Study of 3D finite element tetrahedral mesh automatic generation for complex regions

Based on the classical 3D Delaunay tetrahedral mesh generation method, a 3D constrained Delaunay triangulation algorithm is presented. By restoring the constrained boundary and removing the local degeneracies, the consistency of the solid boundary and the uniqueness of the mesh could be guaranteed. In this way, the constrained Delaunay triangulation method could be applied effectively to generate tetrahedral mesh for any complex 3D solids with the constraints. By controlling the ratio value of the circumradius of the tetrahedron to its shortest edge length (denoted as a), and the ratio of the volume of the tetrahedron to the volume of its circumscribing sphere (denoted as n), the low-quality elements are avoided; and also a method to calculate the a and n which simplifying the calculation process is proposed. For the entity with complicated geometry, especially the entity containing the thin layers, adding constraints could improve the mesh quality and shorten the calculation time. So, by using the method, the 3D finite element mesh for complex region under different geological conditions could be automatically generated in the civil engineering; and the high quality of the mesh which could be guaranteed provides sufficient condition for the high-precision finite element calculation. The verified examples show that the high-quality constrained tetrahedral mesh for any complex 3D solids could be generated by the constrained Delaunay triangulation method; and it could be applied effectively to the finite element mesh generation in engineering.