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