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dc.contributor.authorLi, Weichen
dc.date.accessioned2018-08-20T15:38:57Z
dc.date.available2018-08-20T15:38:57Z
dc.date.created2018-08
dc.date.issued2018-07-31
dc.date.submittedAugust 2018
dc.identifier.urihttp://hdl.handle.net/1853/60305
dc.descriptionPer the request of the author and advisor, and with the approval of the Graduate Education office, an errata was added just after the title page.
dc.description.abstractThe traditional Optimality Criteria (OC) update in topology optimization suffers from slow convergence, thereby requiring a large number of iterations to result in only a small improvement in the performance and design. To address this problem, we propose to use a novel fixed-point formulation of the OC update to accelerate the convergence. Such strategies can achieve higher convergence rates without overly complexifying the update process. In this thesis, we first provide some mathematical background on fixed-point iteration methods. Then, based on theoretical analysis and numerical experiments, we analyze these methods' respective advantages and drawbacks in the context of topology optimization. The analysis focuses on the methods' design update stability, effectiveness in reducing the design cycles, computational cost, and robustness. Through numerical studies, we found one of the methods, called Periodic Anderson Extrapolation (PAE), is the most stable, effective, economic, and robust approach to speed up OC's convergence. The overall update is named Periodically Anderson Extrapolated Optimality Criteria (PAE-OC). Via several 2D and 3D benchmarks, we demonstrate that the PAE-OC can effectively reduce both the number of iterations and computation time. In addition, this scheme shows good robustness with respect to the change of boundary conditions, problem sizes, and parameters. Finally, we show the scalability of the PAE-OC through a 3D problem consisting of more than 3 million degrees of freedom.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectTopology optimization update
dc.subjectOptimality criteria
dc.subjectFixed-point iteration
dc.subjectPeriodic Anderson extrapolation
dc.subjectConvergence speedup
dc.titleFixed point formulation of optimality criteria for efficient topology optimization
dc.typeThesis
dc.description.degreeM.S.
dc.contributor.departmentCivil and Environmental Engineering
thesis.degree.levelMasters
dc.contributor.committeeMemberYavari, Arash
dc.date.updated2018-08-20T15:38:57Z


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