【作者】 胡国辉；

【导师】 何为；

【作者基本信息】 重庆大学 ， 电气工程， 2004， 硕士

【摘要】 有限元法作为一种强有力的工程分析方法被广泛的应用于各种工程领域，对于电气工程领域，有限元法同样是用于各类电磁场、电磁波工程问题定量分析与优化设计的最主要的数值计算方法。而制约有限元分析的瓶颈问题是模型的建立和数据的输入，其核心内容是区域的离散--网格的生成，即有限元法的第一步就是生成分析区域的一个恰当的有限元网格，由于网格划分质量的好坏直接影响到数值分析的精度，因此寻求合适的网格生成算法以实现有限元网格自动生成是进行有限元分析的关键问题，目前各种网格自动生成算法(特别是在二维的分析域中)已经相当成熟，并在实际工程领域得到广泛应用。本文在阐述有限元分析方法的基本原理的基础上，详细讨论了有限元分析在工程电磁场中的具体应用。并从有限元分析系统结构这个角度分析了作为有限元分析前处理部分的有限元网格自动生成系统在工程应用中的理论和实际意义。进行网格剖分首先要建立分析对象的几何模型，鉴于本文的分析对象是医学脑CT扫描图像，为此采用数字化仪从脑CT扫描图像中提取边界特征点，以此形成分析模型的边界轮廓，从而建立分析模型的几何模型。文中在阐述串口通讯的基本原理的基础上详细论述了如何实现数字化仪与计算机之间的串口通讯，最终实现了几何建模的功能。本文重点讨论了网格自动生成算法，通过分析和研究Delaunay三角化方法和The Advancing Front前沿推进法，设计了结合这两种网格生成算法优点的网格自动生成算法，对加权平分设置场域内部节点的方法进行了改进，并提出了利用三角形质量因子判据进行网格修正和采用四倍加密法实现网格加密的网格优化措施。采用面向对象的程序设计思想和C++语言开发了基于Visual C++6． 0平台的有限元网格自动生成系统，并结合具体实例验证了本算法的可行性、通用性、可靠性、和全自动性。本文最后讨论了科学计算可视化的含义和在工程实际应用中的重要意义，结合本有限元网格自动生成系统设计了一个友好的交互式图形用户界面(GUI)，利用OpenGL图形标准对生成的网格图形进行各种图形变换以实现可视化图形处理功能。更多还原

【Abstract】 The Finite Element Method (FEM) has been widely used in many engineering research fields as a strong tool of analyzing projects. For the field of electrical engineering, FEM is also a very important numerical method, which is used in the quantitative analysis and optimum design of engineering problems, such as electromagnetic fields and electromagnetic waves. The foundation of models and the data input are the main bottleneck difficulties which restrict the development and application of FEM. And the kernel of them is the dividing of regions analyzed, e.g. the process of dividing regions is the process of generating meshes, so the generation of fit meshes in the analyzed regions is the first step of FEM. The quality of the meshes directly influences the precision of the numerical analysis, so we can say, it is the key problem in FEA (Finite Element Analysis) that the realization of automatic mesh generation through a fit mesh generation algorithms. Presently, many algorithms of mesh generation (especially for the two-dimension region) have been completely developed and are being widely applied to the practical engineering.This paper discusses in detail the FEA specific application in engineering electromagnetic fields after introducing the fundamentals of FEM. According to the viewpoint of creating FEA system structure, we analyze the theoretical and practical sense of FEM automatic mesh generation system as the pre-processor module of FEA.Constructing geometric model of analyzed object is the first step of mesh generation, in this research subject, we mainly analyze the medical encephalon CT picture ,so we select digital instrument to extract border characteristic points from encephalon CT picture and create the analyzed object geometric model. After describing the fundamentals of serial communication, we discuss in detail how to realize the serial communication between the digital instrument and the computer, finally we realize the function of geometric model building.In this paper we mainly discuss the triangle mesh generation algorithm .By analyzing and researching Delaunay triangulation algorithm and Advancing front algorithm, we design a new algorithm combining the advantages of both methods .At the same time, we improve the weighted method which is used to set internal nodes in analyzed region and take optimum measures to optimize generated mesh by triangle factor of merit method and fourfold mesh encrypt method.At last ,a FEM meshautomatic generation system based on the Visual C++6.0 platform is developed by virtue of Object-Oriented programming idea and C++ Language, meanwhile, correspondingly, combining specific example ,this algorithm is proved to be effective, commonly, reliable, automatic.Lastly, we discuss the implication of scientific visualization and its important significance for practical engineering application. Then we design a interactive GUI to help user to operate this system conveniently. According to the standard of OpenGL, user can executive all kinds of operation of graphic transform and realize the function of visualization processing.更多还原