基于类桁架连续体的柔性机构拓扑优化设计

Topological optimum design of compliant mechanism based on truss-like continuum

以各向异性类桁架连续体为材料模型,以材料在结点位置的密度和主轴方向作为设计变量.结点在指定方向的位移为目标函数,根据有限元分析得到的应力应变场,采用优化准则法优化材料分布形成类桁架连续体.在微机电系统中可直接用各向同性材料,还可通过引入微小间隙使各向同性材料具有方向性.因材料在设计域内是连续分布的,不需要抑制中间密度,避免了其他拓扑优化方法中普遍存在的棋盘格现象、网格依赖性以及局部极值等数值不稳定问题.提供几个算例,并和已有结果进行比较,说明了此方法的有效性.

The anisotropic truss- like continuum is adopted as material model. The densities and principal orientations of material at nodes are selected as design variables. The nodal displacement along the specific direction is selected as the objective function. The stress and strain fields are established by finite element analysis. The truss - like continuum is formed by optimizing material distribution using optimality criteria method. Furthermore plane isotropic continuum with tiny gaps is formed from this result. As material is distributed continuously and intermediate densities are not suppressed, the numerical instabilities, such as checkerboards, mesh -dependence and local minima, which commonly occurs in applications of other topology optimization method, are avoided completely. Several examples are presented and compared with the existed results. The effectiveness of the proposed approach is demonstrated.