形成不同拉压允许应力Michell桁架的有限元方法

提出了形成具有不同拉压允许应力材料的Michell桁架的有限元方法。采用正交异性材料模型,以结点位置杆件的密度和方向作为设计变量,由结点位置的值插值得到有限单元内部的材料性质,材料在设计域内连续分布,这样避免了单元之间材料性质的突变,因此从根本上避免了单元铰接、棋盘格现象以及单元依赖性等数值计算不稳定性问题。提出了一种基于优化准则法的迭代算法,用以形成不同拉压允许应力材料的Michell桁架。由有限元分析得到结点位置处的主应力方向作为杆件方向,根据主应力方向的应变和材料拉压允许应力调整杆件密度。最后由结点位置的杆件方向形成Michell桁架中连续分布杆件。

Finite element method to establish Micheli truss with unequal permissible stresses for tension and compression

The finite element method to establish Michell truss with different permissible stresses for compression and tension was presented.The orthotropic material model was adopted.The densities and orientations of the members at nodes were taken as design variables.The character of material at any point in element was interpolated by the values at nodes.The material was distributed in design domain continuously,which avoided the break of material character between elements.The numerical instabilities,such as 1-node connected hinges,checkerboards and mesh-dependencies,disappeared entirely.Based on optimality criteria method,the iterative algorithm was presented,which was suitable for material with unequal permissible stresses for tension and compression.The member orientations were oriented along the principal stress directions obtained by finite element analysis.The member densities were adjusted according to the strains along the principal stress directions and permissible stresses for compression and tension.The distributive members in Michell truss were formed from the orientations of members at nodes.