变分法

Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface.

首先给出了三维构造中点源电场的边值问题以及相应的变分问题；然后利用有限单元法求解变分问题，采用四面体单元对研究区域进行剖分，在单元中进行三线性函数插值，将变分方程化为线性代数方程组；最后，考虑到节约计算时间，利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组，得到了各节点的电位值，进而计算出地表的视电阻率。

In this paper, the space-time finite element theory and its application technologies are studied and discussed. Furthermore the space-time finite element method is used to analyze the transient characteristics of electromagnetism equipments. The work is important to develop the numerical method for the transient electromagnetic field. The detailed work is as follow.In the basis theory of finite element method used in the transient engineering problem, the functional theory and the finite element theory are applied to studied the existence condition of a generalized variation principle, which is the basis of the space-time finite element method.

本文在完善时空有限元法的基础理论和应用技术并将该方法应用于解决电磁装置的瞬态过程分析等相关方面进行了深入的研究与探讨，该工作对于发展瞬变电磁场问题的数值计算方法具有重要的意义，为此进行了如下几方面的工作：在工程瞬变问题的有限元方法的基础理论方面，本文应用泛函理论和有限元理论，系统讨论了一般工程瞬变问题的变分定理的存在条件及对应的变分定理。

To avoid the trouble to construct the basis functions, we introduce a Lagrange multiplier into the variational formulation to replace the constraint condition for the basis.

本文采用同样的思路用Galerkin 边界元方法求解带有约束条件的与第一类Fredholm 间接边界积分方程等价的变分方程，为避免构造基函数时约束条件的限制，我们采用Lagrange 乘子法，把约束条件放入变分方程中去，形成扩展的变分方程，用线形单元离散后求解。

Moreover, this paper makes an effort in incorporating theCosserat theory in the VCFEM for the elastic-plastic analysis of heterogeneous materialsbased on the PVP. The chapters are divided as follows: In Chapter 1, the author summarizes the study on the equivalent mechanics properties ofheterogeneous materials (including the development of the universal relationship which isirrelevant to the micro structure, the discussion of the limitations of the effective moduli, thecomputation of the effective properties of heterogeneous materials with the micromechanicsmethod and the FEM, and the equivalence of the heterogeneous micropolar materials) and thepresentation, the evolution, the corresponding numerical studies of the Cosserat model and itsapplications in engineering.

本文基于参数变分原理，构建了Cosserat体弹塑性有限元分析模型并用于求解应力集中和应变局部化问题；利用Voronoi有限元法提出了适用于非均质材料宏观弹塑性性能计算的参数二次规划算法；进一步将Cosserat模型应用到Voronoi有限元法中，提出了基于Cosserat理论的Voronoi杂交有限元法，并采用参数变分原理进行新模型的分析计算。

The energy curve of the body-centered cubic structure of theH92 +cluster is calculated by means of variational method.

用变分法计算了H29+团簇的体心立方结构与能量。

Using the Lagrange varitional method and considering the cross phase modulation as perturbation factor, the characteristic of DMS are synthetically analyzed and studied in wavelength division multiplexing and optical time division multiplexing systems for the first time.

运用拉格朗日变分法视XPM为扰动因子，首次综合解析了WDM和OTDM系统中DMS特性，并利用解析结果对不同的系统进行研究。

But the study of non-well-distributed substance of differency in nature in every direction has been ignored in the approximate solution of Voigt and Reuss, and as a result, it is not a overall conclusion.

针对各向异性非均匀体，采用变分法及能量极值原理进行分析，得出了一个比Voight -Reuss和Hashin -Shtrikman上、下限近似解更为精确和合理的上、下限计算公式

By using a one-dimensional variational (1D-Var) method, relative humidity derived from GMS-5 multi-channel satellite images and from NOAA-14′s TIROS Operational Vertical Sounder radiances were corrected by 6-h RH forecasts of the MM5 meso-scale NWP model.

本文采用一维变分法，并将MM5模式的相对湿度6小时预报作为背景信息，对1998年6~7月两种卫星反演地球大气相对湿度资料进行偏差校正试验，以提高其精度。

In this paper, the through truss composite beam is first equalized to a box beam and the progression solutions to the temperature effect of the composite beam are then obtained with the variation method.

首先将下承式桁梁结合梁等效为箱形梁，再用变分法求出了下承式桁梁结合梁温度效应的级数解，并对京沪高速铁路上的一座简支下承式钢桁结合梁桥进行了计算，其结果可供下承式桁梁结合梁设计参考。

During the calculation of the early age temperature field, the early age physical and mechanical performance of concrete varies with its age, therefore in the second chapter we discuss the early age physical and mechanical performance of concrete and its development regulation with time, we emphasize elastic module and the development about the early age strength of concrete varying with time, at the same time consider the effect of shrink and creep upon the early age of concrete, in succession discuss how to confirm the physical parameter of thermodynamics of concrete.

之后讨论了混凝土的热物理参数的确定。为了能够正确合理的应用有限元方法求解早期混凝土温度场问题，第三章论述了求解温度场的有限元方法。第三章首先对热传导的微分方程作了阐述。之后确定温度场的边界条件。本章采用变分原理推导有限单元法计算温度场的公式。因此在第二小节叙述了变分原理，然后阐明了不稳定温度场的计算的三种方法，确定第四章分析中将采用向后差分法求解0#箱梁早期的温度场。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。