Blowup of errors caused by inexact knowledge of the Poisson ratio in some elasticity problems

摘要

We study the effects caused by inexact knowledge of the Poisson's ratio in the linear elasticity problem and derive estimates for the incremental quantity that characterizes the variability of the internal energy and the logarithmic derivative of the energy with respect to the Poisson's ratio. These quantities characterize errors caused by inexact (incomplete) knowledge of material constants, which is typical for computer modelling of physical and engineering problems. We prove that their behaviour is drastically different for two different classes of boundary conditions, namely the boundary conditions of the first class generate solutions that are relatively stable with respect to small variations of the Poisson's ratio, while other conditions generate solutions, for which the quantities blow up if the ratio tends to one half.