Shape Optimization Method Of Tensile Membrane Structures And Analysis Of Optimal Shape

Membrane structure is a kind of tension structure, which carries loads within membrane materials and cables. Membrane and cable have a negligible bending stiffness and have no compression resistance. Prestress must be applied to maintain the shape of membrane structure and carry loads. Consequently, shape and stress distribution of membrane structures have one-to-one correspondence with each other under given boundary condition. The shape of membrane structures not only influences the architectural properties of structures, but also has a connection with the mechanic characteristics and security of structures. At present, the shape of membrane structures is usually designed according to the aesthetic demand. On the other hand, the structural behavior is not discussed carefully. The design generally depends on the experience of designers without conceptual guide. In order to solve this problem, the question"which shape is optimal for structural behavior"is imperative to be answered, which is also helpful for architects at the schematic design stage.In this paper, a new concept and method are presented for optimization of membrane structures based on Genetic Algorithm. Multi-objectives are established according to the characteristics of membrane structures, including maximum stiffness, maximum uniformity of stress and minimum value of reaction. These objectives are formulated in detail with respect to design variables. Especially, three kinds of functions of stiffness are investigated to show their difference and common aspects, which respectively base on strain energy, maximum displacement and average displacement. Further more, Weight Factor Method is introduced to combine the three objectives into a single objective.The optimization program based on Genetic Algorithm is improved on efficiency and convergence. The reasonable sets of algorithm parameters are obtained by analysis on several numerical examples.With this method, two typical kinds of membrane structures (conical and wave-shaped) are optimized respectively under snow load, wind load and combined load. The effects of span and the level of stress are taken into account; finally, the sets of structure parameters for optimal shapes are obtained and the relationships between optimal parameters are discussed. By this research, useful and credible advice is given to concept design of membrane structures.