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

By following the geometric point of view in mechanics, a novel expression of the com-bined hybrid method for plate bending problems is introduced to clarify its intrinsic mech-anism of enhancing coarse-mesh accuracy of conforming or nonconforming plate elements. By adjusting the combination parameter a Є (0,1), and adopting appropriate bending moments modes, reduction of energy error for the discretized displacement model leads to enhanced numerical accuracy. As an application, improvement of Adini' s rectangle is discussed. Numerical experiments show that the combined hybrid counterpart of Adini' s element is capable of attaining high accuracy at coarse meshes.

This paper proposes a quadrilateral finite element method of the lowest orderfor Reissner-Mindlin (R-M) plates on the basis of Hellinger-Reissner variationalprinciple, which includes variables of displacements, shear stresses and bendingmoments. This method uses continuous piecewise isoparametric bilinear interpolationfor the approximation of transverse displacement and rotation. Thepiecewise-independent shear stress/bending moment approximation is constructedby following a self-equilibrium criterion and a shear-stress-enhanced condition. Apriori and reliable a posteriori error estimates are derived and shown to be uniform with respect to the plate thickness t. Numerical experiments confirm the theoreticalresults.

Based on a weighted average of the modified Hellinger–Reissner principle and its dual, the combined hybrid finite element (CHFE) method was originally proposed with a combination parameter limited in the interval (0, 1). In actual computation this parameter plays an important role in adjusting the energy error of discretization models. In this paper, a novel expression of the combined hybrid variational form is used to show the relationship between the resultant method and some Galerkin/least-squares stabilized finite scheme for plate bending problems. The choice of combination parameter is then extended to (-1, 0) S (0, 1). Existence, uniqueness and convergence of the solution of discrete schemes are proved, and the advantage of the parameter extension in computation is discussed. As an application, improvement of Adini’s rectangular element by the CHFE approach is performed.