Topology optimization design of compliant mechanisms under uncertainties

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.