A quadrilateral G1-conforming finite element for the Kirchhoff plate model

A quadrilateral bi-cubic G1-conforming finite element for the analysis of Kirchhoff plates is presented. The rational version of the Gregory patch proposed by Loop et al. (2009) is the starting point of our formulation. This version of the Gregory patch consists in rational enhancement of the bi-cubic Bézier interpolation representing a suitable tool for designing G1-conforming quadrilateral element on C0-conforming un-structured meshes. The element includes as additional degrees of freedom the edge rotations like in the Loof-formulations but is only displacement based.