Extended Nonlinear Force Density Method for Form-Finding of Cable-Membrane Structures

In this paper, an alternative approach was developed for the form-finding of cable-membrane structures. The prestress of a triangular finite element was firstly equivalent to the axial force densities and uniform vertical loads on the three edges. The static equations and tangent stiffness matrices of the cable-membrane were then formulated with the aid of the nonlinear force density method. In order to obtain a high accurate surface of cable-membrane structures, an iterative strategy was presented to solve the nonlinear force density equations and optimize the initial geometrical shape based on the Newton-Raphson method. Eventually, the proposed method was applied to the form-finding of the cable-membrane structure, a hoop truss antenna, and a numerical example was conducted to confirm the efficiency of the method.