Locking-free finite elements for the Reissner-Mindlin plate

Richard S. Falk, Tong Tu

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

Two new families of Reissner-Mindlin triangular finite elements are analyzed. One family, generalizing an element proposed by Zienkiewicz and Lefebvre, approximates (for k ≥ 1) the transverse displacement by continuous piecewise polynomials of degree k + 1, the rotation by continuous piecewise polynomials of degree k + 1 plus bubble functions of degree k + 3, and projects the shear stress into the space of discontinuous piecewise polynomials of degree k. The second family is similar to the first, but uses degree k rather than degree k + 1 continuous piecewise polynomials to approximate the rotation. We prove that for 2 ≤ s ≤ k + 1, the L2 errors in the derivatives of the transverse displacement are bounded by Chs and the L2 errors in the rotation and its derivatives are bounded by Chs min(1, ht-1) and Chs-1 min(1, ht-1), respectively, for the first family, and by Chs and Chs-1, respectively, for the second family (with C independent of the mesh size h and plate thickness t). These estimates are of optimal order for the second family, and so it is locking-free. For the first family, while the estimates for the derivatives of the transverse displacement are of optimal order, there is a deterioration of order h in the approximation of the rotation and its derivatives for t small, demonstrating locking of order h-1. Numerical experiments using the lowest order elements of each family are presented to show their performance and the sharpness of the estimates. Additional experiments show the negative effects of eliminating the projection of the shear stress.

Original languageEnglish (US)
Pages (from-to)911-928
Number of pages18
JournalMathematics of Computation
Volume69
Issue number231
DOIs
StatePublished - Jul 2000

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Finite element
  • Locking-free
  • Reissner-Mindlin plate

Fingerprint Dive into the research topics of 'Locking-free finite elements for the Reissner-Mindlin plate'. Together they form a unique fingerprint.

Cite this