Spatial behaviour in the incompressible linear elastic free cylinder

R. J. Knops, P. Villaggio

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)2113-2135
Number of pages23
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2013
Publication statusPublished - 8 Sept 2001


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


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