Reseatch On A 2D Quadrilateral Mesh Generation Method

Triangular mesh and quadrilateral mesh are the most widely used mesh in two-dimensional mesh generations. The technique for the generation of triangular mesh has been mature, but the technique for the generation of quadrilateral mesh in arbitrary geometries is still rough. In the finite element analysis of plastic deformation, because of the large deformation of metal and in order to improve the precision of finite element analysis, quadrilateral mesh is needed. Therefore most researches focus on the automatic generation of quadrilateral element mesh in arbitrary geometries. An indirect arithmetic of the quadrilateral mesh generation for two-dimensional problem is presented in this paper. The background triangular mesh is generated firstly,then the background triangular mesh is merged to quadrilateral mesh.The background triangular mesh is generated by combining the Delaunay and advancing front methods together. The internal nodes are generated by advancing front method, the equilateral or similar equilateral triangular elements are generated by Delaunay method. This method ensures the convergence of advancing front method.In order to keep the quality of quadrilateral element,the order of merging is controlled by the quality factor calculated in the process of background triangular elements merging to quadrilateral elements. The complete quadrilateral elements are obtained by eliminating the remnant triangular elements and concave quadrilateral elements. Several applications in different geometries are given to show the versatility and applicability of the presented arithmetic.After quadrilateral mesh is generated, the size difference of neighboring elements is reduced and the quality of mesh is improved by using Laplacian smoothing method. The optimization of node numbers is used to shorten the bandwidth of stiffness matrix and improve calculation speed.The criterion for remeshing is given. According to this criterion, the method of remeshing is realized. The field variable transformation between the old mesh and the new mesh is also realized. Numerical simulation examples show that the presented mesh generator can be applied in initial mesh generation and remeshing for the rigid-plastic FEM.