Abstract: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.
