In a recent paper of Arnold, Brezzi, and, 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

Locking-free Reissner-Mindlin elements without reduced integration

BREZZI, FRANCO;MARINI, LUISA DONATELLA
2007-01-01

Abstract

In a recent paper of Arnold, Brezzi, and, 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
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/134453
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 43
  • ???jsp.display-item.citation.isi??? 42
social impact