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Research Papers

A Three-Dimensional Adaptive Mesh Generation Approach Using Geometric Modeling With Multi-Regions and Parametric Surfaces

[+] Author and Article Information
Antonio C. O. Miranda

Professor
Department of Civil Engineering,
University of Brasília,
Brasília, 70910-900, Brazil
e-mail: acmiranda@unb.br

William W. M. Lira

Professor
LCCV—Laboratory of Scientific Computing and Visualization,
Technology Center,
Federal University of Alagoas,
Maceió, 57072-970, Brazil
e-mail: william@lccv.ufal.br

Joaquim B. Cavalcante-Neto

Professor
Department of Computing,
Federal University of Ceará,
Fortaleza, 60020-181, Brazil
e-mail: joaquim@lia.ufc.br

Rafael A. Sousa

Department of Civil Engineering,
Pontifical Catholic University of Rio de Janeiro,
Rio de Janeiro, 22451-900, Brazil
e-mail: rfldesousa@hotmail.com

Luiz F. Martha

Professor
Tecgraf—Computer Graphics Technology Group,
Department of Civil Engineering,
Pontifical Catholic University of Rio de Janeiro,
Rio de Janeiro, 22451-900, Brazil,
e-mail: lfm@tecgraf.puc-rio.br

1Present address: Campus A. C. Simoes, Av. Lourival Melo Mota, Cidade Universitária, Maceió, AL, Brazil. CEP: 57072-900.

Contributed by the Computers and Information Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received March 9, 2012,; final manuscript received March 14, 2013; published online April 22, 2013. Assoc. Editor: Xiaoping Qian.

J. Comput. Inf. Sci. Eng 13(2), 021002 (Apr 22, 2013) (13 pages) Paper No: JCISE-12-1042; doi: 10.1115/1.4024106 History: Received March 09, 2012; Revised March 14, 2013

This work presents a methodology for adaptive generation of 3D finite element meshes using geometric modeling with multiregions and parametric surfaces, considering a geometric model described by curves, surfaces, and volumes. This methodology is applied in the simulation of stress analysis of solid structures using a displacement-based finite element method and may be extended to other types of 3D finite element simulation. The adaptive strategy is based on an independent and hierarchical refinement of curves, surfaces, and volumes. From an initial model, new sizes of elements obtained from a discretization error analysis and from geometric restrictions are stored in a global background structure, a recursive spatial composition represented by an octree. Based on this background structure, the model's curves are initially refined using a binary partition algorithm. Curve discretization is then used as input for the refinement of adjacent surfaces. Surface discretization also employs the background octree-based refinement, which is coupled to an advancing front technique in the surface's parametric space to generate an unstructured triangulated mesh. Surface meshes are finally used as input for the refinement of adjacent volumetric domains, which also uses an advancing front technique but in 3D space. In all stages of the adaptive strategy, the refinement of curves, surface meshes, and solid meshes is based on estimated discretization errors associated with the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes curvature information into account. Numerical examples of simulation of engineering problems are presented in order to validate the methodology proposed in this work.

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Figures

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Fig. 1

The proposed adaptive refinement process

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Fig. 2

Curve refinement based on curve curvature

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Fig. 3

Approximating the curvature by circular arcs

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Fig. 4

A hypothetical model under applied σ tension to explain the steps of octree construction

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Fig. 5

External appearance of background octree based on discretization error analysis

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Fig. 6

Refinement after considering curve curvatures

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Fig. 7

Refinement after considering surface curvatures

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Fig. 8

Refinement after considering maximum cell size at boundary cells and maximum difference of one level between adjacent cells

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Fig. 9

Curve refinement and its corresponding binary tree

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Fig. 10

Measurements in parametric space

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Fig. 11

Example 1: Short cantilever under end shear

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Fig. 12

Example 2: L-shaped domain under horizontal uniform force (face y = 0)

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Fig. 13

Example 3: Biaxial bending of a column footing

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Fig. 14

Example 4: 3D Frame

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Fig. 15

Example 5: Bike suspension rocker

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Fig. 16

Adaptive refinement meshes for example 1

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Fig. 17

Adaptive refinement meshes for example 2

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Fig. 18

Adaptive refinement meshes for example 3

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Fig. 19

Adaptive refinement meshes for example 4

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Fig. 20

Adaptive refinement meshes for example 5

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Fig. 21

Detail of mesh refinement for example 5

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Fig. 22

Comparison of convergence rate

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Fig. 23

Time performance of 3D mesh generator

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