考虑输出刚度不确定性的柔顺机构拓扑优化设计

Topological Design of Compliant Mechanisms Considering Uncertainties of Output Stiffness

为了降低机构性能对输出刚度不确定因素的敏感程度,提出一种考虑输出刚度不确定性的柔顺机构拓扑优化设计方法。采用区间模型描述输出刚度的不确定性,利用多项式混沌展开式(Polynomial chaos expansion, PCE)和Smolyak稀疏网格积分法计算随机响应统计矩,以机构输出位移的期望值最大化和标准差最小化为目标函数,以机构结构体积为约束,建立考虑输出刚度不确定性的柔顺机构稳健性拓扑优化模型,采用移动渐近线优化算法更新设计变量。夹持器和咬合机构数值算例验证提出设计方法的有效性,与确定性拓扑优化结果比较,稳健性拓扑优化设计获得的柔顺机构构型有所不同,机构的输出位移标准差减小,有效地降低机构对输出刚度不确定性的敏感程度。随着加权系数增大,获得的柔顺机构输出位移标准差和期望值减小。随着不确定输出刚度幅值增大,获得的柔顺机构输出位移标准差增大,并且输出位移期望值有所减小。

To reduce the sensitivity of the performance to the uncertainties of the output stiffness, a method for topology optimization of compliant mechanisms considering uncertainties of the output stiffness was proposed. The interval model was employed to describe uncertainties of the output stiffness. The polynomial chaos expansion and Smolyak sparse grid method were applied to calculate the statistical moments of the structural responses. Maximization of the expected value of the output displacement and minimization of the standard deviation of that were developed as the objective function, and the structure volume was used as the constraint. The model for robust topology optimization of compliant mechanisms considering uncertainties of the output stiffness was established. The design variables were updated by the method of moving asymptotes. Numerical examples such as compliant gripper and crunching mechanism were presented to demonstrate the validity of the proposed method. Compared with the results of deterministic topology optimization, the optimal configurations of compliant mechanisms obtained by robust topology optimization were different, and the standard deviation of the output displacement was decreased. Thus, the sensitivity of the mechanical performance to the uncertainties of the output stiffness can be reduced effectively. As the weighting coefficient was increased, the expected value and standard deviation of the output displacement of the mechanism were decreased. As the amplitude was increased, the standard deviation of the output displacement was increased, and the expected value of the output displacement was decreased.