中文摘要：

柔性机构在制造和运行过程中会存在各种不确定因素。基于多椭球凸模型描述,考虑荷载及材料属性的不确定性,采用人工弹簧方法和几何非线性有限元分析手段,提出以输出端位移最大化为目标、具有最小输入端性能约束的柔性机构拓扑优化数学模型。采用伴随法给出设计变量灵敏度计算公式,提出数值计算不稳定性的简易处理方法,利用数学规划法实现优化问题的求解。反向器机构和微夹钳机构的设计算例验证了所提出优化模型的正确性及算法的有效性,并通过与确定性设计结果的比较,说明了在柔性机构拓扑设计阶段考虑不确定性的重要意义。

英文摘要：

Various uncertainties exist in the manufacture and operation process of compliant mechanisms.Based on the uncertain description of the multi-ellipsoid convex model for loading and material properties,a mathematical model for topology optimization of compliant mechanisms with the maximization of output displacement as objective and with the constraint on the minimum input performance is proposed.In this model,the artificial spring method and the geometrical nonlinear finite element method are adopted.The adjoint method is employed to give design sensitivity computing formulae,and a simple treatment technique for numerical instabilities is proposed.The optimization problem is solved by the gradient-based mathematical programming method.Design examples of a force-inverting mechanism and a micro-gripping mechanism verify the correctness of the proposed optimization model as well as the applicability of the proposed numerical techniques.The solution comparison between the present design and the deterministic design shows the importance of incorporating uncertainties in the topology design phase of compliant mechanisms.