A new conforming finite element for Kirchhoff plates

In this work, we present a new formulation for a class of quadrilateral conforming elements for pure bending Kirchhoff plate problems. The rational enrichment of the cubic B´ezier’s basis, proposed by J. Gregory in 1974 for obtaining G1 continuous surfaces is the starting point for the formulation. It presents 20 degrees of freedom and can be generalized in the context of isogeometric analysis including the knot insertion operation and polynomial degrees different than 3. The rational interpolation is modified in order to obtain a formulation able to reproduce states of constant curvature that passes the patch test. Examples demonstrate that the proposed element presents optimal rate of convergence and presents high robustness with respect to mesh distortions even on non-structured meshes.