Topology Optimization Algorithms for Additive Manufacturing

Topology optimization is a powerful free-form design tool that couples finite element analysis with mathematical programming to systematically design for any number of engineering problems. Additive manufacturing (AM), specifically 3D printing, is a manufacturing process where material is added through deposition or melting in a layer-by-layer fashion. Additively manufactured parts are `built' from the bottom up, allowing production of intricate designs without extra effort on the part of the engineer or technician -- complexity is often said to be `free'. This dissertation seeks to leverage the full potential of this burgeoning manufacturing technology by developing several new design algorithms based on topology optimization. These include multi-material projection methods appropriate for multiphase 3D printers, an overhang-prevention projection method capable of designing components that do not need sacrificial anchors in metal AM processes, and models for simultaneously optimizing topology and objects embedded in process. These algorithms are demonstrated on several design examples and shown to produce solutions with capabilities that exceed existing designs and/or that require less post-processing in fabrication. Targeting the capabilities of the Polyjet Stratasys 3D printers, a topology optimization algorithm is developed for the design of multi-material compliant mechanisms in which the algorithm ultimately designs both the topology of the part and the placement of each material -- one stiff, one more compliant. Results -- obtained through development of a both a new multi-material model and through development of a robust topology optimization technique for the elimination of one-node hinges -- show the ability to place both soft and stiff material and lead to dramatic improvements in performance of compliant mechanisms. One of the manufacturing challenges in metal powder-based 3D printing technologies is material curling due to internal stress development from the heating and cooling cycle during the printing process. To counteract this phenomena, sacrificial support material is introduced to anchor the part to the build plate, which must then be removed chemically or mechanically in post-production: a time consuming process. Components requiring no post-printing material removal are achieved through development of a topology optimization algorithm to design components to respect a designer-prescribed maximum overhang angle, such that the optimized part can be manufactured without using sacrificial support anchors. Solutions are shown to satisfy the prescribed overhang constraint, along with minimum feature length scale constraints as needed. Finally, an algorithm is developed considering the ability to embed discrete objects such as stiffeners or actuators within a monolithic printed part. Herein, a hybrid continuum-truss topology optimization algorithm is developed to leverage this potential capability, where the algorithm designs not only the continuum phase, but also places discrete truss members within this phase. With an eye towards future AM capabilities, the algorithm is demonstrated on the more contemporary design problem of strut-and-tie models in reinforced concrete design. It is shown that the algorithm is especially useful for designing within complex design domains in which the flow of forces is not obvious. While an exciting direction, it is noted that further advancements in 3D printing technology are needed to allow for such printed topologies