An implicit strong G1-conforming formulation for the analysis of the Kirchhoff plate model

In this work, we present a quadrilateral plate element for the Kirchhoff plate bending model that satisfies the continuity requirements in implicit way. The element is designed on the basis of the rational Gregory’s enhancement of the bi-cubic Coons patch. This Coons-Gregory patch is based on the boundary data set of a surface, that accounts for both the displacement and the edge rotation along the sides of the element. In this way, an implicitly conforming interpolation with 20-dofs per element is obtained. The Coons-Gregory patch ensures G1-conformity only for the case of structured meshes. Numerical examples show that the proposed formulation is highly efficient with respect to accuracy, rate of convergence and robustness.