Topology Optimization of Tensegrity and Prestressed Cable-Strut Structures Considering Geometric Stiffness

Abstract

Tensegrity and prestressed cable-strut structures have been widely applied in civil engineering such as utilized as large-span structures due to their lightweight features. These structures are usually kinematically indeterminate systems whose stability is ensured by the geometric stiffness provided by member prestress. To design novel structure forms with better performance, the topology design of tensegrity and prestressed cable-strut structures has become an emerging research topic. In existing studies, the topology design of such structures was usually formulated into an optimization problem in which the member topology is treated as the primary optimization variable. To express the equilibrium condition under external loading, formulations based on the force method are adopted in the optimization models. However, the force method-based formulations bring limitations for the topology design of tensegrity and prestressed cable-strut structures. First, structures with kinematic indeterminacy may be mistakenly excluded from feasible solution space because the equilibrium condition of such structures cannot be fully expressed. Second, due to this reason, novel structure forms with better quality in terms of design objective may be ignored, and the obtained solution is not the “true” optimal solution to the topology design problem. Third, structural responses such as nodal displacements and member forces caused by external loads can be inaccurately approximated by the force method-based formulations. The reason for the limitations is that geometric stiffness provided by the member prestress cannot be considered in the force method-based formulations. This study proposes a new topology optimization model for tensegrity and prestressed cable-strut structures in which geometric stiffness provided by the member prestress can be perfectly considered; thus, all the limitations noted here can be completely overcome. Typical examples are adopted to verify the effectiveness and improvement of the proposed approach.