Rectangular finite element of thin plate bending in Hamiltonian system based on ACM element

In Hamiltonian system, a new rectangular finite element is developed. Based on variational principle in Hamiltonian system, by introducing finite element method into plate bending problem, the displacement interpolation of the new rectangular element is the same as that of the ACM element. The new rectangular element has 8 nodes. The order of the stress field is decided by the order of the interpolation of the displacements. Then the stiffness equations are obtained after the domain is discreted. So an 8-node rectangular element based on ACM element is obtained. Some examples are given to show the effectiveness of this 8-node rectangular element. Numerical results are presented for problems involving rectangular plates of two different support conditions: (1) all four sides simply supported; (2) all four sides clamped. A remarkable characteristic of the present element is that the solutions of displacement and moment are obtained simultaneously. The results demonstrate that the accuracy of the new 8-node rectangular element is better than that of the classical ACM element.