In a recent paper of Arnold et al. [D.N. Arnold, F. Brezzi, L.D. Marini, A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate, J. Sci. Comput. 22 (2005) 25-45], the ideas of discontinuous Galerkin methods were used to obtain and analyze two new families of locking free finite element methods for the approximation of the Reissner-Mindlin plate problem. By following their basic approach, but making different choices of finite element spaces, we develop and analyze other families of locking free finite elements that eliminate the need for the introduction of a reduction operator, which has been a central feature of many locking-free methods. For k ≥ 2, all the methods use piecewise polynomials of degree k to approximate the transverse displacement and (possibly subsets) of piecewise polynomials of degree k - 1 to approximate both the rotation and shear stress vectors. The approximation spaces for the rotation and the shear stress are always identical. The methods vary in the amount of interelement continuity required. In terms of smallest number of degrees of freedom, the simplest method approximates the transverse displacement with continuous, piecewise quadratics and both the rotation and shear stress with rotated linear Brezzi-Douglas-Marini elements.
|Original language||English (US)|
|Number of pages||12|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Issue number||37-40 SPEC. ISS.|
|State||Published - Aug 1 2007|
Bibliographical noteFunding Information:
The work of the first author was partly supported by NSF Grant DMS-0411388. The work of the second and fourth author was partly supported by the Italian government Grant PRIN2004. The work of the third author was partly supported by NSF Grant DMS03-08347.
Copyright 2008 Elsevier B.V., All rights reserved.
- Discontinuous Galerkin method
- Locking-free finite elements
- Reissner-Mindlin plates