At this paper two types of initial shapes and loads are introduced, and we assume that the initial shapes and loads are defined by sinusoidal functions. Under this assumption the asymptotical stability of the solutions is established by investigating the eigenvalues of the characteristic polynomial of the system. The exact solution is obtained when the initial shape and the load are given by a linear combination of sinusoidal functions. The asymptotic stability of the arch is completely analysed.

A cable structures have the advantage that cover a large space without column but it is very sensitive to deal with shape control because of its flexibility. Especially, location of control member and needed elongation of member are important things. Therefore, the purpose of this paper is studied on displacement control technique for pre-stressed cable structures by force method considering order of control.