### Abstract

A displacement boundary-value problem is considered for a two-dimensional, simply-connected region consisting of homogeneous, isotropic, linear elastic material. The region is bounded by two straight edges (one of which may be degenerate to a point, however) parallel to the x_{1}-coordinate axis. The straight edges are subject to specified displacements while the other (lateral) boundaries are subject to zero displacement. Explicit upper bounds in terms of the data are obtained for a certain cross-sectional mean-square measure of the first-order displacement derivatives, and it is shown how pointwise bounds on the displacement may be deduced therefrom. For a certain subclass of the problems considered, the estimates obtained are of the exponential decay type which have come to be associated with Saint-Venant's principle. © 1988 Oxford University Press.

Original language | English |
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Pages (from-to) | 223-238 |

Number of pages | 16 |

Journal | Quarterly Journal of Mechanics and Applied Mathematics |

Volume | 41 |

Issue number | 2 |

DOIs | |

Publication status | Published - May 1988 |

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*Quarterly Journal of Mechanics and Applied Mathematics*, vol. 41, no. 2, pp. 223-238. https://doi.org/10.1093/qjmam/41.2.223

**Some decay and other estimates in two-dimensional linear elastostatics.** / Flavin, J. N.; Knops, R. J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Some decay and other estimates in two-dimensional linear elastostatics

AU - Flavin, J. N.

AU - Knops, R. J.

PY - 1988/5

Y1 - 1988/5

N2 - A displacement boundary-value problem is considered for a two-dimensional, simply-connected region consisting of homogeneous, isotropic, linear elastic material. The region is bounded by two straight edges (one of which may be degenerate to a point, however) parallel to the x1-coordinate axis. The straight edges are subject to specified displacements while the other (lateral) boundaries are subject to zero displacement. Explicit upper bounds in terms of the data are obtained for a certain cross-sectional mean-square measure of the first-order displacement derivatives, and it is shown how pointwise bounds on the displacement may be deduced therefrom. For a certain subclass of the problems considered, the estimates obtained are of the exponential decay type which have come to be associated with Saint-Venant's principle. © 1988 Oxford University Press.

AB - A displacement boundary-value problem is considered for a two-dimensional, simply-connected region consisting of homogeneous, isotropic, linear elastic material. The region is bounded by two straight edges (one of which may be degenerate to a point, however) parallel to the x1-coordinate axis. The straight edges are subject to specified displacements while the other (lateral) boundaries are subject to zero displacement. Explicit upper bounds in terms of the data are obtained for a certain cross-sectional mean-square measure of the first-order displacement derivatives, and it is shown how pointwise bounds on the displacement may be deduced therefrom. For a certain subclass of the problems considered, the estimates obtained are of the exponential decay type which have come to be associated with Saint-Venant's principle. © 1988 Oxford University Press.

UR - http://www.scopus.com/inward/record.url?scp=0009284251&partnerID=8YFLogxK

U2 - 10.1093/qjmam/41.2.223

DO - 10.1093/qjmam/41.2.223

M3 - Article

VL - 41

SP - 223

EP - 238

JO - Quarterly Journal of Mechanics and Applied Mathematics

JF - Quarterly Journal of Mechanics and Applied Mathematics

SN - 0033-5614

IS - 2

ER -