Methods in Computational Design and Optimization
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AbstractComputational design allows creation of functional objects by using accurate computational models and 3D printing technologies. As a result, not only is customization of functional objects possible; but it also eliminates the need for expert domain knowledge required to intuitively model the functionality. Shape representation and parameterization, combined with numerical simulation, are used to create an accurate model of the real world response of an object. Then, to achieve the desired functionality, mathematical optimization is used to efficiently search over parameterized space for possible variations and physical energy spaces of an object's design.
By using a structured method to search over these parametric spaces, i.e., using nonlinear and often constraint multi-objective optimization methods, we guarantee the most optimal design of the object. This optimized design is 3D print ready and functional. My work has focused on developing optimization schemes for computational design problems, namely -- walking automata, bistable structures, and contact sound spectrum design. Such problems are variations of physical energy minimization of designs, and I propose ways to optimize them.
For walking automata, starting with an initial unstable non-walking linkage configuration, I develop a sampling based optimization scheme to search the highly nonlinear space of possibly stable walking automata. Further, improvements in the efficiency of the optimization strategy are gained by learning a space of valid linkage configurations. Linkage chains can also be used for creating bistable structures. I quantify static stability of the linkage structure through the geometry of the physical energy and develop a non-linear constraint-optimization scheme to guarantee second-order stability for bistable planar structures. Finally, I study the sound spectrum design of metallic 2D and 3D objects. Here, I develop a hybrid local-global optimization scheme which gives precise control over the frequencies and corresponding amplitudes of objects.
With ubiquitous 3D printing and fast computational models, we can create personalized functional objects. My research helps realize this goal, leading to a world where objects are created for customized functions and increased efficiency. A systematic study of the aforesaid problems provides general recipes for problems of physical energy minimization in computational design.
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