Topology optimization

The optimization system is available after a preferred model is determined. This system uses a modified topology optimization method based on the bi-directional evolutionary structural optimization with subjective preferences (SP-BESO) method [1]. This method can convert a preferred 3D geometry into weights to affect the formation of optimal structures, thereby resulting in diverse and competitive structural designs [2].

Fig. 1. Workflow of the optimization system in VR-BESO: (a) sculpting the preferred model; (b) creating a design domain; (c) defining optimization parameters; (d) defining loading and boundary conditions; (e) creating finite elements; (f) executing the proposed topology optimization method; (g) smoothing the optimal topology; (h) exporting the smoothed result.

The detailed steps of the optimization workflow are shown as follows:

· Step 1, (Fig. 1(a)): Determine a preferred model by using the sculpting system.

· Step 2, (Fig. 1(b)): Generate a design domain by clicking the ‘Create’ button on the ‘Modeling’ panel. The created design domain is a cubic frame surrounding the sculpted model that aligns with the global directions. It should be noted that the size of the design domain can be adjusted by using the two controllers, as introduced in the 'VR system' page.

· Step 3, (Fig. 1(c)): Adjust the optimization parameters on the ‘Parameters’ panel.

· Step 4, (Fig. 1(d)): Set up loading and support areas by clicking the ‘Load’ and ‘Support’ buttons on the ‘Optimization’ panel. The elemental nodes within these areas are subject to the corresponding loading and boundary conditions. Note that the sizes of these areas are also adjustable by using the two controllers, as introduced in the 'VR system' page.

· Step 5, (Fig. 1(e)): Create finite elements by clicking the ‘Apply’ button on the ‘Optimization’ panel.

· Step 6, (Fig. 1(f)): Run the modified topology optimisation method. The finite elements are removed or added simultaneously until the convergence criteria are satisfied.

· Step 7, (Fig. 1(g)): Smooth the zig-zag boundaries of the optimal result by clicking the ‘Smooth’ button on the ‘Optimization’ panel. Note that the smoothing method may result in a slight difference in structural performance, but this study only uses it for visualization [3].

· Step 8, (Fig. 1(h)): Export the final design.

It should be noted that the smoothed outcome can also be used as the preferred model to initialize the subsequent design exploration. Therefore, users can repeatedly execute Step 1–Step 7. This forms an iterative design exploration that enables designers to improve designs and finally find a solution that fulfills subjective and objective design requirements.

References

[1] Z. Li, T. U. Lee and Y. M. Xie, “Interactive structural topology optimization with subjective scoring and drawing systems,” Computer-Aided Design, vol. 160, 103532, 2023. (DOI: 10.1016/j.cad.2023.103532)

[2] Z. Li, T. U. Lee and Y. M. Xie, “Topology optimisation considering subjective preferences: current progress and challenges,” in Proceedings of the IASS Annual Symposium 2023, Melbourne, Australia, Jul. 10–14, 2023, Y. M. Xie, J. Burry, T. U. Lee and J. Ma Eds., 2023, pp. 2430–2440.

[3] Z. Li, T. U. Lee, Y. Yao and Y. M. Xie, “Smoothing topology optimization results using pre-built lookup tables,” Advances in Engineering Software, vol. 173, 103204, 2022. (DOI: 10.1016/j.advengsoft.2022.103204)