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Construction of a Class of Sharp Löwner Majorants for a Set of Symmetric Matrices

Journal of Applied Mathematics. 2020;2020 DOI 10.1155/2020/9091387


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Journal Title: Journal of Applied Mathematics

ISSN: 1110-757X (Print); 1687-0042 (Online)

Publisher: Hindawi Limited

LCC Subject Category: Science: Mathematics

Country of publisher: United Kingdom

Language of fulltext: English

Full-text formats available: PDF, HTML, ePUB, XML



Mauricio Fernández (Institute of Applied Mechanics, University of Stuttgart, Pfaffenwaldring 7, 70569 Stuttgart, Germany)

Felix Fritzen (Institute of Applied Mechanics, University of Stuttgart, Pfaffenwaldring 7, 70569 Stuttgart, Germany)


Blind peer review

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Time From Submission to Publication: 18 weeks


Abstract | Full Text

The Löwner partial order is taken into consideration in order to define Löwner majorants for a given finite set of symmetric matrices. A special class of Löwner majorants is analyzed based on two specific matrix parametrizations: a two-parametric form and a four-parametric form, which arise in the context of so-called zeroth-order bounds of the effective linear behavior in the field of solid mechanics in engineering. The condensed explicit conditions defining the convex parameter sets of Löwner majorants are derived. Examples are provided, and potential application to semidefinite programming problems is discussed. Open-source MATLAB software is provided to support the theoretical findings and for reproduction of the presented results. The results of the present work offer in combination with the theory of zeroth-order bounds of mechanics a highly efficient approach for the automated material selection for future engineering applications.