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Analysis and Algorithms of Optimization Problems pp 111–134Cite as

The design of a two-dimensional domain

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 82))

Abstract

The analysis contained in the paper is not complete in the sense that the designs of perforations and of the external shape of the structure should be conducted in parallel. In consequence the cells would no longer be square. Let us note however that formulae for substitute coefficients may be applied for such irregular cells as well. From variational interpretation given by Propositions 8÷11 it follows that those coefficients will approximate the behaviour of the cells independently of their shapes. Hence the techniques used for perforation design are applicable also in general optimization, where both shape and perforation are taken into account.

The perforated material can be treated as a special example of a composite. Therefore this paper may be considered as a preliminary step toward a truly optimal design of structures. Combining methods of Sections 4 and 6 will be the subject of further study.

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Authors
  1. Antoni Żochowski
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K. Malanowski K. Mizukami

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© 1986 Springer-Verlag

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Żochowski, A. (1986). The design of a two-dimensional domain. In: Malanowski, K., Mizukami, K. (eds) Analysis and Algorithms of Optimization Problems. Lecture Notes in Control and Information Sciences, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007158

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  • DOI: https://doi.org/10.1007/BFb0007158

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16660-3

  • Online ISBN: 978-3-540-39844-8

  • eBook Packages: Springer Book Archive

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