Modular Topology Optimization of Complaint Structures and Mechanisms: Where Free-Material and Topology Optimizations Meet
- Date:
- Time: 14:00 - 15:30
- Address: Sokolovská 83, Praha
- Room: K3
- Speaker: Jan Zeman
The modular design approach has gained considerable interest due to its potential to efficiently address manufacturing, reusability, and sustainability while maintaining performance comparable to its traditional non-modular counterparts. However, designing such products is a challenging task that involves solving an optimization problem on two levels. First, modules must be optimally distributed within a product-scale domain. Second, the topology of individual modules must be optimized to ensure that they work together seamlessly when assembled. Addressing both problems simultaneously is considerably more complex, as it involves the intricate interplay of discrete and continuous features of the problem. In our previous work on the minimum compliance design of modular truss structures, we adopted a concurrent approach, combining a metaheuristic method for updating the modular assembly plan with second-order cone programming to generate optimal truss-like module topologies. However, this approach relied on a convex formulation, which limited its applicability. We now present a computationally more efficient bi-level sequential strategy that bypasses the need for assembly-level metaheuristics and is applicable to continuum structures and mechanisms. In addition, we incorporate manufacturing constraints using a three-field approach and continuity constraints. Our new approach starts with free material optimization on a modular grid. This step yields optimal, element-wise constant stiffness tensors. We then partition these stiffness tensors into a predetermined number of clusters, taking into account any underlying symmetries. Interpreting the clustering results in terms of the Wang tiling formalism yields the assembly plan, where individual codes on module edges reflect the similarity among the optimized stiffness tensors. Finally, the topology of individual modules is determined by standard single-scale topology optimization, with the design space reduced by a mapping that reflects the modular assembly plan. We demonstrate the efficiency of our strategy on four two-dimensional problems, including the modular minimal conformal Messerschmitt-Bölkow-Blohm beam, two modular conformal mechanisms (an inverter and a gripper), and a combined modular design of both mechanisms. The last example was also successfully validated in mechanical testing utilizing an in-house testing machine and digital image correlation.