基于ACM单元的Hamilton体系下薄板弯曲问题

Rectangular Finite Element of Thin Plate Bending in Hamiltonian System Based on ACM Element

基于弹性薄板弯曲问题的Hamilton体系变分原理,将有限元方法引入到Hamilton体系下的板弯曲问题,对位移、应力分别采用不同的插值方式,区域离散后得到刚度方程。以ACM单元为基础,发展了一种新单元,推导了有关公式,编程并计算了有关算例,结果表明基于Hamilton体系的有限元单元的有效性与精确性。

In Hamiltonian system, a 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 rectangular element is the same as that of the ACM element. The 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 8-node rectangular element is better than that of the classical ACM element.