### Abstract

Differential inequalities are derived for two cross-sectional energy fluxes. Integration establishes exponential growth and decay estimates for the cross-sectional mean square displacement, displacement gradient and pressure. The conclusions relate to Saint-Venant's principle for an incompressible elastic cylinder and more generally to the Phragmen-Lindelof principle and Liouville's theorem. Other contributions to the literature are briefly noted.

Original language | English |
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Pages (from-to) | 111-128 |

Number of pages | 18 |

Journal | Journal of Engineering Mathematics |

Volume | 37 |

Issue number | 1-3 |

Publication status | Published - Feb 2000 |

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### Keywords

- Incompressible linear elasticity
- Saint-Venant's principle
- Spatial behaviour

### Cite this

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*Journal of Engineering Mathematics*, vol. 37, no. 1-3, pp. 111-128.

**Alternative spatial behaviour in the incompressible linear elastic prismatic constrained cylinder.** / Knops, R. J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Alternative spatial behaviour in the incompressible linear elastic prismatic constrained cylinder

AU - Knops, R. J.

PY - 2000/2

Y1 - 2000/2

N2 - Differential inequalities are derived for two cross-sectional energy fluxes. Integration establishes exponential growth and decay estimates for the cross-sectional mean square displacement, displacement gradient and pressure. The conclusions relate to Saint-Venant's principle for an incompressible elastic cylinder and more generally to the Phragmen-Lindelof principle and Liouville's theorem. Other contributions to the literature are briefly noted.

AB - Differential inequalities are derived for two cross-sectional energy fluxes. Integration establishes exponential growth and decay estimates for the cross-sectional mean square displacement, displacement gradient and pressure. The conclusions relate to Saint-Venant's principle for an incompressible elastic cylinder and more generally to the Phragmen-Lindelof principle and Liouville's theorem. Other contributions to the literature are briefly noted.

KW - Incompressible linear elasticity

KW - Saint-Venant's principle

KW - Spatial behaviour

M3 - Article

VL - 37

SP - 111

EP - 128

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 1-3

ER -