板料成形数值模拟中无旋转自由度的三角形与四边形壳单元模型

Rotate-free three node triangular and quadrilateral shell elements in sheet metal forming simulations

利用全拉格朗日(TL)格式和Kirchhoff壳体理论,建立了无旋转自由度的三角形和四边形两种壳单元模型。对于有限元计算效率来讲,计算时间是与每个结点自由度呈三次指数关系,这两种壳单元模型的每个结点仅有3个自由度,并且避免了更新拉格朗日(UL)格式所要求的每个时间步均更新参考构形,从而大大提高了计算效率。实例表明,这两种单元模型无论是在计算精度还是在计算效率方面,都可以满足当前工程实际要求。

Using Total Lagrange （TL） format and Kirchhoff shell theory, this paper established rotate-free triangular and quadri- lateral shell element models. For computing efficiency of finite element, computing time is proportional to the third power of de- grees of freedom per node, while the two element models are only 3 degrees of freedom per node, and avoid updating reference conformation at each time steps for Updating Lagrange （UL） format, so increase the computing efficiency remarkably. The ex- ample shows that the two element models can satisfy with practically request of currently engineering.