【作者】 姜冬茹；

【导师】 骆少明；

【作者基本信息】 汕头大学 ， 机械电子工程， 2002， 硕士

【摘要】 对总体分析来说，著名的数学流形或许是现代数学的一个最重要的课题。以数学流形为基础，新发展的数值流形方法是一种有普遍意义的数值方法(简称流形方法)。这种方法是用以计算结构或材料的位移和变形的。 本文的主要工作是采用标准的三维六面体网格(长方体)和传统的有限单元网格来构成三维流形方法的覆盖系统，并将其应用于三维连续体的弹性静力学分析；同时用程序将其成功地实现。 文中首先选取标准的三维六面体网格作为流形方法的基本覆盖，研究了三维数值流形方法的有限覆盖系统、各阶覆盖位移函数、单元权函数的选取、三维数值流形方法中的各种单元矩阵、以及流形单元的数值积分方法(Hammer积分方法)。 针对提出的理论和方法，论文把面向对象的思想引入三维数值流形方法的程序设计中，使程序具有很好的继承型和可移植性。程序将三维数值流形方法的有限覆盖系统抽象为一些独立的数据类，给出了类的描述和它们的实现方法，并用树状结构对这些数据类进行管理。对任意形状的复杂结构体，用流形方法的数据类实现了流形单元有限覆盖系统的全自动生成及网格自动划分。 程序同时完成了两个凸多面体布尔求交的算法问题并用程序精确的将其实现，具有普遍的实际意义；程序处理了边界条件、载荷，成功地解决了三维连续体的弹性静力学分析问题的求解。程序开发的界面友好，操作简便。 用Borland C++ Builder编程，得出正确的结果，很好的验证了网格自动划分和数值计算的正确性。更多还原

【Abstract】 The famous Mathematical Manifold is perhaps one of the most important scientific research tasks in modern mathematics as a whole. The Numerical Manifold Method (NMM) is a newly developed general numerical method based on Mathematical Manifold. The method is used for computing the displacement and distortion of structures and engineering materials.The main works of this dissertation are to adopt the standard 3-dimensional hexahedral meshes and the traditional finite elements to construct the cover system in Manifold Method (MM), and apply MM to the linear statics analysis of three-dimensional continuous object. The analysis processes developed are programmed.First of all, the hexahedral meshes are chosen as the cover system of NMM. The cover system of three-dimensional NMM, displacement functions in the all cover systems, the selection of weight functions, diversified unit matrix and numerical integral method of manifold element (Hammer integral method) are discussed in detail.For the proposed theory and method, the software is designed with Object Oriented Programming (OOP), which can be maintained and extended conveniently. The program abstract the finite cover system of 3D NMM as independent data classes, and give the definition and implement of the classes, and manage these data classes by techniques of tree structure. For complicated object with arbitrary shape, the finite cover system of 3D NMM and mesh can be automatically generated by program through using these classes and trees.The paper also provides algorithmes about Boolean intersection calculation of two protruding polyhedron and the computer programmes for the algorithm. The programmes are of general meanings. Boundary conditions and diversified load conditions are dealt with by program. The User Interface (UI) has favorable maneuverability.The programmes are realized with Borland C++ Builder. The computational solution shows that the automatic mesh system and the programmer developed are correct.更多还原