Research On The Algorithm Of Finite Element Riangle Mesh Generation In Planar Area

With the rapid development of the computer technologies, the finite mesh method has achieved great success both in theory and in application. It has been becoming an important tool in industry engineering design and analysis. More and more voluminous and complicated engineering designs are simulated by it. The basic thought of this method is disparting and combining. Disparting means to dissect the whole into meshes, each of which will be analyzed; while combining means to combine all the meshes together, making a comprehensive analysis to the whole structure. That is to say, the real structure is replaced by dispersing model in the thought.The contents of this thesis belong to the field of finite mesh modeling or pre-processing. It is one of the most important parts of effectively using of pre-processing of the finite mesh analysis in the engineering practice. And it is one of the offsets of CAD/CAE technology. In the software of previous and post processing the engineering analysis, it is the most effective way to use triangle meshes to gain upon the boundary of geography shape with arbitrary complicated sides (a plane or a board, shell structure in the space) to keep the shape's original structured mechanics property. Using finite element triangle mesh generation to gain upon perfectly the boundary of an arbitrary planar plane area is widely adapted by structured engineering finite element, computer graphics, visualization of science computing and other fields. Thus it has great academic and time significance to develop and study effective, reliable algorithms of triangle mesh generation. As a special part of curved surface trianglization, triangle mesh generation technology in planar area also has its actual applying background. Studies on planar triangle generation are being mature no matter in theory or in algorithm. But the current algorithms, relatively, need to be improved in the aspects of adaptability and executing efficiency, which is what the thesis concerns.At the beginning, this thesis gives a brief introduction about the definition of planar finite element triangle mesh generation, its basic process, optimizing principles, its measuring standard, its classification and several common non-structured mesh generating methods. Then the focus is put on the research of the definition and algorithmic implement of AFT method (Advancing Front Technique) in planar finite triangle mesh generation, and the nodes, vector segments, the position relationship between triangle meshes and polygon meshes during the process of the generation. The difficulties of AFT method are also analyzed, and three improved algorithms are put forward. Based on the principle of minimum power together with Fermat point's properties, an improved refined algorithm about based on geometrical multi-grid is put forward. At last, several problems needed to be solved in the mesh generation algorithm are simply prospected.Several difficulties during the implement of AFT algorithm are studies in this thesis. And three improved algorithms are put forward based on these studies.1. Improved algorithm of the right helix AFT in given areaAiming at how to judge the current front point, the thesis puts forward a specific right helix AFT method in given area, which main ideas manifest that firstly boundary sides should be dispersed according to the principle of average division to generate the original active point and front side, and then counter-clockwise, namely, the right helix direction, the active front sides are selected, new nodes and meshes being generated based on the principle of equilateral triangle to increase the efficiency and quality of generating triangle mesh. Equally, the inside sides of the area can be dealt with clockwise, namely, the left helix AFT method.2. Improved Grid-based algorithm in given areaCombining grid methods and AFT method, this thesis puts forward a new triangle mesh generating method. The common grid method is to use generated rectangle grid to cover the area which is going to be dissected, and then to delete those grids outside the area and those that intersect with the boundary of the area. Only those grids covered by the rectangle will be preserved. On the boundary, the grid will be clipped in order to guarantee the integrity of the area boundary. The grid method usually results in inner meshes with regular shape, but the shape along the boundary is usually not good; while the AFT method can generate boundary meshes with good shape, thus the disadvantage is made up. In addition, this method uses three parallel equidistant scanning beams which intersect into a triangle with 60 degree with each other to generate grids, as a result, inside the area; better equilateral triangle grid will be generated.3. Improved algorithm of AFT based on the two neighboring front sides After analyzing the disadvantages of two-point advancing front technique, three-point advancing front technique and two-point combined with three-point advancing front technique, this thesis gives an improved algorithm based on the two neighboring front sides, main thought of which is that the distance and its included angle of vectoring segments of the two neighboring waves decide the generating way of grid unit and nodes, and this method is specially suitable to those whose included angles are less than 30 degree or more than 180 degree. So this method solves the problem that only single connected area can be dissected, and that when the included angle is too small or too large the area cannot be dealt with. As a result, the effect of triangle mesh is intended to perfect.In addition, a triangle mesh refined algorithm is discussed based on geometrical multi-grid method. This thesis points out that as to irregular triangle several times of iterative is needed, the efficiency of which is low because the increase of the amount of the refined girds duplicates each time. Aiming at the two disadvantages mentioned above, a new improved refined algorithm based on the principle of minimum weight in the triangle mesh generation, and it is proved that this improved algorithm actually increase the efficiency of refined generation of triangle mesh, the quantity and quality of the dissected grids.