Robust Topology Optimization Design of Compliant Mechanisms with Multiple Degrees of Freedom Considering Material Uncertainties

To reduce the sensitivity of mechanisms performance to material uncertainties, a method for robust topology optimization of compliant mechanisms with multiple degrees of freedom considering material uncertainties is proposed. Firstly, the expansion optimal linear estimation method is used to discretize the material random field. Polynomial chaos expansion and Smolyak sparse grid integration method are employed to solve the statistical moment of random response. Then, the input coupling and output coupling constraints are introduced. The maximization of the expected value and the minimization of the standard deviation of the weighted sum of the output displacements of compliant mechanisms with multi-input and multi-output are taken as the objective functions. A mathematical model for robust topology optimization of multiple degree-of-freedom compliant mechanisms with coupling constraints is established. The two self-designed numerical examples of multiple degree-of-freedom microactuators are presented. Compared with the results of deterministic topology optimization without coupling constraints, the configurations of compliant mechanisms with multi-input and multi-output obtained by robust topology optimization with coupling constraints is different, and the performance of the mechanisms has better robustness. The input coupling and output coupling effects can be effectively suppressed. The effectiveness of the proposed method is demonstrated.