A Framework for Efficient Hierarchic Plate and Shell Elements

Abstract

The Mindlin–Reissner plate model is widely used for the elastic deformation simulation of moderately thick plates. Shear locking occurs in the case of thin plates, which means slow convergence with respect to the mesh size. The Kirchhoff plate model does not show locking effects, but is valid only for thin plates. One would like to have a method suitable for both thick and thin plates. Several approaches are known to deal with the shear locking in the Mindlin–Reissner plate model. In addition to the well known Mixed Interpolation of Tensorial Components (MITC) elements and other approaches based on a mixed formulation , hierarchic methods have been developed in the recent years. These are based on the Kirchhoff model and add terms to account for shear deformations. We present some of these methods and develop a new hierarchic plate formulation. This new model can be discretised by a combination of C0 and C1 finite elements. Numerical tests show that the new formulation is locking free and numerically efficient. We also give an extension of the model to a hierarchic Naghdi shell based on a Koiter shell formulation with unknowns in Cartesian coordinates.