ABSTRACT

Over the past few decades, the research on the thin plate problems has been carried out by many researchers. Because the C1 continuity which is required by the thin plate element based on the Kirchhoff theory is rather difficult to guarantee for the assumed displacement fields, the focus has switched to the Mindlin-Reissner plate theory, by reason that only the C0 continuity is required for the Mindlin-Reissner plate element. The Mindlin-Reissner plate elements today become the most popular model to calculate the thin and moderately thick plate. But the displacementbased Mindlin-Reissner plate elements commonly suffer from numerical over-stiffness and shear locking which often bring in inaccuracy for the analysis of thin plates. Many successful methods to avoid the shear locking in the displacement-based models have been presented, such as the reduced and selective integration approach, assumed shear strain fields and penaltyparameter modifications (Tessler 1985). As the most commonly used method, the reduced and selective integration can avoid the shear locking effectively but may result in singularity of the system stiffness matrix. Moreover, spurious zero energy modes usually exist in the plate elements. To overcome all the shortcomings mentioned above, the LIM, which was first presented by (Liu & Zhang 1997) for material nonlinear problem, is employed to analyze thin and moderately thick plate.