Skip to main content
SpringerLink
Log in

Automatic two- and three-dimensional mesh generation based on fuzzy knowledge processing

  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

This paper describes the development of a novel automatic FEM mesh generation algorithm based on the fuzzy knowledge processing technique.

A number of local nodal patterns are stored in a nodal pattern database of the mesh generation system. These nodal patterns are determined a priori based on certain theories or past experience of experts of FEM analyses. For example, such human experts can determine certain nodal patterns suitable for stress concentration analyses of cracks, corners, holes and so on. Each nodal pattern possesses a membership function and a procedure of node placement according to this function. In the cases of the nodal patterns for stress concentration regions, the membership function which is utilized in the fuzzy knowledge processing has two meanings, i.e. the “closeness” of nodal location to each stress concentration field as well as “nodal density”. This is attributed to the fact that a denser nodal pattern is required near a stress concentration field. What a user has to do in a practical mesh generation process are to choose several local nodal patterns properly and to designate the maximum nodal density of each pattern. After those simple operations by the user, the system places the chosen nodal patterns automatically in an analysis domain and on its boundary, and connects them smoothly by the fuzzy knowledge processing technique. Then triangular or tetrahedral elements are generated by means of the advancing front method. The key issue of the present algorithm is an easy control of complex two- or three-dimensional nodal density distribution by means of the fuzzy knowledge processing technique.

To demonstrate fundamental performances of the present algorithm, a prototype system was constructed with one of object-oriented languages, Smalltalk-80 on a 32-bit microcomputer, Macintosh II. The mesh generation of several two- and three-dimensional domains with cracks, holes and junctions was presented as examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Asano, T. (1985): Practical use of bucketing techniques in computational geometry. In: Toussaint, G. T. (ed.) Computational Geometry, pp. 153–195. North-Holland

  • BabuskaI.; RheinboldW. C. (1979): Adaptive approaches and reliability estimation in finite element analysis. Comput. Methods Appl. Mech. Eng. 17/18, 519–540

    Google Scholar 

  • BaehmannP. L.; ShephardM. S.; AshleyR. A.; JayA. (1988): Automated metal forming modeling utilizing adaptive remeshing and evolving geometry. Comput. Struct. 30, 319–325

    Google Scholar 

  • BowyerA. (1981): Computing Dirichlet tessellations. Comput. J. 24, 162–166

    Google Scholar 

  • BuratynskiE. K. (1990): A fully automatic three-dimensional mesh generator for complex geometries. Int. J. Numer. Methods Eng. 30, 931–952

    Google Scholar 

  • CareyG. F.; SharmaM.; WangK. C.; PardhananiA. (1988): Some aspects of adaptive grid computations. Comput. Struct. 30, 297–302

    Google Scholar 

  • CavendishJ. C. (1974): Automatic triangulation of arbitrary planar domains for the finite element method. Int. J. Numer. Methods Eng. 8, 679–696

    Google Scholar 

  • ChengJ.-H. (1988): Automatic adaptive remeshing for finite element simulation of forming process. Int. J. Numer. Methods Eng. 26, 1–18

    Google Scholar 

  • FreyW. H. (1987): Selective refinement: A new strategy for automatic node placement in graded triangular meshes. Int. J. Numer. Methods Eng. 24, 2183–2200

    Google Scholar 

  • Goldberg, A.; Robson, D. (1987): Smalltalk-80: The language and its implementation. Addison-Wesley

  • HaberR.; ShephardM. S.; AbelF.; GallagherR. H.; GreenbergD. P. (1981): A general two-dimensional, graphical finite element preprocessor utilizing discrete transfinite mappings. Int. J. Numer. Methods Eng. 17, 1015–1044

    Google Scholar 

  • ImafukuI.; KoderaY.; SayawakiM. (1980): A generalized automatic mesh generation scheme for finite element method. Int. J. Numer. Methods Eng. 15, 713–731

    Google Scholar 

  • JohnstonB. P.; SullivanJ. M.Jr.; KwasnikA. (1991) Automatic conversion of triangular finite element meshes to quadrilateral elements. Int. J. Number. Methods Eng. 31, 67–84

    Google Scholar 

  • Kikuchi, N. (1985): Adaptive grid design methods for finite element analysis. In Proc. 2nd joint ASCE/ASME mechanics conference, pp. 23–26. Albuquerque

  • LoS. H. (1985): A new mesh generation scheme for arbitrary planar domains. Int. J. Numer. Methods Eng. 21, 1403–1426

    Google Scholar 

  • LoS. H. (1991): Automatic mesh generation and adaptation by using contours. Int. J. Numer. Methods Eng. 31, 689–707

    Google Scholar 

  • LudwigR. A.; FlahertyJ. E.; GuerinoniF.; BaehmannP. L.; ShephardM. S. (1988): Adaptive solutions of the Euler equations using finite quadtree and octree grids. Comput. Struct. 30, 327–336

    Google Scholar 

  • Mullineux, G. (1986): CAD: Computational concepts and methods. Kogan Page

  • OhtsuboH.; KitamuraM. (1990): Element by element a posteriori error estimation and improvement of stress solution for two-dimensional elastic problems. Int. J. Numer. Methods Eng. 29, 223–244

    Google Scholar 

  • SchroederW. J.; ShephardM. S. (1988): Geometry-based fully automatic mesh generation and the Delaunay triangulation. Int. J. Numer. Methods Eng. 26, 2503–2525

    Google Scholar 

  • SchroederW. J.; ShephardM. S. (1990): A combined octree/Delaunay method for fully automatic 3-D mesh generation. Int. J. Numer. Methods Eng. 29, 37–55

    Google Scholar 

  • ShephardM. S.; YerryM. A.; BaehmannL. (1986): Automatic mesh generation allowing for efficient a priori and a posteriori mesh refinement. Comput. Methods Appl. Mech. Eng. 55, 161–180

    Google Scholar 

  • SibsonR. (1978): Locally equiangular triangulations. Comput. J. 21, 243–245

    Google Scholar 

  • Stephenson, M. B.; Blacker, T. D. (1989): Using conjoint meshing primitives to generate quadrilateral and hexahedral elements in irregular regions. In Proc. 1989 ASME computer in engineering conference, pp 163–172, Anaheim

  • Szabo, B. A. (1986): Estimation and control of error based on p convergence. In: Babuska, I. et al. (eds.) Accuracy estimates and adaptive refinement in finite element computations, pp. 61–78

  • TsamasphyrosG.; GiannakopoulosA. E. (1986): Automatic optimum mesh around singularities using conformal mapping. Eng. Fract. Mech. 23, 507–520

    Google Scholar 

  • WatsonD. F. (1981): Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. Comput. J. 24, 167–172

    Google Scholar 

  • WooT. C.; ThomasmaT. (1984): An algorithm for generating solids elements in objects with holes. Comput. Struct. 18, 332–342

    Google Scholar 

  • YagawaG.; UedaH. (1989): Behavior of surface crack in plates subjected to tensile loads: Analysis based on fully plastic solutions. Nucl. Eng. Des. 111, 189–196

    Google Scholar 

  • YagawaG.; YoshiokaA.; YoshimuraS.; SonedaN. (1991): A large scale parallel finite element method using supercomputer network. In: AtluriS. N.; BeskosD. E.; JonesR.; YagawaG. (eds.) Proc. Int. Conf. Comput. Eng. Sci. (ICES'91), pp. 1189–1194. Melbourne: ICES Publications

    Google Scholar 

  • YerryM. A.; ShephardM. S. (1984): Automatic three-dimensional mesh generation by the modified-octree technique. Int. J. Numer. Methods Eng. 20, 1965–1990

    Google Scholar 

  • YoshimuraS.; YagawaG.; NakaoK. (1991): AI-based FEM mesh generation. In: AtluriS.N.; BeskosD. E.; JonesR.; YagawaG. (eds.) Proc. Int. Conf. Comput. Eng. Sci. (ICES'91), pp. 1237–1240. Melbourne: ICES Publications

    Google Scholar 

  • YuenM. M. F.; TanS. T.; HungK. Y. (1991). A hierarchical approach to automatic finite element mesh generation. Int. J. Numer. Methods Eng. 32, 501–525

    Google Scholar 

  • ZadehL. A. (1968): Fuzzy algorithms. Inf. Control 12, 94–102

    Google Scholar 

  • ZadehL. A. (1973): Outline of a new approach to the analysis of complex systems and decision process. IEEE Trans. Syst. Man Cybern. SMC-3, 28–44

    Google Scholar 

  • ZienkiewiczO. C.; PhillipsD. V. (1971): An automatic mesh generation scheme for plane and curved surfaces by isoparametric co-ordinates. Int. J. Numer. Methods Eng. 3, 519–528

    Google Scholar 

  • ZienkiewiczO. C.; ZhuJ. Z. (1987): A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Methods Eng. 24, 337–357

    Google Scholar 

  • ZienkiewiczO. C.; LiuY. C.; HuangG. C. (1988): Error estimation and adaptivity in flow formulation for forming problems. Int. J. Numer. Methods Eng. 25, 23–42

    Google Scholar 

  • ZienkiewiczO. C.; ZhuJ. Z.; GongN. G. (1989): Effective and practical h-p-version adaptive analysis procedures for the finite element method. Int. J. Numer. Methods Eng. 28, 879–891

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Nuclear Engineering, University of Tokyo, 7-3-1 Hongo, 113, Bunkyo-ku, Tokyo, Japan

    G. Yagawa, S. Yoshimura & K. Nakao

  2. Central Research Institute of Electric Power Industry, 2-11-1 Iwato-kita, 201, Komae, Tokyo, Japan

    N. Soneda

Authors
  1. G. Yagawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Yoshimura
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Soneda
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. Nakao
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by S. N. Atluri, October 22, 1991

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yagawa, G., Yoshimura, S., Soneda, N. et al. Automatic two- and three-dimensional mesh generation based on fuzzy knowledge processing. Computational Mechanics 9, 333–346 (1992). https://doi.org/10.1007/BF00370013

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00370013

Keywords

Search

Navigation