Topology optimization is a computational process for designing structures and materials that meet some optimality criteria, e.g. minimum weight or maximum stiffness. The technique has gained significant traction among design engineers and has been shown to identify designs where efficient use of materials resulted in unprecedented performance. The objective of this research is to develop a new topology optimization framework capable of designing structural topologies that are robust in the presence of geometric uncertainties. Accounting for dimensional uncertainties in the optimization process is of paramount importance in many engineering applications, for example in processes involving extreme miniaturization of the material architecture, where the physical realization of the optimal design is generally subjected to significant tolerances. The application of this research to state-of-the-art commercially available manufacturing technologies, including additive manufacturing, will greatly impact the development of architected cellular materials and promote technology transfer. Results of this research will be incorporated into graduate courses within the Engineering and Applied Science PhD program at the University of Massachusetts, Dartmouth. This project will provide training for graduate and undergraduate students at UMass Dartmouth (where many students are first generation college students), the University of California, Irvine and Johns Hopkins University.
This research will result in a new design optimization framework capable of designing structural topologies that are robust in the presence of geometric uncertainties. A number of strategies will be explored based on novel integration of stochastic analysis and uncertainty representation and propagation methods with efficient topology optimization techniques and inverse homogenization-based material design frameworks. Stochastic topology optimization frameworks for both continuum and discrete structures will be developed where flaw-tolerance is achieved through careful incorporation of nodal and boundary uncertainties. Novel methodologies for the characterization and representation of geometric uncertainties are planned, including an experimental effort aimed at carefully measuring typical geometric flaws in architected cellular materials fabricated with state-of-the-art additive manufacturing techniques, and quantifying their impact on the statistical variations of the macroscopic mechanical properties. This experimental investigation will feed into the development of a topology optimization framework centered on flaw-tolerance.
