中文摘要：

基于经典三维Delaunay四面体网格的生成算法,介绍了一种三维约束Delaunay三角化网格划分算法,通过对约束的恢复和局部退化的消除,保证了边界的一致性和网格的惟一性,实现了三维约束区域的四面体网格自动生成;通过对四面体的外接球半径与其最短边长度的比值（记为a）和四面体体积与其外接球体积的比值（记为n）的控制,避免质量不佳的单元,使生成的网格达到预期的质量要求,并提出了一种a和n的计算方法,简化了质量参数的计算过程;对几何形状复杂,特别是含有薄层的实体,可通过在实体上增加约束来提高网格的质量和缩短计算时间,使该方法能够实现岩土工程中不同地质条件下的复杂区域的三维有限元网格自动生成,并且能够保证生成的网格质量较好,为高精度的有限元计算提供了充分条件。计算实例表明,该算法能够将复杂三维实体剖分成质量较好的Delaunay四面体网格,可有效地应用于工程中有限元网格的生成。

英文摘要：

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.