Connectivity-driven topology optimization for path-following compliant mechanism: a formulation with predictive volume constraints and adaptive strategies for gray element suppression

We propose a topology optimization (TO) formulation and related optimization scheme for designing compliant mechanisms following a user-defined trajectory. To ensure the broad applicability and achieve precisely control of the outputs, geometric nonlinearity with incremental solutions are considered. A challenge in the design optimization of these structures is the development of formulations with satisfactory balance between (i) precise trajectory control and (ii) proper connectivity between the input/output ports and the support. Previously proposed density-based topology optimization formulations typically lack the promotion of the desired load-transferring connections, or usually complicate the design using mixed shape, size, and topology variables to enforce a minimum connectivity. To simplify design progress using exclusive topology variables, i.e., purely density-based TO methods, we propose a relatively straightforward formulation involving commonly used response functions, such as compliance and volume as constraints. For the constraints, the paper provides a scheme for defining corresponding upper limits. Numerical examples of challenging shell and plate design optimization problems demonstrate the effectiveness of the proposed formulation and scheme in the generation of load-transferring connections while limiting the impact on the performance of the path generation functionality.