### Abstract

In a recent paper the authors presented a model for thin plates with rapidly varying thickness, distinguishing between thickness variation on a length scale longer than, on the order of, or shorter than the mean thickness. They review the model here, and identify the case of long scale thickness variation as an asymptotic limit of the intermediate case, where the scales are comparable. They then present a convergence theorem for the intermediate case, showing that the model correctly represents the solution of the equations of linear elasticity on the three-dimensional plate domain, asymptotically as the mean thickness tends to zero.

Original language | English (US) |
---|---|

Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | Quarterly of Applied Mathematics |

Volume | 43 |

Issue number | 1 |

State | Published - Apr 1985 |

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### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Quarterly of Applied Mathematics*,

*43*(1), 1-22.

**NEW MODEL FOR THIN PLATES WITH RAPIDLY VARYING THICKNESS. II : A CONVERGENCE PROOF.** / Kohn, Robert; Vogelius, Michael.

Research output: Contribution to journal › Article

*Quarterly of Applied Mathematics*, vol. 43, no. 1, pp. 1-22.

}

TY - JOUR

T1 - NEW MODEL FOR THIN PLATES WITH RAPIDLY VARYING THICKNESS. II

T2 - A CONVERGENCE PROOF.

AU - Kohn, Robert

AU - Vogelius, Michael

PY - 1985/4

Y1 - 1985/4

N2 - In a recent paper the authors presented a model for thin plates with rapidly varying thickness, distinguishing between thickness variation on a length scale longer than, on the order of, or shorter than the mean thickness. They review the model here, and identify the case of long scale thickness variation as an asymptotic limit of the intermediate case, where the scales are comparable. They then present a convergence theorem for the intermediate case, showing that the model correctly represents the solution of the equations of linear elasticity on the three-dimensional plate domain, asymptotically as the mean thickness tends to zero.

AB - In a recent paper the authors presented a model for thin plates with rapidly varying thickness, distinguishing between thickness variation on a length scale longer than, on the order of, or shorter than the mean thickness. They review the model here, and identify the case of long scale thickness variation as an asymptotic limit of the intermediate case, where the scales are comparable. They then present a convergence theorem for the intermediate case, showing that the model correctly represents the solution of the equations of linear elasticity on the three-dimensional plate domain, asymptotically as the mean thickness tends to zero.

UR - http://www.scopus.com/inward/record.url?scp=0022052695&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022052695&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0022052695

VL - 43

SP - 1

EP - 22

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

SN - 0033-569X

IS - 1

ER -