## Abstract

Exponentially increasing and decreasing estimates are derived in terms of various mean-square cross-sectional measures for the longitudinal alternative growth and decay behaviour in a semi-infinite prismatic cylinder composed of incompressible homogeneous isotropic linear elastic material. The cylinder is in equilibrium under zero body-force, self-equilibrated base load and traction-free lateral boundary. The method relies upon the derivation and integration of a pair of differential inequalities for the cross-sectional energy flux and a function related to its first-order counterpart. Attention is predominantly directed to a qualitative description, although the final section considers quantitative aspects. Numerical evaluation of the estimates, facilitated by the constants involved being dependent upon the cross-sectional geometry, enables easy comparison with the exact solutions known for the circular cylinder.

Original language | English |
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Pages (from-to) | 2113-2135 |

Number of pages | 23 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 457 |

Issue number | 2013 |

DOIs | |

Publication status | Published - 8 Sept 2001 |

## Keywords

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