Least-weight design of perforated elastic plates for given compliance: Nonzero Poisson's ratio
type: Item
instance of: scholarly article
title: Least-weight design of perforated elastic plates for given compliance: Nonzero Poisson's ratio
zbMATH Open document ID: 0618.73104
DOI: 10.1016/0045-7825(88)90004-7
author: T. G. Ong
author: G. I. N. Rozvany
author: W. T. Szeto
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1988-01-01T00:00:00Z
review text: In earlier papers of the authors and \textit{R. Sandler}, \textit{N. Olhoff} and \textit{M. P. Bendsaee} [Int. J. Solids Struct. 23, 521-536 (1987; Zbl 0606.73105) and ibid. 537-550 (1987; Zbl 0606.73106)] least-weight solutions were derived for perforated elastic plates having (a) a constant thickness (b) a prescribed compliance value and (c) a Poisson ratio of zero value. In view of earlier mathematical studies by Kohn, Stand, Lurie et al., the above results were based on a microstructure in which ribs of first- and second-order infinitesimal spacing run in the two principal directions. It was found, however, that the optimal solution for axially symmetric plates always consists of (i) unperforated regions or/and (ii) regions with ribs in only one (i.e. the radial) direction. In view of extensive recent study of this problem by leading mathematicians, the above conclusions have important implications. In the current paper, the foregoing results are extended to plates having a nonzero Poisson ratio and the theory is illustrated with examples. Tow solutions given are valid for both prescribed compliance and prescribed defections. This investigation shows that in some unconstrained shape optimization problems the optimal solution cannot be obtained by conventional numerical (e.g. finite element) methods.
Mathematics Subject Classification ID: 74P99
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 4003689
zbMATH Keywords: elimination of nonoptimal layouts
zbMATH Keywords: simply supported uniformly loaded circular plates
zbMATH Keywords: clamped circular plate
zbMATH Keywords: uniform load
zbMATH Keywords: central point load
zbMATH Keywords: least-weight solutions
zbMATH Keywords: perforated elastic plates
zbMATH Keywords: constant thickness
zbMATH Keywords: prescribed compliance
zbMATH Keywords: Poisson ratio of zero value
zbMATH Keywords: microstructure
zbMATH Keywords: ribs of first- and second-order infinitesimal spacing
zbMATH Keywords: optimal solution
zbMATH Keywords: axially symmetric plates
zbMATH Keywords: unperforated regions
zbMATH Keywords: regions with ribs
zbMATH Keywords: nonzero Poisson ratio
zbMATH Keywords: unconstrained shape optimization
MaRDI profile type: Publication
full work available at URL: 0045-7825(88)90004-7
OpenAlex ID: W2073112870
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description: scientific article; zbMATH DE number 4003689