3-Dimensional Numerical Manifold Method And Its Object-Oriented Programming(3D NMM And OOP)

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.