Director of Research (if dissertation) or Advisor (if thesis)
Tortorelli, Daniel A.
Department of Study
Mechanical Sci & Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Topology Optimization
Homogenization
Robust Design
Abstract
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.
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