The sufficient conditions for an extremum in problems of optimizing the shapes of elastic plates
type: Item
instance of: scholarly article
title: The sufficient conditions for an extremum in problems of optimizing the shapes of elastic plates
zbMATH Open document ID: 0604.73093
DOI: 10.1016/0021-8928(85)90053-X
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: The problems of selecting the thickness distributions of elastic plates in order to maximize the fundamental free vibrations frequency, as well as to minimize the strain potential energy, are considered. Necessary and sufficient conditions are obtained for a weak local extremum in such optimal design problems. These conditions retain their form even for reciprocal problems: minimization of plate weight when there are constraints on the fundamental frequency or the strain potential energy. The conditions obtained include an integral estimate on the maximum growth of second derivatives of the thickness distributions that satisfy the necessary extremum conditions.
Mathematics Subject Classification ID: 74P99
Mathematics Subject Classification ID: 74K20
zbMATH DE Number: 3976549
zbMATH Keywords: thickness distributions
zbMATH Keywords: maximize the fundamental free vibrations frequency
zbMATH Keywords: minimize the strain potential energy
zbMATH Keywords: Necessary and sufficient conditions
zbMATH Keywords: weak local extremum
zbMATH Keywords: optimal design
zbMATH Keywords: reciprocal problems
zbMATH Keywords: minimization of plate weight
zbMATH Keywords: integral estimate
zbMATH Keywords: maximum growth of second derivatives
author: Alexander S. Bratus
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3976549