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Mathematical theory of a relaxed design problem in structural optimizationVarious attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.
Document ID
19940004699
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Kikuchi, Noboru
(Michigan Univ. Ann Arbor, MI, United States)
Suzuki, Katsuyuki
(Michigan Univ. Ann Arbor, MI, United States)
Date Acquired
August 16, 2013
Publication Date
January 1, 1990
Publication Information
Publication: NASA. Langley Research Center, The Third Air Force(NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization
Subject Category
Numerical Analysis
Accession Number
94N71454
Funding Number(s)
CONTRACT_GRANT: DHHS-PHS-G-2-R01-AR34399-04
CONTRACT_GRANT: N00014-88-K-0637
CONTRACT_GRANT: NAG3-1160
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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