To design free-form structures with reasonable mechanical behaviors and rich geometrical shapes

the principles of traditional form-finding methods by physical experiments were referred

and a numerical form-finding method for free-form structures was proposed based on the combination of the Dynamic Relaxation method and the Local Linearization method. As the zero bending moment type free-form structure has the same form with the flexible membrane structure which has the same loading distributions and boundary conditions

the form-finding of free-form shell structures can be realized by membrane structures. In the proposed method

equilibrium forms under different driving forces

such as the gravity

pneumatic pressure

pretension force

were generated by Dynamic Relaxation method

and the form-control problem aiming to meet the requirements of architectural design was explored by adjusting the initial parameters of the model using the Local Linearization method. The poposed form-finding method was applied to the inverse-hanging type shells

the pneumatic type shells and the tension type shells separately. For the inverse-hanging type shells

a model made by Isler was simulated

and the results were compared with the data by 3D scanning to verify the accuracy of the proposed method. For the pneumatic type shells

the multi-region controlling strategy was used to realize the form-finding of complicated shapes. For the tension type shells

the behaviors of a shell genertated by the form-finding method were analized to illustrate the zero bending moment feature. It can be concluded that the proposed method is more effective and applicable

which is helpful to realize the harmonious design of architecture and structure.