中文摘要：

研究了基于离散Kirchhoff理论(DKT)的DKT9和DKT6平板弯曲单元,推导了各自的应变-位移矩阵,实现了两种板单元与线形三角形(CST)薄膜单元的叠加.考虑了薄膜内力及弯曲应力的综合作用,较为真实地反映了实际变形情况,在开发的一步模拟法求解器InverStamp/onestep中得到了实现.通过一筒形件的拉深成形分别对这两种单元进行了分析.通过比较,证明了在板料成形一步模拟法中两种单元均能够较为真实地反映实际变形情况,DKT6比DKT9板单元具有较好的计算效率,计算精度相差不大.

英文摘要：

Because of low order, simplicity, efficiency and compatible displacement, triangular plate elements based on discrete Kirchhoff theory (DKT) are the hot spots in fields such as sheet metal. The theories of DKT9 and DKT6 plate bending elements were searched and the strain-displacement matrixes were deduced individually. The constant strain triangular (CST) membrane element and plate bending elements were superposed to take into account of membrane force and bending effect, which in turn reflects the real forming process more precisely. The mentioned two DKT elements were implemented in the developed in-house one step solver InverStamp/one-step. The application to cylindrical box deep drawing presented with comparisons between the two elements witnesses high efficiency and acceptable reliability of DKT6 plate element.