SUMMARY

Functionally Graded Lattice (FGL) Structures have shown improved performance over uniform lattice structures in different fields. These structures contain unit-cells of varying porosity based on different functional requirements, which alters the properties of the structures. Another form of functional grading can be seen lattice structures that are not exhibit variation in the unit-cell porosities, but also the size of the unit-cells. These structures are closely similar to materials in nature; hence we will refer to them in this research as Naturally Functionally Graded Lattice (NFGL) structures. However, current methods to generate these structures are limited compared to FGLs. They rely on the use of computationally expensive processes that utilize FEM, stochastic methods that can create uncertainty in the properties of the generated designs, or impose restrictions on the unit-cell size ratio that can be achieved due to the use of dithering filters.

To address these issues, this research aims to develop a framework to generate unrestricted NFGLs in a computationally efficient manner and in a deterministic way. For this purpose, the algorithm will utilize a developed simplified sphere packing algorithm with a uniform grid of nodes that conforms to the design domain surface, in order to generate the nodes that will serve as the base nodes for the NFGL structure based on a density field input. Once the nodes are generated, the algorithm will create Delaunay Triangulations from the generated nodes to create a mesh that will be used to create the struts and diameters of the NFGL structure. To further improve the performance of the generated structure, a similarity analysis using the Mean Structural Similarity (MSSIM) to correlate the similarity of the NFGL structure with the density field input is carried out. The similarity analysis will help in assessing and improving the performance of the NFGL structure based on the MSSIM value. Furthermore, application examples will be provided to compare the performance of NFGL structures against FGL structures.