Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis

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Abstract

This paper describes a new computational method for fully automated triangulation of the trimmed parametric surfaces used in finite element analysis. The method takes as input the domain geometry and a node-spacing function, and then generates a mesh, or a set of connected triangles, that satisfies basic requirements such as (1) precise control over node spacing or triangle size, (2) node placement that is compatible with domain boundaries, (3) generation of well-shaped triangles, and (4) continuous remeshing and local remeshing capabilities. The approach consists of two stages: placing initial nodes using recursive spatial subdivision, and relaxing the mesh by assuming the presence of proximity-based, repulsive/attractive internode forces and then performing dynamic simulation for a force-balancing configuration of nodes. In both stages, algorithms are developed in accordance with the observation that a pattern of tightly packed spheres mimics Voronoi polygons, from which well-shaped Delaunay triangles can be created by connecting the centers of the spheres.

References (34)

  • W.H Frey et al.

    Mesh relaxation: a new technique for improving triangulations

    International Journal for Numerical Methods in Engineering

    (1991)
  • H.N Gursoy

    Shape interrogation by medial axis transform for automated analysis

  • E.A Heighway

    A mesh generator for automatically subdividing irregular polygons into quadrilaterals

    IEEE Trans. Magn.

    (1983)
  • B.P Johnston et al.

    Automatic conversion of triangular finite element meshes to quadrilateral elements

    International Journal for Numerical Methods in Engineering

    (1991)
  • N.S Lee

    Adaptive procedures for nonlinear elastic and elasto-plastic finite element analysis

  • R Lohner et al.

    Generation of three-dimensional unstructured grids by the advancing-front method

  • S Meshkat et al.

    Three-dimensional automatic unstructured grid generation based on Delaunay tetrahedrization

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    This work was partly supported by IBM Japan, Ltd. and Ford Motor Co.

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