Geometrically nonlinear design of compliant mechanisms: Topology and shape optimization with stress and curvature constraints

Abstract

In this work, we exploit a sequential topology and shape optimization framework to design compliant mechanisms. We pay particular attention to a refined and exact design of flexure hinges via shape optimization in a geometrically nonlinear setting. We propose improved adaptive shape and domain refinement strategies for the embedding domain discretization method (EDD) to achieve numerically and geometrically accurate designs of the flexure hinges. Furthermore, to account for durability and manufacturability of the flexure hinges, we employed local stress constraints and a curvature constraint. The local stress constraints are integrated into an augmented Lagrange functional together with the output displacement to form a combined objective response. The design update is realized by employing and adapting the traction method for the specifics of the embedded boundary. Hence, the curvature constraint does not appear in a standard response form, but is rather introduced into the auxiliary boundary value problem (BVP) of the traction method via a penalty functional. The novelties of this work include: (1) enhanced adaptive shape and domain refinement strategies for EDD; (2) geometrically nonlinear shape optimization using EDD; (3) adapted traction method with curvature constraint.