Über ein eindimensionales Modell der finiten Elastostatik

Abstract

The deformation of a rod $S=[0,1]$ is given by a diffeomorphism $w:S\to S_w=[0,w(1)]$ from the set $\{w\in W_2^2(0,1):w(0)=0,w^{\prime }(s)>0(s\in S)\}$. The function ln $w’$ appears as measure of deformation. The function $w$ is solution to a second order ordinary differential equation with the second boundary condition $w^{\prime }(1)=p\in {\mathbb{R}}^{+}$. By an open - and - closed argument we show that the set of those $p$ for which the boundary problem is uniquely solvable, is all ${\mathbb{R}}^{+}$.