Skip to main content
SpringerLink
Log in

Strict upper error bounds on computed outputs of interest in computational structural mechanics

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

This paper introduces new strict error bounds of computed outputs of interest for time-dependent nonlinear problems in quasi-statics as well as in dynamics. All sources of errors, including modeling errors, are taken into account. Therefore, such error bounds are also suitable tools for analyzing various approximations, particularly in dynamics. Small-displacement problems without softening, such as (visco)plasticity problems, are included through the classical thermodynamics framework involving internal state variables; the material models are not necessarily standard.

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. Babus˘ka I and Strouboulis T (2001). The finite element method and its reliability. University press, Oxford

    Google Scholar 

  2. Ladevèze P and Pelle J-P (2004). Mastering calculations in linear and nonlinear mechanics. Springer, NY

    Google Scholar 

  3. Ladevèze P and Oden J-T (1998). Advances in adaptative computational methods in mechanics. Elsevier, Amsterdam

    Google Scholar 

  4. Wiberg NE, Diez P (eds) (2006) Special Issue. Computer methods in applied mechanics and engineering

  5. (2003). Error controlled adaptive finite elements in solid mechanics. Wiley, New York

    Google Scholar 

  6. Eriksson K, Estep D, Hansbo P and Johnson C (1995). Introduction to adaptive methods for partial differential equations. In: Isereles, A (eds) Acta numerica., pp 105–159. Cambridge University Press, Cambridge

    Google Scholar 

  7. Becker R and Rannacher R (1996). A feed-back approach to error control in finite element methods: basic analysis and examples. East-West J Numer Math 4: 237–264

    MathSciNet  MATH  Google Scholar 

  8. Rannacher R and Sutt meier FT (1998). A posteriori error control and mesh adaptation for finite element models in elasticity and elasto-plasticity. In: (eds) Advances in adaptative computational method in mechanics., pp 275–292. Elsevier, Amsterdam

    Chapter  Google Scholar 

  9. Ladevèze P, Rougeot P, Blanchard P and Moreau JP (1999). Local error estimators for finite element linear analysis. Comput Methods Appl Mech Eng 176: 231–246

    Article  MATH  Google Scholar 

  10. Strouboulis T, Babus˘ka I, Datta D, Copps K and Gangaraj SK (2000). A posteriori estimation and adaptive control of the error in the quantity of interest - Part 1: A posteriori estimation of the error in the Von Mises stress and the stress intensity factors. Comput Methods Appl Mech Eng 181: 261–294

    Article  MathSciNet  MATH  Google Scholar 

  11. Cirak F and Ramm E (1998). A posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem. Comput Methods Appl Mech Eng 156: 351–362

    Article  MathSciNet  MATH  Google Scholar 

  12. Prudhomme S and Oden JT (1999). On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors. Comput Methods Appl Mech Eng 176: 313–331

    Article  MathSciNet  MATH  Google Scholar 

  13. Parès N, Bonet J, Huerta A and Peraire J (2006). The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations. Comput Methods Appl Mech Eng 195(4–6): 406–429

    Article  MATH  Google Scholar 

  14. Peraire J and Patera AT (2006). Bounds for linear-functional outputs of coercive partial differential equations; local indicators and adaptive refinements. In: (eds) Advances in adaptive computational methods in mechanics., pp 199–216. Elsevier, Amsternam

    Google Scholar 

  15. Greenberg HJ (1948). The determination of upper and lower bounds for the solution of Dirichlet problem. J Math Phys 27: 161–182

    MATH  Google Scholar 

  16. Washizu K (1953). Bounds for solutions of boundary value problems in elasticity. J Math Phys 32: 117–128

    MathSciNet  MATH  Google Scholar 

  17. Ladevèze P (2006). Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems. Comptes Rendus Académie des Sciences - Mécanique, Paris 334: 399–407

    Google Scholar 

  18. Ladevèze P and Moës N (1998). A new a posteriori error estimation for nonlinear time-dependent finite element analysis. Comput Methods Appl Mech Eng 157: 45–68

    Article  MATH  Google Scholar 

  19. Chamoin L, Ladevèze P (2006) Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods. Int J Numer Methods Eng; online, DOI: 10.1002/nme. 1978

  20. Chamoin L, Ladevèze P (2007) A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems (submitted)

  21. Ladevèze P (1999). Nonlinear computational structural mechanics - new approaches and non-incremental methods of calculation. Springer, New York

    MATH  Google Scholar 

  22. Bui HD (1993) Introduction to inverse problems in material mechanics. Eyrolles Paris (in french)

  23. Ladevèze P, Moës N and Douchin B (1999). Constitutive relation error estimations for (visco) plasticity finite element analysis with softening. Comput Methods Appl Mech Eng 176: 247–264

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LMT-Cachan (ENS-Cachan/CNRS/Paris 6 University), 61 Avenue du Président Wilson, 94235, Cachan Cedex, France

    Pierre Ladevèze

Authors
  1. Pierre Ladevèze
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pierre Ladevèze.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ladevèze, P. Strict upper error bounds on computed outputs of interest in computational structural mechanics. Comput Mech 42, 271–286 (2008). https://doi.org/10.1007/s00466-007-0201-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-007-0201-y

Keywords

Search

Navigation