Stabilized Hybrid Lower Order Quadrilateral Elements For Reissner-Mindlin Plates And Convergence Analysis

Based on the energy compatibility condition, two kinds of low order hybrid quadri-lateral elements for Reissner-Mindlin plate are presented in the article, namely RMSQ1and MRMSQ1. Both two elements use continuous isoparametric bilinear interpolationsfor the deflection/rotations displacement. RMSQ1 element contains two variables, dis-placements and shear stress, and the 4-parameter shear stress mode, which is designedin each element independently, is deduced by the energy compatibility condition; basedon the RMSQ1 element, by introducing one kind of 5-parameter bending mode whichsatisfies the energy compatibility condition too, the MRMSQ1 element is obtained.Then the locking-free convergence of both two elements is proven mathematically, andoptimal order of convergence, independent of the plate thickness, is obtained. It'sshown by the standard numerical examples that both two elements can avoid the lock-ing phenomenon, and have good accuracy. MRMSQ1 element has better performancethan RMSQ1 element.