New rectangular plate elements based on twist-Kirchhoff theory

作者：Brezzi F; Evans J A^*; Hughes T J R; Marini L D

来源：Computer Methods in Applied Mechanics and Engineering, 2011, 200(33-36): 2547-2561.

DOI：10.1016/j.cma.2011.04.012

• Plates
• Finite elements
• One-point quadrature
• Twist-Kirchhoff theory

We introduce a new framework for the development of thin plate finite elements, the "twist-Kirchhoff theory". A family of rectangular 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 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. These are also generalized to the higher-order elements in the family. Numerical tests corroborate the theoretical results.

• 出版日期2011