A posteriori error estimation for equilibrium finite elements in elastostatic problems

  • Orlando J.B. Almeida Pereira Universidade Tecnica de Lisboa
  • José P. Moitinho de Almeida Universidade Tecnica de Lisboa

Abstract

Equilibrated solutions, locally satisfying all the equilibrium conditions, may be obtained by using a special case of the hybrid finite element formulation. Equilibrium finite element solutions will normally present compatibility defaults, which may be directly used to estimate the error of the solution, a posteriori. Another approach is to construct a compatible solution using the stresses and displacements available from the hybrid solution. From this dual solution, an upper bound for the global error is obtained. In this paper, the hybrid equilibrium element formulation, the occurrence of spurious kinematic modes and the use of super-elements, in 2D and 3D, are briefly reviewed. Compatibility defaults for 2D and 3D are presented, together with an expression for an element error indicator explicitly based on such defaults. A local procedure for recovering conforming displacements from the equilibrium finite element solution is also presented. The h-refinement procedure is adapted to prevent irregular refinement patterns.

Keywords

References

[1] J .P.M. Almeida, J .A.T. Freitas, An alternative approach to the formulation of hybrid equilibrium finite elements. Comp. Struet., 40: 1043- 1047, 1991.
[2] J.P.M. Almeida, O.J.B.A. Pereira. A set of hybrid equilibrium finite element models for the analysis of three-dimensional solids. Int. J. Numer. Methods Engrg., 39: 2789- 2802, 1996.
[3] I. Babuska, W. C. Rheinbolt. A posteriori error estimates for the finite element method. Int. J. Numer. Methods Engrg., 12: 1597-1615, 1978. .
[4] J.F. Debongnie. A general theory of dual error bounds by finite elements. Report LMF / D5, University of Liège, 1983.
[5] J.A.T . Freitas. Formulation of elastostatic Hybrid-Trefftz stress elements. Comp. Meths. Appl. Meeh. Engrg., 153: 127- 151, 1998.
Published
Mar 24, 2023
How to Cite
ALMEIDA PEREIRA, Orlando J.B.; MOITINHO DE ALMEIDA, José P.. A posteriori error estimation for equilibrium finite elements in elastostatic problems. Computer Assisted Methods in Engineering and Science, [S.l.], v. 8, n. 2-3, p. 439-453, mar. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1187>. Date accessed: 21 nov. 2024.
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