Design of minimal mass load-bearing tensegrity lattices

Lattice metamaterials have demonstrated promising characteristics such as having tunable/unconventional properties and being lightweight. This work centers on the design of tensegrity-based lattices, known as "T-bar" structures, capable of supporting compressive loads with minimum mass. Analytical formulas for the calculation of the mass of these structures under externally applied forces and pre-stress are derived. These formulas account for local failure of the T-bar structures (material yielding and buckling of its individual members). A numerical approach is introduced to assess the global stability of the structures under external forces and pre-stress and to account for global buckling in the design process. The mass of the structure is minimized by adjusting its shape and topology while global buckling is simultaneously prevented using two different design methods: i) optimizing the pre-stress distribution in the structure, and ii) optimizing the cross-section areas of the tensegrity members. Using either method, the results show that 2D and 3D T-bars possess a global minimum mass design for a given externally applied force and length. The computed results also show that designs obtained by optimizing the cross-section areas of the members have lower mass than those obtained by optimizing the pre-stress distribution. (C) 2020 Elsevier Ltd. All rights reserved.