### Abstract

A thin elastic plate, supported along the boundary, is loaded either by a single concentrated force at a given internal point, or by two equal and opposite concentrated forces at given internal diametrically opposite points. In each problem, the compliance, defined as the work done by the load, can be reduced on stiffening the plate by the addition to the boundary of an elastic strip whose cross-section is variable but whose total volume is prescribed. The cross-sectional area that minimises the compliance provides the optimal reinforcement for both problems. The respective compliances are compared with those obtained when the plate's boundary is reinforced by a strip of uniform cross-section and of the given volume. © Springer-Verlag Berlin Heidelberg 2006.

Original language | English |
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Pages (from-to) | 427-433 |

Number of pages | 7 |

Journal | Structural and Multidisciplinary Optimization |

Volume | 32 |

Issue number | 5 |

DOIs | |

Publication status | Published - Nov 2006 |

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*Structural and Multidisciplinary Optimization*,

*32*(5), 427-433. https://doi.org/10.1007/s00158-005-0598-x

}

*Structural and Multidisciplinary Optimization*, vol. 32, no. 5, pp. 427-433. https://doi.org/10.1007/s00158-005-0598-x

**Exact solutions in the reinforcement of a circular plate under concentrated loads.** / Knops, R. J.; Villaggio, P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Exact solutions in the reinforcement of a circular plate under concentrated loads

AU - Knops, R. J.

AU - Villaggio, P.

PY - 2006/11

Y1 - 2006/11

N2 - A thin elastic plate, supported along the boundary, is loaded either by a single concentrated force at a given internal point, or by two equal and opposite concentrated forces at given internal diametrically opposite points. In each problem, the compliance, defined as the work done by the load, can be reduced on stiffening the plate by the addition to the boundary of an elastic strip whose cross-section is variable but whose total volume is prescribed. The cross-sectional area that minimises the compliance provides the optimal reinforcement for both problems. The respective compliances are compared with those obtained when the plate's boundary is reinforced by a strip of uniform cross-section and of the given volume. © Springer-Verlag Berlin Heidelberg 2006.

AB - A thin elastic plate, supported along the boundary, is loaded either by a single concentrated force at a given internal point, or by two equal and opposite concentrated forces at given internal diametrically opposite points. In each problem, the compliance, defined as the work done by the load, can be reduced on stiffening the plate by the addition to the boundary of an elastic strip whose cross-section is variable but whose total volume is prescribed. The cross-sectional area that minimises the compliance provides the optimal reinforcement for both problems. The respective compliances are compared with those obtained when the plate's boundary is reinforced by a strip of uniform cross-section and of the given volume. © Springer-Verlag Berlin Heidelberg 2006.

UR - http://www.scopus.com/inward/record.url?scp=33749256965&partnerID=8YFLogxK

U2 - 10.1007/s00158-005-0598-x

DO - 10.1007/s00158-005-0598-x

M3 - Article

VL - 32

SP - 427

EP - 433

JO - Structural and Multidisciplinary Optimization

JF - Structural and Multidisciplinary Optimization

SN - 1615-147X

IS - 5

ER -