Elastic strings under vertical loads
The author analyzes the nonlinear equation of an elastic string subject to a symmetrical vertical load \(p(s)=p(-s)\) and a stress strain law \(T=f(e)\) when either u (the horizontal displacement) or T (the stress) is prescribed at both ends. As the second problem, the stress problem, poses no serious problem the author concentrates on the first problem, the displacement problem. On quite general assumptions on p and T the author proves the existence and uniqueness of tensile solutions and he demonstrates that compressive solutions are not necessarily unique. Furthermore, he shows that tensile solutions are kinematically stable. The opposite, the instability of compressive solutions, is only obtained approximately.
horizontal displacement or stress prescribed at both ends
compressive solutions not necessarily unique
instability of compressive solutions obtained approximately
scientific article; zbMATH DE number 3845177