Topology optimization of compliant mechanisms with stress constraints and manufacturing error robustness

Abstract

This work proposes a robust formulation to address the compliant mechanism design problem subject to both stress constraints and manufacturing uncertainty. The proposed formulation is an extension of the robust approach for compliant mechanism design based on eroded, intermediate and dilated projections. The novelty in this proposal comes from inclusion of a stress failure criterion in each projected field, in order to ensure compliant mechanisms that satisfy the stress failure criterion even in the presence of uniform manufacturing variations. The objective of the optimization problem is the minimization of the maximum displacement at the output port of the mechanism, given eroded, intermediate and dilated designs, subjected to upper and lower volume constraints and one stress constraint per finite element on each of the three projected fields. The objective function is weighted by the volume of the dilated topology, in order to avoid possible numerical instabilities that may occur when the upper volume constraint is not active. Several examples are solved and the optimized results are post-processed with body-fitted finite element meshes. Numerical results demonstrate that: 1) the proposed stress-constrained robust approach provides results in which both maximum stress and output displacements are robust with respect to uniform boundary variations; however, while the maximum stress is almost insensitive to manufacturing variations, the output displacement does show some degradation when compared with the traditional robust approach; 2) the traditional robust approach, i.e., without the stress considerations, provides results in which the maximum stress has unpredictable and non-smooth behavior after uniform boundary variation; and 3) the stress-constrained deterministic approach, i.e., without considering the manufacturing uncertainty, provides results in which both maximum stress and output displacements are non-robust with respect to uniform boundary variations.