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.
|Number of pages||23|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 8 Sep 2001|
- Incompressible linear elasticity
- Saint-Venant's principle
- Spatial behaviour