The combined hybrid nite element method for plate bending problems allows arbitrary combinations f de ection 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 nite element models. For a given displacement approximation, appropriate choices of the bending moment mode and the combination parameter ∈(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 de ection 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.

By following the geometric point of view in mechanics combined with mathematical analysis, a novel expression of the combined hybrid variational principle is introduced to clarify its intrinsic mechanism of enhancing coarse-mesh-accuracy and stability of lower-order displacement schemes. It is pointed out that the combined hybrid scheme achieving energy optimization leads to enhancement of accuracy at coarse meshes. By this mechanism’s bringing to light the two factors (adding energy-compatible bubbles and adjusting the combination parameter) governing this enhancement, this paper presents a sound procedure for optimizing a combined hybrid scheme in a manner independent of the choice of assumed stresses. The e ectiveness of the procedure is veri ed by improving Allman' s membrane element with drilling d.o.f.' s. The numerical benchmark tests indicate that the combined hybrid counterpart of Allman' s membrane element is capable of attaining the degree of accuracy of linear strain (i.e. 2-order) element at coarse meshes without distortion. Copyrigh

Several methods have been developed in the literatures of computational mechanics to improve the performance of the conventional lower-order displacement finite elements which yield poor results for problems with bending and for nearly incompressible medium. This paper is devoted to a unified analysis of convergence for Pian–Sumiharas, Chen-Cheungs and Piltner-Taylor s enhanced stress/strain schemes. By virtue of the energy compatibility and the rank condition, error estimates for these typical finite elements of high prformance are obtained in a unified framework, and especially, weakly locking-free error estimates with respect to the Poisson s ratio m in energy norms are obtained uniformly for v ≤ (1-Ch) =2 as h → 0, where C is a constant independent of m and the mesh size h. Very much the same about the three methods is pointed out.

A hybrid stress quadrilateral macro-element HQM is proposed. Compatible linear displacements are used on its two triangular sub-domains, and a 5-parameter incomplete linear stress mode is suggested. Equivalence to another quadrilateral element HQ4 with compatible isoparametric bilinear displacements is proven. Due to elimination of stress parameters at the element level, the computational cost of HQM/HQ4 is as same as that of Q4. Numerical tests show that the element is accurate, insensitive to mesh distortions, and free from Poisson locking.

and satisfying the energy compatibility condition is shown to be an ultimate key to obtaining optimal tress modes. By using compatible isoparametric bilinear (Q4) displacements and 5-parameter energy ompatible stresses of the combined hybrid nite element CH(0-1), a robust 4-node plane stress element ECQ4 is derived. Equivalence to another hybrid stress element LQ6 with 9-parameter complete linear stresses based on a modi ed Hellinger–Reissner principle is established. A convergence analysis is given and numerical experiments show that elements ECQ4\LQ6 have high performance, i.e. are accurate at coarse meshes, insensitive to mesh distortions and free from locking. Copyright? 2003 John Wiley & Sons, Ltd.