Energy‐adjustable mechanism of the combined hybrid finite element method and improvement of Zienkiewicz's plate‐element

Abstract

AbstractThe combined hybrid finite element method for plate bending problems allows arbitrary combinations of deflection interpolation and bending moment approximations. A novel expression of the approach discloses the energy‐adjustable mechanism of the hybrid variational principle to enhance accuracy and stability of displacement‐based finite element models. 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's 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 at an element level, the computational 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 can attain high accuracy at coarse meshes. Copyright © 2005 John Wiley & Sons, Ltd.