Generalized mixed variational methods for Reissner plate and its applications

Based on the mechanism of shear locking phenomenon and potential functional of Reissner plate bending problem, the generalized mixed variational principle for Reissner plate analysis is presented by parameterized Lagrange multiplier method. The proposed variational functional contains splitting factors which are able to adjust the shear potential energy and shear complementary energy components in it. The generalized mixed finite element formulation of bilinear quardrilateral element for Reissner plate bending analysis is established in terms of the new variational principle. The stiffness of the finite element model can be changed by the alteration of the splitting factors. Thus both the free of shear locking and higher accuracy are obtained by the choice of appropriate splitting factors. The most important is that this paper gives one self-adaptative way to choose the splitting factors for thin and moderately thick plates. This results in the comparative order of magnitude between the bending stiffness and shear stiffness for the arbitrary thickness. In the application of two-by-two exact Gaussian integration scheme to the proposed mixed element model, numerical examples show that free of locking is obtained even in the thin plate limit and high accuracy is given for moderately thick plate.