Structural Topology Analysis and Optimization Methods for Large-scale Problems and High-order Discretizations

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Fu, Yicong
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Daniel Guggenheim School of Aerospace Engineering
The Daniel Guggenheim School of Aeronautics was established in 1931, with a name change in 1962 to the School of Aerospace Engineering
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https://hdl.handle.net/1853/77924
Abstract
Established in 1988, structural topology optimization has become a promising method for designing high-performance structures with unconventional and sophisticated patterns that are not straightforward for human engineers to comprehend and develop. On the other hand, topology optimization faces challenges to be adopted for wider engineering applications, such as the demanding development and computational cost of the numerical simulation, and the occasional lack of robustness of solving the underlying mathematical optimization problems. This dissertation aims to contribute to both mathematical programming algorithms specific to topology optimization, and high-order numerical schemes and discretizations. For the first part, a benchmarking study is performed that identifies some performance deficiency of the nonlinear optimizers on certain types of structural topology optimization problems compared to the method of moving asymptotes. Then a quasi-Newton correction technique is proposed that is compatible with general-purpose second-order optimization methods that employ a quasi-Newton approximation scheme. Superiority are demonstrated based on linear compliance and natural frequency problems. Suitability for large-scale problems of the proposed optimization method is also demonstrated. For the second part, an Galerkin method-oriented algorithmic differentiation (AD) approach is developed to speed up the code development of complex physical models for both the forward analysis and the sensitivity evaluation, and then demonstrated using a high-order finite element framework. Next, a high-order cut-element continuous Galerkin difference (cut-CGD) method is developed that employs various stencil construction techniques and treatments of the void domain to improve robustness for topology optimization. Finally, with the developed AD method and the cut-CGD method, a topology optimization framework based on the level-set method is developed that is capable of performing high-order analyses for both the bulk physics within the analysis domain, and also physics on the cut interface of the domains.
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2025-04-28
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