Optimization for energy absorption of 3-dimensional tensegrity lattice with truncated octahedral units

Abstract

Tensegrity structures have recently found new applications as energy absorbers in the field of aerospace engineering. In this study, we introduce an optimization method to maximize the energy absorption capability of a 3D tensegrity lattice composed of truncated octahedral units. The stored strain energy of the tensegrity lattice subjected to forced vertical displacement is maximized under constraints on the stress, structural material volume, and volume occupied by the lattice. The force density of the bar that defines the shape of each unit is regarded as a parameter, and the design variables are the cross-sectional areas of cables and bars as well as the level of prestresses on the lattice. Buckling of the bars is extensively utilized to significantly increase energy absorption. The nonlinear behavior of bars allowing buckling is modeled as a smoothed function of bi-linear elastic material, in which imperfection in the bar shape is also taken into account. Numerical examples show that tensegrity lattices, with flexibility in the vertical direction and adequate (shear) stiffness in the horizontal direction, can be obtained by solving the optimization problem. It is also shown that energy absorption by the structure scales cubically when its sizes and prestress level are uniformly scaled.