Form-finding and shape optimization of bio-inspired branching structures based on graphic statics

Abstract Structure’s internal force transfer efficiency is the bases of pursuing the creative structural form. This paper reveals the mechanical mechanisms of the bio-inspired branching structures and further presents a numerical form-finding and shape optimization method for bio-inspired branching structures based on graphic statics with the constraints of strength, stiffness of boundary conditions are considered. Efficient structural form is obtained by connecting the internal force equilibrium and the structural performance in designing process. The reciprocal diagrams in graphic statics are used to solve the form-finding problem to generate compression or tension-only tree-like structure. Establishing the formula of the evaluation criteria of internal force transfer efficiency to characterize the structural performances, the criteria is compared with the continuum topology optimization method, the shape of tree-like structure is optimized by maximizing the structural efficiency under static loads. As a result, suitable external constraints can make a structure efficient and improve the structural redundancy, material properties determine the structural form, which in turn affects the structural behavior. Consequently, the interrelation mechanisms between material-property, structural-form, and structure-performance of the highly efficient bio-inspired branching structures are found. The internal force transfer efficiency and the strength and stiffness of boundary condition are the main factors to determine the optimal solution in the topological design exploration of load-bearing structure, these factors could be controlled to obtain the effective and elegant structural form for practical fabrication. The proposed numerical method could provide intuitive understanding and real-time feedback for the optimal solution, avoid the single solution obtained by the conventional optimization techniques and limited control to modify the output topology. Besides, more structural performance (e.g. buckling, vibration) can be considered in the structural designing process.