Study On The Algorithm Of Quadrilateral Finite Element Mesh Generation

Nowadays, the 21st century, no doubt has the automotive industry become one of pillar industries of China's national economy. However, on the road of localization, automobile enterprises have met so many difficulties.As far as auto body design is concerned, how to design an auto body in line with the market and meeting the publics'taste is so difficult. Auto body is made up of covering parts manufactured accordingly in need of some molds. But the capability of die design is always hampering the rate of automotive products of our country and handicapping the upgrading of auto's core quality. Lacking of the knowledge accumulation about this respect has become a choke point of auto's evolutionary cycle and the improving of auto's quality. At present, most auto enterprises use traditional methods when it refers to the designing and manufacturing of forming die of auto covering parts, in other words, process analysis and die design depend mainly on experience. The level of the alternant plotting and modeling in use of software technology is only more than entry-level. So rapid numerical simulation design of stamping die plays an incalculable role in auto body design and is very important for quickening the speed of die design, improving the quality of it and reducing the cost of die.CAD/CAE/CAM has made a great success with the development of computer technology in recent years, not only in the respect of theory but the application. FEM has become an indispensable numerical calculation tool to engineering and product structure analysis, such as in field of aviation, aerospace, machinery and civil engineering structures. It is also an important means to solve various problems of mechanical and irreplaceable tool to promote the engineering technology's developing. Finite element mesh is an important part of forming finite element model and a premise of finite element analysis. The form of mesh generation directly influences compute precision and compute scope. Generating the mesh is very complicated and easily comes into an abnormal situation. At the same time, both the reliability of finite element analysis result and the time that the analysis process consumes are directly affected by the quality of a mesh. As a result, researching how to generate high quality mesh rapidly is extremely valuable for finite element analysis. In practical application, the finite element method needs two processes: pro-process and post-process. In the pro-process the whole geometry must be curved into the defined and efficient finite element mesh. As automatic mesh generation has a potentially huge market of application and with the widely application of finite element methods recently years, mesh generation technology has been deeply researched and developed. And many mesh generation methods have come out. Because automatic method of the generation for all-quadrangle mesh is more difficult than that for triangle mesh, most of automatic generation methods describe how to generate triangle mesh. But, in respect to the accuracy and approximation to discrete domain, quadrilateral mesh is superior to the triangle one. Someone proposed the method of quadrilateral automatic mesh generation algorithm including automatic generation quad-tree method and interactive mapping method. There is still no perfect algorithm for quadrilateral meshes generation and never will be there an approach to mesh generation once and for all. In this paper, author will introduce a simple but efficiency quadrangle finite element mesh generation method.This thesis'main topics are shown as follows:This paper presents a similar approach to Advancing Front Method while this method use border as a processed object and generate grids selectively to meet the request, so the unit with a better quality will be generated firstly. About the judgment of nodes'intersection, proposed a new way of nodes managing which can avoid the time consumption of the judgment of mesh front's intersection with other border as the Paving Method and AFM to increase the speed of mesh generating. Proposed the adjustment after quadrilateral mesh generation, like smoothing, and explain how to deal with the non-standard grids in details and adjust the mesh to the optimal shape on the whole. When use this article's algorithm to generate quadrilateral mesh it will refresh the border after some meshes have been formed and look for the location in which the best grid will be generated, and then the whole area will be filled with meshes. Different with the Paving Method and AFM, this method is not generating mesh inward or outward blindly for there will be some bad units in the process of mesh generating, so to deal with this situation, the program need to search for the location where the normal units will be formed. Here we can divided the location associated with good grids into three categories:The first one is the position where the optimal unit will be formed, that is the two neighboring nodes'interior angles are suitable for quadrilateral mesh generation, in other words, the two angles are close to rectangular. So when the other two nodes are linked, there will be one almost perfect quadrilateral grid.The second is there is only one small node's interior angle in the border, we can use the rule in the Paving method to find out the forth node with counterparts. After adding two lines, there will come out one quadrilateral unit.The third situation about the border is there are no objects as above and the boundary line is a little straight. In this situation, we should look for the interior nodes adjacent to the ones in the border, and then add three lines to form a quadrilateral unit. When the three classes are all present in the same border, the grid which needs fewer lines will be generated first.In practical applications, we found that the second class girds accounting for the largest proportion, so I proposed an idea that subdividing the second class objects to generate. The node with the only small interior angle can form grid within a certain scope which will be subdivided into some more accurate range. There will generate some girds in the same small range at the same time but not only one when the meshes are being generated. As the above rule, the girds with a good quality are generated superior to the bad ones. In this way, the speed is improved in a large extent.It designed an algorithm of mesh optimization in respect of structure. Structural optimization by adjusting the mesh topology, optimize the mesh in the respect of quadrilateral diagonals, angle, deleting nodes and deleting elements to ensure the later meshes'shape and size.