressed by DOF of the inner heat source layer were put forward with temperature and heat flux boundarys between adjacent layer.

单馈反射面赋形天线是未来星载天线发展的一个重要形式，分析了基于物理光学、几何光学和几何绕射理论的理想反射面辐射场；介绍了基于几何光学的反射面天线赋形方法；针对赋形过程中辐射场的快速分析要求，比较分析了基于物理光学的Fourier-Bessel和Jacobi-Bessel级数展开方法以及GB展开分析方法；利用GB展开快速分析方法在20GHz频率下对0.6m口径的天线进行赋形分析，实现中国大陆的30dB增益覆盖，通过数值计算研究了固定增益期望下的口径尺寸随频率的变化，以及频率为20GHz的不同尺寸天线赋形后的覆盖目标区域最大增益的变化情况。

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 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。

The method for calculating the expression of the trapezoidal corrugation slow-wave structure is studied in detail,which uses Fourier series expandedness.

利用傅里叶级数展开，给出了一种求解梯形慢波结构表达式的方法。通过数值模拟，研究了级数展开次数对求解精度的影响。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

Energy density and particle density in high energy heavy-ion collisions are calculated with infinite series expansion method and Gauss-Laguerre formulas in numerical integration separately, and the results of these two methods are compared, the higher terms and linear terms in series expansion are also compared.

分别用无穷级数展开方法和数值积分计算中的高斯拉盖尔求积法对高能重离子碰撞中能量密度和粒子密度数值进行计算，并对结果及级数展开中的高次项和一次项的大小进行了比较。

It is also the base of structure optimization.According to main object characteristics of structural dynamics design,structuraleigenveetor sensitivity computation is,first,be studied.A Neumann series expansionmethod is proposed in accordance with the modal method and is developed to agreewith the structure with rigid body modes.A rapid Neumann series expansion methodfor eigenvector sensitivity is formed;it may greatly improve the efficiency ofcomputing eigenvector derivation.

本文根据结构动力学设计的主要目标特性，首先进行了结构特征向量灵敏度分析研究：形成了计算特征向量灵敏度的Neumann级数展开法，并将其扩展到适用于具有刚体模态的结构特征向量灵敏度分析；研究出计算特征向量灵敏度的快速Neumann级数展开法，该方法大大提高了特征向量灵敏度分析的效率；建立了无需K-1运算的结构特征向量灵敏度分析的共轭梯度迭代法。

Based on the theory of modal superposition and power series expansion, a modal superposition method for the sensitivity analysis of FRF is proposed in this paper.

基于模态展开和幂级数展开原理，提出了一种频响函数灵敏度分析的模态展开法。

In SMFSIA/CAG, to increase computational efficiency in solving the matrix equation, both the speed of the iterative convergence and the matrix-vector multiplication are picked up based on iterative theory. The extended formula of the high order Taylor's series about the horizontal distance is derived. The relationship between the Taylor's series or the neighborhood distance and the efficiency of the arithmetic are analyzed.

在SMFSIA/CAG中，基于迭代法的原理，通过加快迭代收敛速度和加速矩阵向量积两个方面对该算法进行了改进，推导了关于平面展开的高阶泰勒级数展开公式，并对近场相关距离和泰勒级数展开阶数对算法效率的影响进行了分析。

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。