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Zeitschrift für Analysis und ihre Anwendungen

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Volume 10, Issue 2, 1991, pp. 183–192
DOI: 10.4171/ZAA/440

Published online: 1991-06-30

Über ein eindimensionales Modell der finiten Elastostatik

Arno Langenbach

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 $\mathbb R^+$.

Keywords: finite elasticity, boundary value problems, ordinary differential equations

Langenbach Arno: Über ein eindimensionales Modell der finiten Elastostatik. Z. Anal. Anwend. 10 (1991), 183-192. doi: 10.4171/ZAA/440