Generalized Finite Element Method in Mixed Variational Formulation: A Study of Convergence and Solvability

  • W. Góis
  • S. P. B. Proença
Conference paper
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 5)

Abstract

The Generalized Finite Element Method (GFEM) is first applied to hybrid-mixed stress formulations (HMSF). Generalized shape approximation functions are generated by means of polynomials of three independent approximation fields: stresses and displacements in the domain and displacements field on the static boundary. Firstly, the enrichment can independently be conducted over each of the three approximation fields. However, solvability and convergence problems are induced mainly due to spurious modes generated when enrichment is arbitrarily applied. With the aim of efficiently exploring enrichments in HMSF, an extension of the patch-test is proposed as a necessary condition to ensure enrichment, thus preserving convergence and solvability. In the present work, the inf-sup test based on Babuška-Brezzi condition was used to demonstrate the effectiveness of the Patch-Test. In particular, the inf-sup test was applied over selectively enriched quadrilateral bilinear and triangular finite element meshes. Numerical examples confirm the Patch-Test as a necessary but not sufficient condition for convergence and solvability.

Key words

Generalized finite element method hybrid-mixed stress formulation Babuška-Brezzi condition inf-sup test 

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Copyright information

© Springer 2007

Authors and Affiliations

  • W. Góis
    • 1
  • S. P. B. Proença
    • 1
  1. 1.Structural Engineering Department, São Carlos School of EngineeringUniversity of São PauloSão CarlosBrazil

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