Locking-free Reissner–Mindlin elements without reduced integration
- 作者：Douglas N. Arnold ; Franco Brezzi ; Richard S. Falk ; L. Donatella Marini
- 关键词：Locking-free finite elements ; Reissner-Mindlin plates ; Discontinuous Galerkin method
- 刊名：Computer Methods in Applied Mechanics and Engineering
- 出版年：2007
- 期刊代码：27_00457825
- 类别：cp
- 出版时间：1 August 2007
- 卷：196
- 期：37-40
- 页码：3660-3671
- 文件大小：288 K
摘要
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.
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.