Spatial Behaviour in Pre-stressed Constrained Elastic Cylinders

Considered within the theory of small deformations superposed upon large is spatial behaviour for a prestressed laterally constrained elastic cylinder in equilibrium under zero body force and for sets of elastic coefficients that are not positive-definite. Certain cross-sectional integral measures are shown to be logarithmically convex implying at least exponentially increasing growth behaviour. For sufficiently long cylinders, this conclusion contradicts at most quadratic growth, and consequently the theory ceases to be valid indicating possible initiation of buckling and similar phenomena.     

On oblique impact of a rigid rod against a Winkler foundation

A simplified model of a rigid rod obliquely projected against an elastic wall is studied. The wall is a Winkler substrate, and the motion is assumed planar. Gravitational and frictional effects are ignored. Properties of the motion during impact are derived mainly by application of inequalities and demonstrate that, for example, the time of impact and depth of penetration vary inversely as powers of the foundation’s elastic coefficient.