Robust Optimization of Surface Topology for Jointed Connections 37 (a) (b) (c) (d) Fig. 7 EPMC results for BRB with quadratic topologies: (a) x2, (b) y2, (c) xy (d) x2 −y2. Each topology compared with flat and amplitude varied as 10µm, 100µmand1000µm, for both positive and negative direction and x-quadratic profiles. For the xy-topology, the growth is less, though significant. The increase in damping factor due to perturbation 4 is 55.8% for flat design (Figure 5), where it got reduced to 17.7% for xy design. A more detailed investigation with the surface profile might be able to mitigate the effect of these strong perturbations. Conclusion and Future Work This work represents a foundational step towards robust optimization of bolted connections. Specifically, it focuses on analyzing various interface topologies to identify an optimal design with minimal sensitivity to manufacturing errors. The BRB is employed as an example problem; it is found that by modifying the interface to have xy curvature, the design can be made robust to manufacturing variability. The EPMC method has proven effective for analyzing vibration characteristics at higher amplitude levels. Additionally, the use of ZTEs at the interface offers a highly effective modeling approach, allowing for detailed interfacial contact mechanics to be captured without the need for re-meshing with each surface topology change. Future work will aim to experimentally validate these findings and explore the use of more sophisticated optimization algorithms. A key requirement will be the development of metrics to quantify the variability in behavior for each interface topology. One potential approach is to introduce a sensitivity metric to measure the variability of the damping factor ζ such as ||(ζDesign + Perturb−ζDesign)/ζFlat||2. Other than this response metric, another system parameter metric can also be defined as the ratio of gap variance in the perturbed system to that of the nominal design. Additionally, the design of such surfaces must
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