Locking-free finite elements for the Reissner-Mindlin plate

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 estimat...

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Richard S. Falk, Tong Tu
• Keywords: Continuous Piecewise Polynomials, MOC 2000, Piecewise Polynomials, Transverse Displacement