Abstract:  Aiming at the initial form-finding design of space cable membrane structure，an iterative strategy of antenna form-finding for boundary cable tension design and cable net shape design is proposed based on the force density method and the method of controlling the grid area.Firstly，the membrane reflector is discretized into triangular membrane elements to obtain the equivalent effective density of membrane elements.Combined with the structural characteristics of cable net，the static equilibrium equation of cable net and membrane is obtained.The tension of all internal cable segments of the cable network is equal，and the tension design of boundary cable segments is realized by controlling the size of grid area.In order to design the shape of the front cable net，according to the paraboloid equation of the front cable net，the free node coordinates of the front cable network are updated，the vertical cable tension is readjusted，and the grid area is controlled.Finally，the shape design of the antenna is realized through the iterative process.The example of radial rib cable membrane reflector antenna shows that this method can obtain the design results that meet the shape requirements and tension distribution.

Key words: space membrane structure, force density method, grid area, membrane element, form-finding, radial rib cable membrane reflector antenna