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 $\{w \in W^2_2 (0, 1): w(0) = 0, w' (s) >0 (s \in S) \}$. 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 $w'(1) = p \in \mathbb R^+$. By an open - and - closed argument we show that the set of those $p$ for which the boundary problem is uniquely solvable, is all $\mathbb R^+$.