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Multiplicity of the maximum eigenvalue in structural optimization problems
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, Faculty of Science & Engineering.
2016 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 53, no 5, 961-965 p.Article in journal (Refereed) Published
Abstract [en]

Many problems in structural optimization can be formulated as a minimization of the maximum eigenvalue of a symmetric matrix. In practise it is often observed that the maximum eigenvalue has multiplicity greater than one close to or at optimal solutions. In this note we give a sufficient condition for this to happen at extreme points in the optimal solution set. If, as in topology optimization, each design variable determines the amount of material in a finite element in the design domain then this condition essentially amounts to saying that the number of elements containing material at a solution must be greater than the order of the matrix.

Place, publisher, year, edition, pages
Springer Publishing Company, 2016. Vol. 53, no 5, 961-965 p.
Keyword [en]
Maximum eigenvalue – Multiplicity – Structural optimization
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-125066DOI: 10.1007/s00158-015-1380-3ISI: 000374972500003OAI: oai:DiVA.org:liu-125066DiVA: diva2:902686
Note

Funding agencies: Swedish Foundation for Strategic Research [AM13-0029]

Available from: 2016-02-12 Created: 2016-02-12 Last updated: 2016-05-31

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Thore, Carl-Johan
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Solid MechanicsFaculty of Science & Engineering
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