Asymptotic behaviour in the nonlinear elastic beam (Q802361)

The authors consider the problem of estimation of decay of stress in a semi-infinite prismatic cylinder composed of a nonlinear homogeneous elastic material, which is loaded over its base and has its lateral sides held a zero displacement. The decay estimates consist of integral inequalities. Decay estimates for linear materials are also developed; as expected, they are of simpler form. The paper closes with a demonstration that one of the key hypotheses is a necessary condition for the decay estimates to hold.