Virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

The virtual element method allows to revisit the construction of Kirchhoff-Love elements because the C1-continuity condition is much easier to handle in the VEM framework than in the traditional finite element methodology. Here we study the two most simple VEM elements suitable for Kirchhoff-Love plates as stated in (Brezzi and Marini (2013)). The formulation contains new ideas and different approaches for the stabilization needed in a virtual element, including classic and stabilization. An efficient stabilization is crucial in the case of C1-continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for C0-continuous elements. This project aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilization. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. These C1-continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates.