Finite-Element Analysis for the Naive User

  • Burkard Wördenweber

Abstract

The paper describes the role of mesh generation mediating between computer aided design and finite-element analysis. It illustrates one particular approach to mesh generation which reduces the need for mesh visualization and interaction. The method relies on engineering expertise to derive an appropriate test object for analysis from the geometric model. It then proceeds to generate an initial coarse mesh which may subsequently be refined to suit object geometry, material properties and load case specification. The method avoids the sensitive calculations necessary for adaptive methods and permits analysis at different levels of complexity and cost.

The paper introduces the recent developments within the BUILD geometric modeler, a product of the University of Cambridge Computer and Engineering Departments. In particular, the application program for finite-element mesh generation, together with its underlying algorithms, is described in detail.

Keywords

Manifold Nite Univer 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Akyus and Utku 1968]
    F. A. Akyus, S. Utku, “An Automatic Node-Relabeling Scheme for Band-Width Minimization of Stiffness Matrices,” AIAA Journal, Vol. 6, No. 4, April 1968, pp. 728–730.CrossRefGoogle Scholar
  2. [Allan 1978]
    D. K. Allan, “Classification and Coding,” Monograph No. 2, Brigham Young University, Provo Utah, 1978.Google Scholar
  3. [Armit 1970]
    A. P. Armit, “Computer Systems for Interactive Design of Three-Dimensional Shapes,” Ph.D. Dissertation, Computer Laboratory, University of Cambridge, Cambridge, England, 1970.Google Scholar
  4. [Babuska and Rheinboldt 1982]
    I. Babuska, W. C. Rheinboldt, “A Survey of A Posteriori Error Estimates and Adaptive Approaches in the Finite Element Method,” Technical Note BN-981, University of Maryland, College Park, Maryland, 1982.Google Scholar
  5. [Baumgart 1972]
    B. G. Baumgart, “Winged Edge Polyhedron Representation,” Computer Science Department Report No. STAN-CS-320, Stanford University, Stanford, California, 1972.Google Scholar
  6. [Biederman and Babuska 1982]
    M. Biederman, I. Babuska, “The Finite Element Method for Parabolic Equations, A Posteriori Error Estimators and Adaptive Approaches,” Technical Note BN-983/4, University of Maryland, College Park, Maryland, 1982.Google Scholar
  7. [Braid 1975]
    I. C. Braid, “The Synthesis of Solids Bounded by Many Faces,” Communications of the ACM, Vol. 18, No. 4, April 1975, pp. 209–216.CrossRefGoogle Scholar
  8. [Braid 1979a]
    I. C. Braid, “Notes on a Geometric Modeler,” CAD Group Document 101, Computer Laboratory, University of Cambridge, Cambridge, England, 1979.Google Scholar
  9. [Braid 1979b]
    I. C. Braid, “Geometric Modeling — Ten Years On,” CAD Group Document 103, Computer Laboratory, University of Cambridge, Cambridge, England, 1979.Google Scholar
  10. [Braid and Hillyard 1977]
    I. C. Braid, R. C. Hillyard, “Geometric Modeling in Algol 68,” CAD Group Document 92, Computer Laboratory, University of Cambridge, Cambridge, England, 1977.Google Scholar
  11. [Egeland and Araldsen 1974]
    O. Egeland, P. O. Araldsen, “Sesam-69—A General Purpose Finite Element Method Program,” Computers amp; Structures, Vol. 4, January 1974, pp. 41–68.CrossRefGoogle Scholar
  12. [Forrest 1969]
    A. R. Forrest, “Curves and Surfaces for Computer-Aided Design,” Ph.D. Dissertation, Computer Laboratory, University of Cambridge, Cambridge, England, 1969.Google Scholar
  13. Gill 1972]Google Scholar
  14. J. I. Gill, “Computer-Aided Design of Shell Structures Using the Finite Element Method,” Ph.D. Dissertation. Computer Laboratory, University of Cambridge, Cambridge, England, 1972.Google Scholar
  15. [Hillyard 1978]
    R. Hillyard, “Dimensions and Tolerances in Shape Design,” Ph.D. Dissertation, Computer Laboratory, University of Cambridge, Cambridge, England, 1978.Google Scholar
  16. [Kyprianou 1980]
    L. K. Kyprianou, “Shape Classification in Computer-Aided Design,” Ph.D. Dissertation, Computer Laboratory, University of Cambridge, Cambridge, England, 1980.Google Scholar
  17. [Leyvraz 1976]
    R. Leyvraz, “Iterative Generation of Optimal Triangular Grids for the Solution of 2-Dimensional Field Problems,” Proceedings of COMPUMAG (Oxford, England, March 31-April 2, 1976 ), Rutherford Laboratories, SRC, Chilton, Didcot, Oxon., England, 1976.Google Scholar
  18. [Requicha and Voelcker 1977]
    A. A. G. Requicha, H. B. Voelcker, “Constructive Solid Geometry,” Technical Memo No. 25, Production Automation Project, University of Rochester, Rochester, New York, 1977.Google Scholar
  19. [Solomon 1983]
    B. J. Solomon, “Surface Intersections for Solid Modeling,” Ph.D. Dissertation, Computer Laboratory, University of Cambridge, Cambridge, England, 1983.Google Scholar
  20. [Stiny 1975]
    G. Stiny, Pictorial and Formal Aspects of Shape and Shape Grammars, Birkhauser Verlag, Basel, Switzerland, 1975.Google Scholar
  21. [Stiny 1977]
    G. Stiny, “Ice Ray: A Note on the Generation of Chinese Lattice Designs,” Environment and Planning B, Vol. 4, No. 1, June 1977, pp. 89–99.CrossRefGoogle Scholar
  22. [Szabo and Babuska 1982]
    B. J. Szabo, I. Babuska, “Stress Approximation by the h- and p-Version of the Finite Element Method,” Report WV/CCM-82/1, Center for Computational Mathematics, Washington University, St. Louis, Missouri, 1982.Google Scholar
  23. [Varady 1982]
    T. Varady, “An Experimental System for Interactive Design and Manufacture of Sculptured Surfaces,” Computers in Industry, Vol. 3, Nos. 1 and 2, March and June 1982, pp. 125–135.Google Scholar
  24. [Wördenweber 1981]
    B. Wördenweber, “Automatic Mesh Generation of 2- and 3-Dimensional Curvilinear Manifolds,” Ph.D. Dissertation (available as Computer Laboratory Technical Report No. 18 ), University of Cambridge, Cambridge, England, 1981.Google Scholar
  25. [Wördenweber 1983a]
    B. Wördenweber, “Finite-Element Mesh Generation from Geometric Models,” COMPEL, International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 1, No. 4, 1983, pp. 23–33.CrossRefGoogle Scholar
  26. [Wördenweber 1983b]
    B. Wördenweber, “Surface Triangulation for Picture Production,” IEEE Computer Graphics and Applications, Vol. 3, No. 8, November 1983, pp. 45–51.CrossRefGoogle Scholar
  27. [Wördenweber 1984]
    B. Wördenweber, “Finite Element Mesh Generation,” accepted for publication, Computer Aided Design Journal, 1984.Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Burkard Wördenweber
    • 1
  1. 1.University of CambridgeCambridgeEngland

Personalised recommendations