Über ein eindimensionales Modell der finiten Elastostatik

  • Arno Langenbach

    Humboldt-Universität zu Berlin, Germany


The deformation of a rod S=[0,1]S = [0,1] is given by a diffeomorphism w:SSw=[0,w(1)]w: S \to S_w = [0, w(1)] from the set {wW22(0,1):w(0)=0,w(s)>0(sS)}\{w \in W^2_2 (0, 1): w(0) = 0, w' (s) >0 (s \in S) \}. The function ln ww’ appears as measure of deformation. The function ww is solution to a second order ordinary differential equation with the second boundary condition w(1)=pR+w'(1) = p \in \mathbb R^+. By an open - and - closed argument we show that the set of those pp for which the boundary problem is uniquely solvable, is all R+\mathbb R^+.

Cite this article

Arno Langenbach, Über ein eindimensionales Modell der finiten Elastostatik. Z. Anal. Anwend. 10 (1991), no. 2, pp. 183–192

DOI 10.4171/ZAA/440