Adaptive generation and local refinement methods of three-dimensional hexahedral element mesh

The mesh density has an important affect on finite element analysis of engineering problems. This paper studies the adaptive and local refinement techniques of hexahedral element meshes. A set of refinement templates and its converting rules of refinement fields are established. The refinement field propagation problem is solved using two corner templates and an isolated node template. A relative curvature criterion for constructing refinement source point fields is proposed by introducing the relative area of STL (stereo lithography) facets into the curvature criterion. The adaptive refinement of meshes can be easily realized using the constructed refinement source point fields. Examples show that the relative curvature criterion can more accurately capture the curvature features of solid models than the conventional curvature refinement criterion. To facilitate users and obtain the effective local refinement, this paper proposes a local refinement technique. The levels of local refinement can be self-controlled by users. The geometric features can be easily identified before each level of refinement. The effective refinement of nodes, elements, element-edges, element-surfaces, mesh-boundaries, mesh-faces and local regions can be realized. The accuracy and robustness of the adaptive and local refinement algorithms presented in this paper are demonstrated using several examples. The mesh refinement quality and flexibility are improved significantly.