New rectangular plate elements based on twist-Kirchhoff theory

We introduce a new framework for the development of thin plate finite elements, the ``twist-Kirchhoff theory.'' A family of quadrilateral plate elements is derived that takes advantage of the special structure of this new theory. Particular attention is focused on the lowest-order member of the family, an eight degree-of-freedom, four-node quadrilateral element with mid-side rotations whose stiffness matrix is exactly computed with one-point Gaussian quadrature. We prove a convergence theorem for it and various error estimates for the rectangular configuration. These are also generalized to the higher-order elements in the family. Numerical tests corroborate the theoretical results.