### Abstract

In earlier papers [1, 2], least-weight solutions were derived for perforated elastic plates having (a) a constant thickness, (b) a prescribed compliance value, and (c) a Poisson's ratio of zero value. In view of earlier mathematical studies by Kohn, Strang, 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's ratio and the theory is illustrated with examples. Two solutions given are valid for both prescribed compliance and prescribed deflections. This investigation shows that in some unconstrained shape optimization problems the optimal solution cannot be obtained by conventional numerical (e.g. finite element) methods.

Original language | English |
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Pages (from-to) | 301-322 |

Number of pages | 22 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 66 |

Issue number | 3 |

DOIs | |

Publication status | Published - Feb 1988 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications

### Cite this

*Computer Methods in Applied Mechanics and Engineering*,

*66*(3), 301-322. https://doi.org/10.1016/0045-7825(88)90004-7