Lightweight design of tensegrity Michell truss subject to cantilever loads

Abstract

This study introduces an analytical design approach for lightweight cantilever tensegrity structures based on the Michell truss pattern. The topological configuration is determined by generating the parameters of Michell spirals, including structural complexity and geometric parameters. The static equilibrium analysis reveals that the force per unit load for each member is determined by the direction angle of the load, the outer and inner radii of the spiral pattern, and the structural complexity. A minimal mass optimization algorithm is employed to compute the optimal complexity of the cantilevered system, subject to yielding and buckling failure constraints. Numerical calculations are conducted to verify the lightweight design theory for cantilevered structures in relation to load magnitude, load direction, lever arm distance, and material choices. The results not only validate the design methodology for tensegrity structures but also advocate for an innovative structural design approach that integrates parametric theoretical analysis and numerical optimizations for diverse loading scenarios.