## Abstract

This paper extends Keller's classic solution for the optimal design of columns to the case of plates. After the introduction of nondimensional variables, a calculus of variations technique is used to derive an optimality condition, which states that "the strain-energy density is proportional to the thickness of an optimal plate design." The case of a simply supported plate is then discussed, using a truncated Fourier series solution. For a square, isotropic plate, the buckling load of the optimal design is larger than that of the uniform plate by a factor of 1.71 + 1.37 v (v is Poisson's ratio). An appendix is included which discusses Keller's original solution and shows how it can be applied when a fourth-order differential equation is used rather than the second-order one used by Keller. This appendix also discusses the use of a truncated Fourier series and Rayleigh's method as an approximation of Keller's result, thus laying the groundwork for the use of Fourier series in the plate problem.

Original language | English |
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Pages (from-to) | 850-858 |

Number of pages | 9 |

Journal | Journal of Structural Engineering |

Volume | 116 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jan 1990 |

Externally published | Yes |

## ASJC Scopus subject areas

- Civil and Structural Engineering
- Building and Construction
- Materials Science (all)
- Mechanics of Materials
- Mechanical Engineering