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Author: Chen, Shikui
Supervisor: Chen, Wei
Institution: Northwestern University, Evanston, Illinois
Topology optimization has played a critical role in engineering design due to its capability of creating innovative design concepts by formulating a design problem as an optimal material distribution problem. While vast literature on topology optimization exists, most of the current work is focused on deterministic structural design without the consideration of uncertainty and multi-physics phenomena which are ubiquitous in real-world problems. The primary goals of this dissertation are twofold: First, to develop a new method for Robust Shape and Topology Optimization (RSTO) which can bridge the present gap between design under uncertainty and topology optimization. Second, to extend the contemporary level-set based topology optimization approach to a broader area of multi-material and multi-physics shape and topology optimization.
Typical design under uncertainty consists of three fundamental issues: uncertainty modeling, uncertainty propagation, and probabilistic optimization. These issues exist in a more challenging form in RSTO when combined with the infinite dimensional characteristics of topology optimization and random field uncertainty. In Chapters 2 to 4 of this dissertation, these key research issues are directly addressed by integrating the state-of-the-art level set methods for shape and topology optimization and the latest research development in design under uncertainty. A unified, mathematically rigorous and computationally efficient framework is developed for RSTO considering various sources of high-dimensional uncertainties, including those in operational conditions, materials, and geometry. In particular, the unique capability of topology optimization under geometric uncertainty distinguishes the proposed method from existing work in topology optimization under uncertainty.
To meet the challenge in identification of fast, accurate methods and rational criteria for the design of multi-material and multi-physics devices, a level-set based topology optimization approach is developed in Chapter 5 of this dissertation to synthesize mechanical energy harvesting devices for self-powered micro systems. The energy harvester design problem is formulated as a variational problem, where the optimal geometry is sought by maximizing the energy conversion efficiency of the device. The reconciled level set (RLS) method is employed for multi-material representation. Designs of piezoelectric energy harvesting devices with both single and multiple materials are identified, all of which constitute obvious improvements to existing designs.
As a by-product of the research, the level-set representation is introduced into metamodel-based design optimization in Chapter 6, which results in a multi-response and multistage metamodeling approach for generic optimization problems. The systematic integration of level-set representation with metamodel uncertainty quantification offers the flexibility of building metamodels for multiple responses (objective/constraints) simultaneously and possesses superior efficiency in design exploration.
In summary, this dissertation represents significant advances in using level-set methods for engineering design. It entails the first attempt in achieving a unified RSTO framework for mitigating risks caused by comprehensive sources of uncertainty including operating conditions, materials, and geometric uncertainties. Extending level-set based topology optimization to multimaterial and multi-physics optimization will result in a wide range of advanced applications. The implementation of level set method to metamodel-based design provides a flexible and efficient approach to real-world engineering design problems.