Construction of polyhedral finite element meshes based upon marching cube algorithm

• Published in: Advances in engineering software (1992) Vol. 128; pp. 98 - 112
• Main Authors: Kim, Sangjun, Sohn, Dongwoo, Im, Seyoung
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2019
• Subjects: Geometric adaptability; Marching cube algorithm; Mesh generation; Polyhedral finite element; Smoothed finite element method; Smoothed finite element method; Marching cube algorithm; Polyhedral finite element; Geometric adaptability; Mesh generation
• ISSN: 0965-9978
• DOI: 10.1016/j.advengsoft.2018.11.014

•An automatic algorithm for generating polyhedral meshes was systematically developed.•Hexahedral elements near the given STL surface were categorized into polyhedral volume topologies based on the MC algorithm.•Topology ambiguities of the MC algorithm were effectively resolved to provide an appropriate mesh for complex geometry.•The effectiveness was demonstrated through numerical analysis using the smoothed finite element method. Hexahedral meshes that exhibit the superiority in terms of solution accuracy and convergence rate are preferred to other types of meshes in the finite element analysis. However, the construction of the hexahedral meshes for complex geometries is still considered troublesome due to their poor geometric adaptability. This paper presents an efficient grid-based scheme to automatically generate polyhedral meshes including the hexahedral elements, and thus to provide hexahedral-dominant meshes for three-dimensional geometry with complex shapes. On the basis of the marching cube algorithm with a background grid composed of a regular arrangement of cubes, surface topologies for the background cubes are defined to represent the three-dimensional boundaries of a given domain. Then, in order to generate a three-dimensional finite element mesh, the surface topologies of the marching cube algorithm are systematically expanded to polyhedral volume topologies. Meanwhile, a topology ambiguity problem inherent in the marching cube algorithm is effectively resolved to generate an appropriate polyhedral mesh even for an arbitrary complex geometry. Several examples including biostructure modeling demonstrate that the proposed mesh generation scheme can easily discretize complex three-dimensional domains with hexahedral-dominant meshes, which are composed of the polyhedral elements near the domain boundaries and the hexahedral elements that come from the background cubes inside the domains. Furthermore, to show the applicability and effectiveness of polyhedral meshes in the finite element analysis, some structural analyses are performed using the smoothed finite element method that can be straightforwardly adapted to polyhedral elements of arbitrary shape.