AFT Algorithm For Unstructured Adaptive Finite Element Mesh Generation

The Finite Element Method (FEM) is an effective numerical analysis method. It becomes an important part of the technology of Computer Aided Engineering (CAE) combining with the Computer Aided Design (CAD). As the complexity of engineering analysis problems increases, the Adaptive Finite Element Analysis (AFEA) that integrates FEM and error estimation method is applied widely. So how to generate adaptive finite element mesh that can reflect physical and geometric characteristics of the structure is a necessary step to apply AFEA.Unstructured adaptive finite element mesh generation method based on Advancing Front Technique (AFT) is studied in this thesis.Firstly, the advancing-by-layer method and the backward principle are presented to improve and control the mesh generation process of AFT. The fronts are divided into two categories by introducing active fronts and inactive fronts, so fronts can march from boundary of the region, which means advancing by layer. This method improves the element quality near the boundary. The local valid fronts and invalid fronts can be recognized and filtered respectively by introducing the backward principle. This way, the mesh generation process of AFT can be controlled and can be applied to mesh generation for structures with internal features.Secondly, four key issues dominating the effectiveness and efficiency of AFT are addressed. They are node spacing function definition, element validity check, front management and kernel polyhedron triangulation. Local autonomy element size computation method based on local front searching is proposed to address the definition problem of the node spacing function; a new data structure integrating the vector, map, multimap and KDTree is proposed to manage the fronts and speed up processing noticeably; a linear programming model and a nonlinear optimization model are proposed to triangulate the kernel polyhedron.At the end, an adaptive mesh generation scheme is proposed by combining AFT and Background method. Improved background method in which elements and nodes in background mesh are managed by structured grid is proposed to solve the node location and size computation problem and thus increase the element size computation speed in background method.Concretely, the contents of the thesis are arranged as follows:In chapter1, the background and framework of the thesis are introduced.In chapter2, the finite element mesh generation methods are briefly reviewed. They are classified into five categories, which are general structured mesh generation methods, general unstructured mesh generation methods, surface mesh generation methods, hexahedral meshgeneration methods and adaptive mesh generation methods.In chapter3, the advancing-by-layer method and the backward principle are proposed to improve and control AFT. By introducing active front and inactive front concept, AFT can generate mesh with high quality around boundary of the region. By introducing the backward principle, AFT can generate mesh for structures containing internal features, such as cracks.In chapter4, element check methods and element size computation methods are studied. Element check is a key part in the implementation of AFT. It includes element validity check, element quality check and element size check. Element size computation method according to the size of local adjacent fronts is proposed. It can provide desired element size without knowing control sources and node spacing function.In chapter5, the data structure for front management is studied. An effective data structure for 3D AFT is proposed. It integrates vector, map, multimap and KDTree, so the fronts can be managed effectively and can be retrieved efficiently through this data structure.In chapter6, kernel polyhedron triangulation is studied. A linear programming and a nonlinear optimization model are proposed to triangulate Schoenhardt polyhedron and its variants. These two models can guarantee the convergence of Schoenhardt polyhedron triangulation.In chapter7, the adaptive mesh refinement method is studied. The m...