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oai:www.ideals.illinois.edu:2142/24071 2023-07-10 col_2142_5131 col_2142_14787 com_2142_5130 com_2142_9630 com_2142_234

Tortorelli, Daniel A. Brittain, Kevin 2011-05-25T14:59:51Z 2011-05-25T14:59:51Z 2011-05-25T14:59:51Z 2011-05 We describe a systematic approach for the robust optimal design of linear elastic structures subjected to unknown loading using minmax and topology optimization methods. Assuming only the loading region and norm, we distribute a given amount of material in the design domain to minimize the principal compliance, i.e. the maximum compliance that is produced by the worst-case loading scenario. We evaluate the principal compliance directly by satisfying the optimality conditions which take the form of a Steklov eigenvalue problem and thus we eliminate the need of an iterative nested optimization. To generate a well-posed topology optimization problem we use relaxation which requires homogenization theory. Examples are provided to demonstrate our algorithm. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-04-27T21:07:20Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Brittain_Kevin.pdf: 637625 bytes, checksum: 68ae8353ae33e304e7e6e7f1e8332b23 (MD5) Made available in DSpace on 2011-05-25T14:59:51Z (GMT). No. of bitstreams: 2 Brittain_Kevin.pdf: 637625 bytes, checksum: 68ae8353ae33e304e7e6e7f1e8332b23 (MD5) license.txt: 4064 bytes, checksum: 6bbbabf6fc5b776c38d28fe49384fc88 (MD5) http://hdl.handle.net/2142/24071 en Copyright 2011 by Kevin Brittain Topology Optimization Homogenization Robust Design Minmax topology optimization Mechanical Sci & Engineering 1917 Mechanical Engineering 0133 University of Illinois at Urbana-Champaign Thesis M.S. MS:Mechanical Engineerng -UIUC 10KS0133MS