用三角形单元建立拓扑优化类桁架连续体

Topology Optimization of Truss-Like Continuum Structures by Triangle Elements

为克服用矩形单元划分不规则区域的困难,使得结点和单元的分布可控性好,采用三角形常应变单元建立拓扑优化的类桁架连续体.以杆件在结点位置的方向和密度作为设计变量,采用优化准则法进行优化.在迭代过程中,将杆件的方向调整到主应力方向,根据主应力方向的应变调整杆件的密度.通过对单元进行局部加密,能够明显改善杆件汇交点处的拓扑优化结果.算例表明,方法是合理的、有效的.

To overcome the difficulty in dividing irregular design domain by rectangular elements and to distribute the nodes and elements reasonably, the topology optimal truss-like continuum structures are established by triangle elements with constant strain. The densities and orientations of members at nodes are taken as design variables, which is optimized by optimality criteria method. During the iteration, the member orientations are aligned along the principal stress directions. The member densities are adjusted according to the magnitudes of strains along the principal stress. By local mesh refinement, the structures at members＂ intersection become explicit. The rationality and efficiency of the presented method is demonstrated by examples.