Improvement Of Zienkiewicz Plate-element By Combined Hybrid Methods

The combined hybrid finite element method (CHFEM) is of the mechanism of enhancing coarse-mesh accuracy of conventional displacement elements. The combined hybrid scheme without energy error leads to enhancement of accuracy at coarse meshes. For plate bending problems, it allows arbitrary combinations of deflection interpolation and bending moment approximations. A novel expression of the combined hybrid method for plate bending problems is introduced to clarify its intrinsic mechanism of enhancing coarse-mesh accuracy and stability of lower order displacement schemes. For a given displacement approximation, appropriate choices of the bending moment mode and the combination parameter α ∈ (0,1) can lead to accurate energy approximation which generally yields numerically high accuracy of the displacement and bending moment approximations.By virtue of this mechanism, improvement of Zienkiewicz triangular plate-element is discussed. The deflection is approximated by Zienkiewicz incomplete cubic interpolation. And three kinds of bending moments approximations are considered: a 3-parameter constant mode, a 5-parameter incomplete linear mode, and a 9-parameter linear mode. Since the parameters of the assumed bending moments modes can be eliminated out at an element level, thecomputational cost of the combined hybrid counterparts of Zienkiewicz's triangle are as same as that of Zienkiewicz's triangle. Numerical experiments show that the combined hybrid versions are convergent at different meshes and can attain high accuracy at coarse meshes.