On two formulations of an optimal insulation problem |
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Authors: | E Munoz G Allaire M P Bendsøe |
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Affiliation: | (1) Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France;(2) Department of Mathematics, Technical University of Denmark, 2800 Lyngby, Denmark |
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Abstract: | Two formulations for the design of the optimal insulation of a domain are investigated by computational means. The results
illustrate the similarities and differences that result from the two approaches. One method is in the format of a topology
design problem of distributing insulating material in a domain surrounding a non-design domain that is heated by a given heat
source; this problem is treated in both a relaxed format and a penalized material format. The other approach deals with the
optimal distribution of a thin layer of insulation on the boundary of the non-design domain; this problem is more in the realm
of shape design, or rather, it is similar to optimal design of support conditions for structures. In both cases, mathematical
programming is used, but for the shape design case, it is applied to the non-linear analysis problems that arise when the
optimal design is explicitly solved for. |
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Keywords: | Insulation Topology optimization Shape design |
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