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Locking effects in the finite element approximation of elasticity problems

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Summary

We consider the finite element approximation of the 2D elasticity problem when the Poisson ratiov is close to 0.5. It is well-known that the performance of certain commonly used finite elements deteriorates asv→0, a phenomenon calledlocking. We analyze this phenomenon and characterize the strength of the locking androbustness of varioush-version schemes using triangular and rectangular elements. We prove that thep-andh-p versions are free of locking with respect to the error in the energy norm. A generalization of our theory to the 3D problem is also discussed.

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Authors and Affiliations

  1. Institute of Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA

    Ivo Babuška

  2. Department of Mathematics and Statistics, University of Maryland Baltimore County, 21228, Baltimore, MD, USA

    Manil Suri

Authors
  1. Ivo Babuška
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  2. Manil Suri
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Additional information

The work of this author was supported in part by the Office of Naval Research under Naval Research Grant N00014-90-J-1030

The work of this author was supported in part by the Air Force Office of Scientific Research, Air Force Systems Command, U.S. Air Force, under grant AFOSR 89-0252

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Babuška, I., Suri, M. Locking effects in the finite element approximation of elasticity problems. Numer. Math. 62, 439–463 (1992). https://doi.org/10.1007/BF01396238

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  • DOI: https://doi.org/10.1007/BF01396238

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