TY - JOUR

T1 - Locking-free Reissner-Mindlin elements without reduced integration

AU - Arnold, Douglas N.

AU - Brezzi, Franco

AU - Falk, Richard S.

AU - Marini, L. Donatella

N1 - Funding 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.

PY - 2007/8/1

Y1 - 2007/8/1

N2 - 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.

AB - 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.

KW - Discontinuous Galerkin method

KW - Locking-free finite elements

KW - Reissner-Mindlin plates

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U2 - 10.1016/j.cma.2006.10.023

DO - 10.1016/j.cma.2006.10.023

M3 - Article

AN - SCOPUS:34447104607

SN - 0045-7825

VL - 196

SP - 3660

EP - 3671

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 37-40 SPEC. ISS.

ER -