Topology optimization for prestressed cable-truss structure considering geometric nonlinearity

This work presents a topology optimization method for prestressed cable-truss structures considering geometric nonlinearity. Based on the large deformation kinematics theory, we establish a multi-node cable element model, which can fully take into account the geometric nonlinearity caused by external loads and prestress. Besides, nonlinear hyperelasticity principles are used to deal with cable materials’ unidirectional stress characteristics. To consider the impact of prestress on the global structural stiffness, we carried out the rebalancing of prestress and construct an objective function of prestress-modified compliance. Then, we equate the cable-truss structure as a particular two-phase material structure and realize the material interpolation based on a discrete material optimization-like method. Finally, we perform the adjoint sensitivity analysis of the objective function and solve the optimization problem through the gradient-based algorithm. Therefore, we establish a topology optimization method for prestressed cable-truss structures with stiffness as the objective, continuous density/size parameters as variables, and mass fraction as constraints. This method’s feasibility and reliability are demonstrated in 2D and 3D numerical examples.