Topology optimization of active tensegrity structures

Abstract

Existing studies on active tensegrity structure optimum design only focus on sizing and/or shape optimization i.e., the structural element topology does not change during the design process, which vastly limits the design space and further improvement of mass-saving performance. This study investigates the optimum design of active tensegrity structures through topology optimization, which has never been done to the best of the authors’ knowledge. Structural member topology and actuator layout are considered as binary design variables and their coupling relation is handled by auxiliary constraints. Member cross-sectional areas are treated as discrete design variables considering practical availability. Member prestress, actuator length changes, and other necessary auxiliary parameters are defined as continuous variables and designed simultaneously. Equilibrium conditions, member yielding, cable slackness, strut buckling, and the limitations on the nodal displacements as well as other design requirements are formulated as constraints. Linearization algorithm is proposed to transform the bilinear expressions in the objective and constraint functions to allow the problem to be solved to global optimum. Typical benchmark examples indicate that the topology-optimized active designs obtained through the proposed approach can further decrease the material consumption compared with sizing-optimized active tensegrity designs hence leading to more lightweight structures.