Skip to main content
SpringerLink
Log in

Interactive-adaptive geometrically nonlinear analysis of shell structures

  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

This paper presents an investigation of interactive-adaptive techniques for nonlinear finite element structural analysis. In particular, effective methods leading to reliable automated, finite element solutions of nonlinear shell problems are of primary interest here. This includes automated adaptive nonlinear solution procedures based on error estimation and adaptive step length control, reliable finite elements that account for finite deformations and finite rotations, three-dimensional finite element modeling, and an easy-to-use, easy-to-learn graphical user interface with three-dimensional graphics. A computational environment, which interactively couples a comprehensive geometric modeler, an automatic three-dimensional mesh generator and an advanced nonlinear finite element analysis program with real-time computer graphics and animation tools, is presented. Three examples illustrate the merit and potential of the approaches adopted here and confirm the feasibility of developing fully automated computer aided engineering environments.

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

  1. Fredriksson, B.; Mackerle, J. (1984) Structural Mechanics: Finite Element Computer Programs, 4th edn, Linkøping, Sweden, Advanced Engineering Corp.

    Google Scholar 

  2. Noor, A. K.; Babuška, I. (1987) Quality assessment and control of finite element solutions, Finite Elements in Analysis and Design, 3, 1–26.

    Google Scholar 

  3. PDA Engineering, Costa Mesa, California (1988) PATRAN Plus User Manual.

  4. Structural Dynamics Research Corporation, Milford, Ohio (1992) I-DEAS (Integrated Design Engineering Analysis Software) User Manuals.

  5. Det Norske Veritas Sesam A.S., Høvik, Norway (1993) SESAM User's Manual, SESAM System.

  6. Haugen, B.; Mathisen, K.M. (1989) Large-scale vectorized three-dimensional geometric nonlinear shell analysis on a CRAY X-MP/28 utilizing sparse matrix methods. In Proceeding of the First International Conference on Applications of Supercomputers in Engineering (ASE89), volume FFSAA, pp. 189–205, Southampton, England

  7. Farhat, C.; Crivelli, L. (1989) A general approach to nonlinear FE computations on shared-memory multiprocessors, Comp. Meths. Appl. Mech. Engrg. 72, 153–171.

    Google Scholar 

  8. Damhaug, A.C. (1992) Sparse solution of finite element equations, Dr. Ing. Dissertation, Department of Structural Engineering, The Norwegian Institute of Technology, Trondheim, Norway.

    Google Scholar 

  9. Damhaug, A.C.; Mathisen, K.M.; Okstad, K.M. (1994) The use of sparse matrix methods in finite element codes for structural mechanics applications, Comp. Syst. Engrg., 4, 355–362

    Google Scholar 

  10. Bathe, K.-J., Dvorkin, E.N. (1983) On the automatic solution of nonlinear finite element equations, Comp. Struct., 17, 871–879.

    Google Scholar 

  11. Lee, S.H.; Hsieh, S.S. (1991) Applications of a self-adaptive algorithm to non-linear finite element analysis, Int. J. Numer. Meths. Engrg, 32, 1057–1077.

    Google Scholar 

  12. Shephard, M.S. (1985) Finite element modeling with an integrated geometric modeling environment: Part II Attribute specification, domain differences and indirect element types, Engrg. Comp., 1, 73–85.

    Google Scholar 

  13. Weiler, K.J. (1986) Topological structures for geometric modelling, PhD Thesis, Center for Interactive Computer Graphics, Rensselaer Polytechnic Institute, Troy, New York.

    Google Scholar 

  14. Delmas, J.E.; Tembulkar, J.M. (1990) Geometry based automated finite element modeling and analysis. In FEM in the Design Process, Proceedings of the 6th World Congress on Finite Element Methods, Banff, Alberta, Canada, Robinson J. (editor), pp. 280–286, Great Bidlake Manor, UK, Robinson and Associates.

    Google Scholar 

  15. Shephard, M.S. (1988) Approaches to the automatic generation and control of finite elements meshes, Appl. Mech. Rev., 41, 169–185.

    Google Scholar 

  16. Peraire, J.; Vahdati, M.; Morgan, K.; Zienkiewicz, O.C. (1987) Adaptive meshing for compressive flow computations, J. Comp. Phys., 72, 449–466.

    Google Scholar 

  17. Shephard, M.S.; Georges, M.K. (1991) Automatic three-dimensional mesh generation by the finite octree technique, Int. J. Numer. Meths. Engrg., 32, 709–749.

    Google Scholar 

  18. Leal, D. (1991) Progress towards a standard for finite element data. In Proceedings of the 3rd International Conference on Quality Assurance and Standards in Finite Element Analysis, Stratford-upon-Avon, UK, September, NAFEMS.

  19. Hunten, K.A. (Editor) (1991) FEA Reference Model, ISO TC184/SC4/WG3 Document N21.

  20. Riks, E. (1972) The application of Newton's method to the problem of elastic stability, J. Appl. Mech., 39, 1060–1066.

    Google Scholar 

  21. Wempner, G.A. (1971) Discrete approximations related to nonlinear theories in solids, Int. J. Solids Struct., 7, 1581–1599.

    Google Scholar 

  22. Crisfield, M.A. (1981) A fast incremental/iterative solution procedure that handles snap-through, Comp. Struct., 13, 55–62.

    Google Scholar 

  23. Schweizerhof, K.H.; Wriggers, P. (1986) Consistent linearization for path following methods in nonlinear FE analysis, Comp. Meths. Appl. Meth. Engrg., 59, 261–279.

    Google Scholar 

  24. Fried, I. (1984) Orthogonal trajectory accession to the nonlinear equilibrium curve, Comp. Meths. Appl. Mech. Engrg., 47, 283–297.

    Google Scholar 

  25. Zienkiewicz, O.C.; Zhu, J.Z. (1987) A simple error estimator and adaptive procedures for practical engineering analysis. Int. J. Numer. Meths. Engrg., 24, 337–357.

    Google Scholar 

  26. Hinton, E.; Campbell, J.S. (1974) Local and global smoothing of discontinuous finite element functions using a least squares method, Int. J. Numer. Meths. Engrg., 8, 461–480.

    Google Scholar 

  27. Zienkiewicz, O.C.; Zhu, J.Z. (1992) The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique, Int. J. Numer. Meths. Engrg., 33, 1331–1364.

    Google Scholar 

  28. Blacker, T.; Belytschko, T. (1994) Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements, Int. J. Numer. Meths. Engrg., 37, 517–536.

    Google Scholar 

  29. Zhu, J.Z.; Zienkiewicz, O.C. (1988) Adaptive techniques in the finite element method, Commun. Appl. Numer. Meths., 4, 197–204.

    Google Scholar 

  30. Okstad, K.M. (1994) Adaptive methods for nonlinear finite element analysis of shell structures, Dr. Ing. Dissertation, Department of Structural Engineering The Norwegian Institute of Technology, Trondheim, Norway

    Google Scholar 

  31. Okstad, K.M.; Mathisen, K.M. (1994) Towards automatic adaptive geometrically nonlinear shell analysis. Part I: Implementation of anh-adaptive mesh refinement procedure, Int. J. Numer. Methods. Engrg., 37, 2657–2678.

    Google Scholar 

  32. Fyrileiv, O. (1991) FENRIS—Finite Element NonlineaR Integrated System, user's manual, Veritas Sesam Systems A.S., Høvik, Norway.

    Google Scholar 

  33. Aamnes, K. (1993) GL view Command Summary, SINTEF Industrial Mathematics, Trondheim, Norway.

    Google Scholar 

  34. Mangerud, A.: Mathisen, K.M.; Okstad, K.M.; Syljuåsen, Ø.A. (1993) FENRIX—Finite Element NonlineaR Integrated X-environment, Users Manual, Technical Report R-8-93, Department of Structural Engineering, The Norwegian Institute of Technology, Trondheim, Norway.

    Google Scholar 

  35. Arnholm, C. (1989) SIF Results Interface File, File Description, Veritas Sesam Systems A.S., Høvik, Norway.

    Google Scholar 

  36. Bergan, P.G.; Nygård (1985) Nonlinear shell analysis using free formulation finite elements. In Proceedings of the Europe-US Symposium on Finite Element Methods for Nonlinear Problems, Trondheim, Norway, Bergan, P.G.; Bathe, K.-J.; Wunderlich, W. (Editors) New York and Tokyo, Springer-Verlag.

    Google Scholar 

  37. Nygård, M.K. (1986) The free formulation for nonlinear finite elements with applications to shells, Dr. Ing. Dissertation, Division of Structural Mechanics, The Norwegian Institute of Technology, Trondheim, Norway.

    Google Scholar 

  38. Simo, J.C.; Fox, D.D. (1989) On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization, Comp. Methds. Appl. Mech. Engrg., 72, 267–304.

    Google Scholar 

  39. Simo, J.C.; Fox, D.D.; Rifai, M.S. (1989) On a stress resultant geometrically exact shell model. Part II: The linear theory: computational aspects, Comp. Meths. Appl. Mech. Engrg, 73, 53–92.

    Google Scholar 

  40. Simo, J.C.; Fox, D.D.; Rifai, M.S. (1990) On a stress resultant geometrically exact shell model. Part III: Computational aspects of the nonlinear theory, Comp. Meths. Appl. Mech. Engrg., 79, 21–70.

    Google Scholar 

  41. Perić, D.J.; Owen D.R.J. (1991) The Morely thin shell finite element for large deformations problems: Simplicity versus sophistication. In Proceedings of the 4th International Conference on Nonlinear Engineering Computations (NEC-91), Split, Yugoslavia, Biaćanić, N.; Marović, P.; Owen, D.R.J.; Mihanović, A. (Editors).

  42. McCleary, S.L.; Knight, N.F. Jr. (1990) Error detection and control for nonlinear shell analysis. In FEM in the Design Process, Proceedings of the 6th World Congress on Finite Element Methods, Banff, Alberta, Canada, Robinson, J. (Editor) pp. 192–201, Great Bidlake Manor, UK, Robinson and Associates.

    Google Scholar 

  43. Hartung, R.F.; Ball, R.E. (1973) A comparison of several computer solutions to three structural shell analysis problems, Technical Report AFFDL-TR-73-15, U.S. Air Force.

  44. Almroth, B.O.; Brogan, F.A. (1981) Computational efficiency of shell elements. In Nonlinear Finite Element Analysis of Plates and Shells, Hughes, T.J.R.; Pifko, A.; Jay, A. (Editors), volume 48, pp. 147–165, ASME.

  45. Knight, N.F., Jr.; McCleary, S.L.; Macy, S.C.; Aminpour, M.A. (1989) Large-scale structural analysis: The structural analyst, the CSM testbed and the NAS system, Technical Memorandum, 100643, NASA Langley Research Center, Hampton, Virginia.

    Google Scholar 

  46. Almroth, B.O.; Brogan, F.A.; Stanley, G.M. (1979) Structural Analysis of General Shells, Vol. II: User Instructions for the STAGS(C-1) Computer Code, Lockheed Report LMSC-D33873.

Download references

Author information

Authors and Affiliations

  1. Department of Structural Engineering, The Norwegian Institute of Technology, N-7034, Trondheim, Norway

    Kjell Magne Mathisen & Knut Morten Okstad

Authors
  1. Kjell Magne Mathisen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Knut Morten Okstad
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mathisen, K.M., Okstad, K.M. Interactive-adaptive geometrically nonlinear analysis of shell structures. Engineering with Computers 12, 63–83 (1996). https://doi.org/10.1007/BF01299393

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01299393

Keywords

Search

Navigation