Elastic strings under vertical loads

Abstract

The general nonlinear equations of an elastic string of length 2L subject to a symmetric vertical dead loadp(s)=p(−s) are analyzed. Existence of unique tensile and not necessarily unique compressive solutions with fixed horizontal displacementsu(±L)=±u o is proved for a general class of stress strain lawsT=f(e). The kinetic stability of tensile solutions (e>0) is verified exactly. Kinetic instability of compressive solutions (e<0) is obtained only approximately, because a rigorous analysis leads to an unusual indefinite eigenvalue problem that has not been solved yet.