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.

[1]  Chul-Hyun Park,et al.  Adaptive refinement of all-hexahedral elements for three-dimensional metal forming analysis , 2006 .

[2]  François Guibault,et al.  Constructing Anisotropic Geometric Metrics using Octrees and Skeletons , 2003, IMR.

[3]  Guoqun Zhao.  AUTOMATIC GENERATION AND REGENERATION ALGORITHM OF HEXAHEDRAL MESH , 2006 .

[4]  Yoshitaka Wada,et al.  Effective adaptation technique for hexahedral mesh , 2002, Concurr. Comput. Pract. Exp..

[5]  Steven J. Owen,et al.  A Survey of Unstructured Mesh Generation Technology , 1998, IMR.

[6]  S. Owen,et al.  H-Morph: an indirect approach to advancing front hex meshing , 1999 .

[7]  Adam C. Woodbury,et al.  Adaptive mesh coarsening for quadrilateral and hexahedral meshes , 2010 .

[8]  Scott A. Mitchell,et al.  Whisker weaving: Invalid connectivity resolution and primal construction algorithm , 1995 .

[9]  Steven E. Benzley,et al.  A Comparison of All Hexagonal and All Tetrahedral Finite Element Meshes for Elastic and Elasto-plastic Analysis , 2011 .

[10]  Steven E. Benzley,et al.  Conformal Refinement of All-Hexahedral Element Meshes Based on Multiple Twist Plane Insertion , 2004, IMR.

[11]  Patrick M. Knupp.  A method for hexahedral mesh shape optimization , 2003 .

[12]  Guoqun Zhao,et al.  Adaptive hexahedral mesh generation based on local domain curvature and thickness using a modified grid-based method , 2007 .

[13]  A. Kumar,et al.  Automatic hexahedral mesh generation using a new grid-based method with geometry and mesh transformation , 2005 .

[14]  Ted D. Blacker,et al.  Automated Conformal Hexahedral Meshing Constraints, Challenges and Opportunities , 2001, Engineering with Computers.

[15]  Ted D. Blacker,et al.  Plastering: A new approach to automated, 3D hexahedral mesh generation. Progress report 1 , 1992 .

[16]  Robert Schneiders,et al.  Octree-Based Hexahedral Mesh Generation , 2000, Int. J. Comput. Geom. Appl..

[17]  Guoqun Zhao,et al.  Adaptive generation of hexahedral element mesh using an improved grid-based method , 2007, Comput. Aided Des..

[18]  Jin Zhu,et al.  Background Overlay Grid Size Functions , 2002, IMR.

[19]  M. Sabin,et al.  Hexahedral mesh generation by medial surface subdivision: Part I. Solids with convex edges , 1995 .

[20]  Yong-Taek Im,et al.  Hexahedral mesh generation for remeshing in three-dimensional metal forming analyses , 2003 .

[21]  Matthew L. Staten,et al.  BMSweep: Locating Interior Nodes During Sweeping , 1999, Engineering with Computers.

[22]  Yongjie Zhang,et al.  Adaptive and Quality Quadrilateral/Hexahedral Meshing from Volumetric Data. , 2006, Computer methods in applied mechanics and engineering.

[23]  P. Knupp.  Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part II—A framework for volume mesh optimization and the condition number of the Jacobian matrix , 2000 .

[24]  P. Knupp.  Algebraic mesh quality metrics for unstructured initial meshes , 2003 .

[25]  Boris N. Azarenok,et al.  A method of constructing adaptive hexahedral moving grids , 2007, J. Comput. Phys..

[26]  Kenji Shimada,et al.  Skeleton-based computational method for the generation of a 3D finite element mesh sizing function , 2004, Engineering with Computers.

[27]  R. Schneiders,et al.  A grid-based algorithm for the generation of hexahedral element meshes , 1996, Engineering with Computers.

[28]  T. Blacker,et al.  Seams and wedges in plastering: A 3-D hexahedral mesh generation algorithm , 1993, Engineering with Computers.

[29]  Yi Su,et al.  Automatic hexahedral mesh generation for multi-domain composite models using a hybrid projective grid-based method , 2004, Comput. Aided Des..

[30]  T. Tam,et al.  2D finite element mesh generation by medial axis subdivision , 1991 .

[31]  Steven E. Benzley,et al.  A Multiple Source and Target Sweeping Method for Generating All Hexahedral Finite Element Meshes , 2007 .

[32]  François Guibault,et al.  Three-dimensional anisotropic geometric metrics based on local domain curvature and thickness , 2005, Comput. Aided Des..

[33]  Yasushi Ito,et al.  Octree‐based reasonable‐quality hexahedral mesh generation using a new set of refinement templates , 2009 .

[34]  M. Price,et al.  Hexahedral Mesh Generation by Medial Surface Subdivision: Part II. Solids with Flat and Concave Edges , 1997 .

[35]  Cecil Armstrong,et al.  Hexahedral meshing using midpoint subdivision and integer programming. , 1995 .

[36]  Steven J. Owen,et al.  Hex-dominant mesh generation using 3D constrained triangulation , 2001, Comput. Aided Des..