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Stress Smoothing in Large Strain, Large Rotation Problems

  • V. Kompiš
  • J. Búry
Part of the International Centre for Mechanical Sciences book series (CISM, volume 433)

Abstract

Stress smoothing using Trefftz polynomials as interpolation functions in connection with moving least squares (MLS) procedure is shown to be efficient approach for infinitesimal elasticity and plasticity. In the case of large displacements the smoothing procedure based on the classical polynomial interpolation over the domain of influence gives satisfactory smoothing effect in the internal points of the domain, but not in the vicinity of the domain boundaries with prescribed tractions. In such points the static boundary conditions are included into the procedure, which leads to the nonlinear MLS problem.

Keywords

Move Little Square Displacement Gradient Smoothing Procedure Static Boundary Condition Undeformed Configuration 
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References

  1. Bala§ J., Sladek V. and Slâdek J. (1989), Stress Analysis by Boundary Element Method, Elsevier, AmsterdamGoogle Scholar
  2. Belytschko T., Liu W. K.and Moran B. (2000), Nonlinear Finite Elements for Continua and Structures, J. Wiley.Google Scholar
  3. Blacker T. and Belytschko T. (1994), Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements, Int. J. Num. Meth. Eng., 37, 517–536.CrossRefMATHMathSciNetGoogle Scholar
  4. Boroomand B. and Zienkiewicz O.C. (1997), Recovery by equilibrium in patches (REP). Int. J. Num. Meth. Eng., 40, 137–164.CrossRefMathSciNetGoogle Scholar
  5. Fra§tia L. (2000), On certain improvements of element-free Galerkin method, in Proc. of Conference Numerical Methods in Continuum Mechanics, CD-ROM ed. Kompi§ V., Zmindak M. and Maunder E.A.W., MC Energy, Zilina.Google Scholar
  6. Jirousek J. and Zielinski A.P. (1995), Survey of Trefftz type element formulations, LSC Int. Report 95/06, EPFL Lausanne.Google Scholar
  7. Kompis V. (1994), Finite element satisfying all governing equations inside the element, Comp. & Struct. 4, 273–278.CrossRefGoogle Scholar
  8. Kompis V. and Búry J. (1999), Hybrid-Trefftz finite element formulation based on fundamental solution, in Discretization Methods in Structural Mechanics, eds. Mang H.A. and Rammerstorfer F.G., 181–187, Kluwer Acad. Publ.Google Scholar
  9. Kompis V., Konkol F. and Va§ko M. (2001), Trefftz-polynomial reciprocity based FE formulation, Computer Assis. Mech. and Eng. Sci., 8, 385–395.MATHGoogle Scholar
  10. Kompis V., Novak P. and Handrik M. (2000) Finite displacement in reciprocity based FE formulation, in Proc. of Conference Numerical Methods in Continuum Mechanics, CD-ROM ed. Kompi§ V., Zmindak M. and Maunder E.A.W., MC Energy, Zilina.Google Scholar
  11. Kompis V., Zmindak M., Jakubovicova L. (1999), Error estimation in multi-domain BEM (Reciprocity Based FEM). In ECCM’99, European Conference on Computational Mechanics, CD-ROM ed. Wunderlich W., TU Munich.Google Scholar
  12. Kvamsdal T. and Okstad K.M. (1998), Error estimation based on superconvergent patch recovery using statically admissible stress fields. Int. J. Num. Meth. Eng., 42, 443–472.CrossRefMATHMathSciNetGoogle Scholar
  13. Lu Y. Y., Belytschko T. and Gu L. (1994), A new implementation of the element free Galerkin method, Comput. Meth. Appl. Mech. Engng., 113, 397–414.CrossRefMATHMathSciNetGoogle Scholar
  14. Maunder E.A.W. (2001), A Trefftz patch recovery method for smooth stress resultants and applications to Reissner-Mindlin equilibrium plate models, Computer Assis. Mech. and Eng. Sci., 8, 409–424.MATHGoogle Scholar
  15. Maunder E.A.W. and Kompi§ V. (2000), Stress recovery techniques based on Trefftz functions, in Proc. of Conference Numerical Methods in Continuum Mechanics, CD-ROM ed. Kompis V., Zmindak M. and Maunder E.A.W., MC Energy, Zilina.Google Scholar
  16. Tabbara M., Blacker T. and Belytschko T. (1994), Finite element derivative recovery by moving least square interpolants. Comput. Meth. Appl. Mech. Engrg., 117, 211–223.CrossRefMATHGoogle Scholar
  17. Wiberg N.-E., Abdulwahab F. and Zivkas S. (1994), Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. Int. J. Num. Meth. Eng., 37, 3417–3440.CrossRefMATHGoogle Scholar
  18. Zienkiewicz O.C. and Zhu J.Z. (1992), The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique. Int J. Num. Meth. Eng., 33, 1331–1364.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • V. Kompiš
    • 1
  • J. Búry
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of ŽilinaŽilinaSlovak Republic

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