非协调曲边四边形十二自由度平板弯曲单元

Incompatible Curved Quadrilateral Plate Bending Element with 12 Degrees of Freedom

本文利用精确元法,给出一个十二自由度曲边四边形板弯曲单元.该方法不需要变分原理,适用于任意正定和非正定偏微分方程.利用这个方法,单元之间的协调条件很容易满足,仅须位移和内力在单元节点上连续,即可保证所得到的解收敛于精确解.利用本文方法所获得的解,无论是位移还是内力可同时有二阶收敛精度.文末给出数值算例.表明了本文所得到的单元有非常好的精度.

This paper presents a new curved quadrilateral plate element with 12 degrees of freedom by the exact element method[1]. The method can be used to arbitrary non-positive and positive definite partial differential equations without variation principle. Using this method, the compatibility conditions between elements can be treated very easily, if displacements and stress resultants are continuous at nodes between elements. The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed. Numerical examples are given at the end of this paper, which show the excellent precision and efficiency of the new element.