Topology Optimization of Architected Latticeswith Geometric Primitives

This thesis advances novel computational techniques to design multi-material, multi-scale and programmable truss lattices. The architecture of lattice materials can be engineered to exhibit desired behavior. I focus on truss lattices made of cylindrical struts, which lead to open-cell designs that are more amenable to additive manufacturing. In this work, I use topology optimization to determine the optimal design of the periodic unit cell to attain extremized mechanical properties. Finite element analysis of the unit cell and numerical homogenization are employed to determine the effective properties of the lattice. To efficiently perform the analysis of the unit cell for any lattice layout without having to re-mesh, this work uses the geometry projection method, in which a high-level parametric representation of the struts is mapped onto a density field discretized on a fixed mesh. The techniques advanced in this work aim to push the performance limits of lattices by formulating novel design methodologies that exploit design possibilities beyond merely optimizing the spatial layout of the struts. Three mechanisms are considered towards this end. First, I formulate a topology optimization technique to design multi-material lattices, whereby each strut is made of a single material out of a prescribed set, and in which the optimization simultaneously determines the struts layout and selects the best material for each strut. Second, I advance techniques to design two-scale lattices with transversely isotropic struts that are either hollow or reinforced by long fibers. I extend this formulation to consider the simultaneous design of a structural component made of a uniform-thickness skin and a two-scale lattice infill. The third mechanism considers programmable lattices whose struts can be activated/deactivated by some physical means, thus rendering different effective properties. I advance topology optimization techniques to simultaneously design the layout and program the open/close state of the struts to obtain multiple desired properties