中文摘要：

采用拓扑优化方法在给定设计区域内寻求材料的最佳分布，以获得布局合理的2-DOF微动平台新构型。在考虑平台所受载荷的情况下，采用变密度法及连续体柔性结构互能与应变能的比值法，建立了平台单自由度方向上的拓扑优化目标函数，并基于线性加权法建立了2-DOF平台的多目标拓扑优化数学模型，通过对所建模型求解，得到了具有对称双圆弧柔性薄板式弹性单元体的2-DOF微动平台的新构型。对平台的静动态特性进行了有限元分析及实验测试，结果表明：在150V驱动电压作用下，z、y方向的位移分别为16．7μm、15．46μm，位移耦合分别为0．47μm、0．50μm，x,y方向的固有频率均为1．725kHz，在20N阶跃输入力作用下，z、y方向的响应时间均约为13ms。

英文摘要：

To get the optimal distribution of the material in the given design area, a new configuration of 2-DOF micro-positioning stage was obtained using the topology optimization method. Based on the variable density method and the ratio method between the mutual potential energy and strain energy, the objective function of the stage in one degree of freedom for topology optimization was established, in which the load cases of the stage were considered. Based on the linear weighted method, the mathematical model of the stage for multi-objective topology optimization was developed as well. Then, the initial prototype of the stage, which has elastic unit body based on symmetrical double circular flexible sheet, was obtained by solving the obtained model. The static and dynamic performances of the stage were analysed using finite element methods and tested through experiments. Experimental results shows that, under the highest driving vohage of 150 V, the displacements of the stage in x and y directions are 16.7 μm and 15.46μm respectively, the coupling displacements in that two directions are 0.47 μm and 0.50 μm respectively, and the natural frequencies of that two directions are both 1. 725 kHz. Meanwhile, under the input step force of 20 N, the response time of the stage in the two directions are both approximately 13 ms.