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From Solid Modeling to Finite Element Analysis

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Application Development Systems
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Abstract

Solid modeling, finite element mesh generation and analysis of finite element solutions are obviously tightly connected in the design redesign cycle. However, practical realizations of each of these aspects of mathematical analysis of solid objects requires a significant amount of internal independence. Each aspect has to be justified on its own merits and their actual development reflects this independence. Together they form a powerful system and separately they perform useful functions which can interface with other computer codes and systems.

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References

  1. Bowyer, A., “Computing Dirichlet Tesselations”, The Computer Journal, Vol. 24, 162–166 (1981).

    Article  MathSciNet  Google Scholar 

  2. Boyse, J.W., “Data structure for a solid modeller”, General Motors Research Publication, GMR-2768 (1979).

    Google Scholar 

  3. Boyse, J.W. and Gilchrist, J.E.,“GMSOLID-Interactive modeling for design and analysis of solids”, IEEE Computer Graphics and Applications, Vol. 2, pp. 27–40 (1982).

    Article  Google Scholar 

  4. Boyse, J.W. and Rosen, J.M.,“GMSOLID-A System for interactive design and analysis of solids”, Society of Automotive Engineers Technical Paper Series, No.810196 (1981).

    Book  Google Scholar 

  5. Brostow W. and Dussault J.P, “Construction of Voronoi polyhedra”, Journal of Computational Physics, Vol. 29, pp. 81–92 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  6. Cavendish, J.C., “Automatic triangulation of arbitrary planar domains for the finite element method”, International Journal for Numerical Methods in Engineering, Vol. 8, pp. 679–696 (1974).

    Article  MATH  Google Scholar 

  7. Cavendish, J.C., Field, D.A. and Frey, W.H., “An approach to automatic three-dimensional finite element mesh generation”, General Motors Research Publication, GMR-4533 (1983).

    Google Scholar 

  8. Dongarra, J.J., Moler, C.B., Bunch, J.R. and Stewart, G.W., LINPACK Users’ Guide, Society for Industrial and Applied Mathematics, Philadelphia, PA (1979).

    Book  Google Scholar 

  9. Field, D.A., “An algorithm for determining invertible quadratic isoparametric finite element transformations”, Mathematics of Computation, Vol. 37, pp. 347–360 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  10. Field, D.A., “Algorithms for determining invertible two and three dimensional quadratic isoparametric finite element transformations”, International Journal for Numerical Methods in Engineering, Vol. 19, pp. 789–802 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  11. Field, D.A. and Hatton, M.B.,“Plotting three dimensional finite element solutions on planar cross sections”, General Motors Research Publication, GMR-4608 (1984).

    Google Scholar 

  12. Field, D.A. and Morgan, A.P.,“A quick method for determining whether a second degree polynomial has a solution in a given box”, IEEE Computer Graphics and Applications, Vol. 2, pp. 65–68 (1982).

    Article  Google Scholar 

  13. Finney, J.L., “A procedure for the construction of Voronoi polyhedra”, Journal of Computational Physics, Vo1. 32, pp. 137–143 (1979).

    Article  Google Scholar 

  14. Forsythe, G. and Moler, C.B., Computer Solution of Linear Algebraic Systems, Prentice-Hall (1967).

    MATH  Google Scholar 

  15. Frederick, C.O., Wong, Y.C. and Edge, F.W., “Two-dimensional automatic mesh generation for structural analysis”, International Journal for Numerical Methods in Engineering, Vol. 2, pp. 133–144 (1970).

    Article  Google Scholar 

  16. Frey, A.E., Hall, C.A. and Porsching, T.A., “An application of computer graphics to three dimensional finite element analyses”, Computers and Structures, Vo1. 10, pp. 149–154 (1979).

    Article  Google Scholar 

  17. Garcia, C.B. and Zangwill, W.I., “Finding all solutions to polynomial systems and other systems of equations”, Mathematical Programming, Vol. 16, pp. 159–176 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  18. Gago, J.P. de S.R., Kelly, D.W., Zienkiewicz, O.C., and Babuska, I., “A posteriori error analysis and adaptive processes in the finite element method: part I–adaptive mesh refinement”, International Journal for Numerical Methods in Engineering, Vol. 19, pp. 1621–1656 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  19. Gordon, W.J., “Spline-blended surface interpolation through curve networks”, J. Math. Mech., Vol. 10, pp. 931–952 (1968).

    Google Scholar 

  20. Gordon, W.J. and Hall C.A., “Construction of curvilinear coordinate systems and applications to mesh generation”, International Journal for Numerical Methods in Engineering, Vol. 7, pp. 461–477 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  21. Hall, C.A., Porsching T.A. and Sledge, F., “STRSIT: contour plotting of stresses on planes of intersection”, Computers and Structures, Vol. 12, pp. 221–224 (1980).

    Article  MATH  Google Scholar 

  22. IMSL Library Reference Manual, 7500 Bellaire Boulevard, Houston, Texas.

    Google Scholar 

  23. Kelly, D.W., Gago, J.P. de S.R., Zienkiewicz, O.C., and Babuska, I., “A posteriori error analysis and adaptive processes in the finite element method: part II — error analysis”, International Journal for Numerical Methods in Engineering, Vol. 19, pp. 1593–1619 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  24. Lawson, C.L., “Software for C surface interpolation” Software III, Academic Press, New York, pp. 159–192 (1977).

    Google Scholar 

  25. Meek, J.L. and Beer, G., “Contour plotting of data using isoparametric element representation”, International Journal for Numerical Methods in Engineering, Vol. 10, pp. 954–957 (1976).

    Article  Google Scholar 

  26. Morgan, A.P., “A method for computing all solutions to systems of polynomial equations”, ACM Transctions on Mathematical Software, Vol. 9, pp. 1–17 (1983).

    Article  MATH  Google Scholar 

  27. MOVIE.BYU, contact Hank Christiansen, Civil Engineering, 368 CB BYU, Provo, Utah 85602.

    Google Scholar 

  28. MSC/NASTRAN, The MacNeal-Schwindler Corporation, 815 Colorado Boulevard, Los Angeles, California 90041.

    Google Scholar 

  29. Nguyen-Van-Phai, “Automatic mesh generation with tetrahedron elements”, International Journal for Numerical Methods in Engineering, Vol. 18, pp. 273–289 (1982).

    Article  MATH  Google Scholar 

  30. PDA: PATRAN User’s Guide, PDA Engeneering, 1560 Brookhollow Drive, Santa Anna, California, 92705.

    Google Scholar 

  31. Rogers, C.A., Packing and Covering, Cambridge Mathematical Tracts, No.54, Cambridge university Press.

    Google Scholar 

  32. Sarraga, R.F., “Algebraic methods for intersections of quadric surfaces in GMSOLID”, Computer Vision, Graphics, and Image Processing, Vol. 22, pp. 222–238 (1983).

    Article  Google Scholar 

  33. Sarraga, R.F. and Waters, W.C., “Free-form surfaces in GMSOLID: goals and issues”, General Motors Research Publication, GMR4481 (1983).

    Google Scholar 

  34. Sibson, R., “Locally equitriangular triangulations”, The Computer Journal, Vol. 21, pp. 243–245 (1978)

    Article  MathSciNet  Google Scholar 

  35. Suhara, J. and Fukuda J., “Automatic mesh generation for finite element analysis”, in Advances in Computational Methods in Structural Mechanics and Design, University of Alabama Press, pp. 607–624 (1974).

    Google Scholar 

  36. SUPERTAB interactive finite element model generation system, Structural Dynamics Research Corporation, Cincinnati, Ohio.

    Google Scholar 

  37. Voelker, H.B. and Requicha, A.A.G., “Geometric Modelling of Mechanical Parts and processes”, Computer, Vol. 10, pp. 48–57 (1977).

    Article  Google Scholar 

  38. Watson, D. F., “Computing the n-dimensional Delaunay tesselation with applications to Voronoi polytopes”, The Computer Journal, Vol. 24, No. 2, pp. 167–172 (1981).

    Article  MathSciNet  Google Scholar 

  39. Zienkiewicz O.C. and Phillips D.V., “An Automatic mesh generation scheme for plane and curved surfaces by isoparametric co-ordinates”, International Journal for Numerical Methods in Engineering, Vol. 3, pp. 519–528 (1971).

    Article  MATH  MathSciNet  Google Scholar 

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© 1986 Springer-Verlag Tokyo

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Field, D.A. (1986). From Solid Modeling to Finite Element Analysis. In: Kunii, T.L. (eds) Application Development Systems. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68051-2_12

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  • DOI: https://doi.org/10.1007/978-4-431-68051-2_12

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68053-6

  • Online ISBN: 978-4-431-68051-2

  • eBook Packages: Springer Book Archive

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