About this Abstract |
Meeting |
2022 Annual International Solid Freeform Fabrication Symposium (SFF Symp 2022)
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Symposium
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2022 Annual International Solid Freeform Fabrication Symposium (SFF Symp 2022)
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Presentation Title |
Using Mean Curvature of Implicitly Defined Minimal Surface Approximations to Generate New Unit Cells for Lattice Design |
Author(s) |
Joseph W. Fisher, Simon W. Miller, Joseph Bartolai, Michael A. Yukish |
On-Site Speaker (Planned) |
Joseph W. Fisher |
Abstract Scope |
Triply Periodic Minimal Surfaces (TPMS) are smoothly varying surfaces that exhibit zero mean curvature at all points on the surface. TPMS can be modeled with high accuracy using discrete differential geometry techniques. However, generating a useful number of unit cells with this approach would be computationally expensive, and variable lattices would be impossible. Level sets of Fourier series approximations are often used instead. While these approximations have continuous geometry, they no longer retain zero mean curvature like the exact TPMS. In this paper, we calculate the mean curvature of the commonly used approximations of the gyroid and D-surface TPMS. Using isosurfaces of the mean curvature from these approximates, we define, similar but unique surface topologies. The development of these surfaces expands the list of lattices available to designers, broadening the lattice design space. Application to other approximations and further study of the application of these new surfaces is discussed. |
Proceedings Inclusion? |
Definite: Post-meeting proceedings |