Mesh generation and adaptive refinement of all-hexahedral elements for three-dimensional finite element analysis

Abstract

Adaptive mesh generation is a necessary and sufficient condition for accurate and effective computation of the finite element analysis. Adaptive mesh generation for tetrahedral element mesh has received extensive attention over the years. For hexahedral element mesh, however, adaptive mesh generation is usually limited due to the complexity of maintaining conformal connectivity of elements. In many three-dimensional forging simulations, the master-grid method is adopted as the hexahedral mesh generation method, because the method is robust and reliable to construct the intermediate mesh during forging simulation. However, almost equal-sized element mesh is employed regardless of the local characteristics of the deforming region In order to overcome this drawback, a new refinement technique for hexahedral element mesh is proposed by selecting the element regions to be refined and iteratively inserting the zero-thickness element layers (ZTLs) along the necessary interfaces of elements. First, the proposed refinement technique is applied to two-dimensional quadrilateral element mesh. With quadrilateral element meshes, the applicability of mesh density control by inserting ZTLs is verified and the parameters that mainly affect the mesh density distribution are considered. One of the two main parameters is the number of ZTLs and the other is the number of the element regions to be refined. Instead of adjusting two parameters simultaneously, the number of ZTLs is fixed and then ZTLs are inserted around the refinement region, which is iteratively selected with respect to the criterion of selecting refinement region. Numerical examples show that the proposed refinement algorithm refines the quadrilateral element mesh with a good agreement with the predefined desired mesh density. The algorithm is expanded to three-dimensional hexahedral element mesh. To generate the mesh refined adaptive to the gradient of physical property, the desired mesh density is obtained from Z-...