一种四边形广义协调薄板弯曲单元

A Generalized Compatibility Quadrilateral Thin Plate Bending Element

为了降低位移型任意四边形薄板弯曲有限元构造的难度,基于修正最小势能变分原理,提出了一种新的广义协调位移的设计方法,并且构造出一种任意四边形网格下的位移型薄板弯曲单元Q8P。这种单元能够通过常应力分片检查,当弯矩,扭矩和横向剪力沿着单元边界的分布为常值时,由于位移在单元边界非逐点协调而产生的附加能量为零。这种新型的广义协调单元保证了有限元解的收敛性,计算效率高,具有较高的数值精度,并且对网格畸变不敏感。

In order to get over the difficulty in designing the displacement type quadrilateral thin plate bending element, based on the modified minimum potential energy principle, a new method to construct the generalized compatible displacement is proposed, and a displacement type quadrilateral thin plate bending element Q8P is presented in this paper. The new element passes the constant stress patch test. When the boundary bending moment, twisting moment and transverse shear are constants, the additional energy caused by the nonconforming displacement vanishes. This element is convergent, efficient and promises high accuracy. Moreover, it is insensitive to mesh distortion.