Adaptive Mesh Refinement Techniques for Structural Problems

  • E. Oñate
  • J. Castro


In this paper some adaptive mesh refinement (AMR) strategies for finite element analysis of structural problems are discussed. Two mesh optimality criteria based on the equal distribution of: (a) the global error, and (b) the specific error over the elements are studied. It is shown that the correct evaluation of the rate of convergence of the different error norms involved in the AMR procedures is essential to avoid oscillations in the refinement process. The behaviour of the different AMR strategies proposed is compared in the analysis of some structural problems.


Finite Element Method Structural Problem Global Error Finite Element Solution Adaptive Mesh Refinement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Zienkiewicz, O.C. and Zhu, J.Z., “A simple error estimator and adaptive procedure for practical engineering analysis”, Int. Num. Meth. Engrg., 24, 337–357, 1987.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Zienkiewicz, O.C., Zhu, J.Z., Liu, I.C., Morgan, K. and Peraire, J., “Error estimates and adaptive from elasticity to high speed compressible flow”, in J.R. Whiteman, ed., MAFELAP 87, 483–512, Academic Press, New York, 1988.Google Scholar
  3. [3]
    Zhu, J.Z. and Zienkiewicz, O.C., “Adaptive techniques in the finite element method”, Comm. Appl. Numer. Methods, 4, 197–204, 1988.MATHCrossRefGoogle Scholar
  4. [4]
    Zienkiewicz, O.C., Zhu, J.Z. and Gong, N.G., “Effective and practical h — p version adaptive analysis procedures for the finite element method”, Internat. J. Numer. Methods Engrg., 28, 879–891, 1989.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Zienkiewicz, O.C., Zhu, J.Z., “The three R’s of engineering analysis and error estimation and adaptivity”, Comp. Meth. in Appl. Mech. and Engng, 82, 95–113, 1990.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Zienkiewicz, O.C., Zhu, J.Z., “Error estimates and adaptive refinement for plate bending problems”, Internat. J. Numer. Methods Engrg., 28, 2839–53, 1989.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Atamaz-Sibai, W. and Hinton, E., “Adaptive mesh refinement with the Morley plate element”, Proc. of NUMETA 90 conference held at Swansea 1990, 2, 1044–57, Elserver App. Sc, London 1990.Google Scholar
  8. [8]
    Atamaz-Sibai, W., Hinton, E. and Selman, A., “Adaptive mesh refinement with Mindlin-Reissner elements”, Proc. 2nd Int. Conf. Computer Aided Analysis and Design of Concrete Structures, Apr. 1990, Zell-am-see, Austria, 1, 303–15, Pineridge Press, Swansea, U.K.Google Scholar
  9. [9]
    Selman, A., Hinton, E. and Atamaz-Sibai, W., “Edge effects in Mindlin-Reissner plates using adaptive mesh refinement”, Eng. Comp., 7. 3. 217–27, 1990.CrossRefGoogle Scholar
  10. [11]
    Zienkiewicz, O.C. Taylor, R.L., Papadopoulus, P. and Oüate, E., “Plate bending with discrete constraints. New Triangular element”, Comp, and Struct., 35, 4, 505–22, 1990.Google Scholar
  11. [11]
    Zienkiewicz, O.C. Taylor, R.L., Papadopoulus, P. and Oüate, E., “Plate bending with discrete constraints. New Triangular element”, Comp, and Struct., 35, 4, 505–22, 1990.MATHCrossRefGoogle Scholar
  12. [12]
    Onate, E., Zienkiewicz, O.C. and Taylor R.L., “Consistent formulation of shear constrained Reissner-Mindlin plate Elements”, in Discretization Methods in Struct. Mech., G. Kuhn and H. Mang (Eds.), Springer-Verlag, 1990.Google Scholar
  13. [13]
    Onate, E., Zienkiewicz, O.C. Suárez, B. and Taylor, R.L., “A general methodology for deriving shear constrained Reissner-Mindlin plate elements”, Int. J. Num. Meth. Engng., To be published 1991.Google Scholar
  14. [14]
    Papadopoulus, P. and Taylor, R.L., “A triangular element based on Reissner-Mindlin plate theory”, Int. J. Num. Meth. Engng., 5, 1029–51. 1990.CrossRefGoogle Scholar
  15. [15]
    Onate, E. and Castro, J., “Some new plate elements based on assumed shear strain fields”, European Conf. on New Advances in Computat. Struct. Mehc, Giens, France, April, 1991.Google Scholar
  16. [16]
    Onate, E., Castro, J. and Kreiner, R., “Error estimations and mesh adaptivity techniques for plate and shell problems”, presented at the 3rd. International Conference on Quality Assurance and Standards in Finite Element Methods, Stratford-upon-Avon, England, 10–12 September, 1991.Google Scholar
  17. [17]
    Bugeda, G., “Utilización de técnicas de estimación de error y generación automática de mallas en procesos de optimización estructural”, Ph D. Thesis, Universitat Polytècnica de Catalunya, 1990.Google Scholar
  18. [18]
    Bugeda, G. and Oliver, J., “Automatic adaptives remeshing for structural shape optimization”, European Conf. on New Advances in Computat. Struct. Mech., Giens, France, April, 1991.Google Scholar
  19. [19]
    Wu, J., Zhu, J.Z., Smelter, J. and Zienkiewicz, O.C., “Error estimation and adaptivity in Navier-Stokes incompressible flow”, Computational Mechanics, 6, 4, 259–71, 1990.MATHCrossRefGoogle Scholar
  20. [20]
    Zienkiewicz, O.C. and Taylor, R.L., “The finite element method”, Mc Graw Hill, I, 1989; II, 1991.Google Scholar
  21. [21]
    Peraire, J., “A finite element method for convection dominated flows”, Ph. D. Thesis, Civil Eng. Dept. University College of Swansea, U.K. 1986.Google Scholar
  22. [22]
    Peiro, J., “A finite demente procedure for the solution of the Euler equations on unstructured meshes”, Ph.D. Thesis, Civil Eng. Dept., University College of Swansea, U.K., 1989.Google Scholar
  23. [23]
    Zienkiewicz, O.C. and Zhu, J.Z., “Superconvergence derivative recovery techniques and a posteriory error estimation in the finite element method. Part I and part II”. Inst. Num. Meth. Engng., Swansea CR/671/91, June 1991, (To appear in Int. J. Num. Meth. Engng.).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • E. Oñate
    • 1
  • J. Castro
    • 1
  1. 1.International Center for Numerical Methods in EngineeringUniversidad Politécnica de CataluñaBarcelonaEspaña

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