A design methodology for lattice and tensegrity structures based on a stiffness and volume optimization algorithm using morphological indicators

Abstract

This article presents a design methodology based on a stiffness and volume optimization algorithm for three-dimensional nonlinear hyperstatic and pre-stressed structures composed of elements only subjected to axial forces, with a special emphasis on tensegrity structures. The algorithm is based on dimensionless numbers called morphological indicators that allow finding, within a given family of structures, the geometry related to a maximum stiffness or a minimum volume of materials or the best ratio between stiffness and volume. The algorithm takes into account the buckling of the struts and different materials for cables and struts. This article first demonstrates the optimization algorithm and then gives numerical confirmations and examples.

Optimization of Footbridges Composed of Prismatic Tensegrity Modules

“…For a prestress statep judiciously chosen, b min is defined as the particular value of b that leads to a situation in which the axial force into the least-tensioned cable after consideration of the external loadF and self-weightG is equal to zero, which means that no cable slacks when b ¼ hb min and h ! 1 In this paper, h ¼ 1 and b ¼ b min will be assumed, and the way to find the value b min is discussed in Latteur et al (2017). The impact of h s 1 is discussed in the conclusion of this paper.…”

“…Their methodology consisted of finding the analytic expression of a dimensionless mass indicator in function of the topology and to minimize it under material yielding or buckling constraint. Finally, Latteur et al (2017) presented a design methodology based on a stiffness and volume=mass optimization algorithm for three-dimensional (3D) nonlinear hyperstatic and prestressed structures composed of elements subjected only to axial forces, with a special emphasis on tensegrity structures. The methodology is based on dimensionless numbers called morphological indicators that allow reducing the number of parameters to consider for the stiffness and mass optimization process.…”

“…This paper focuses mainly on topics related to tensegrity footbridges. Concerning morphological indicators and other design methodologies for tensegrity structures, a detailed state of the art can be found in Latteur et al (2017).…”

“…The aim of this paper is to develop and use the design methodology demonstrated in Latteur et al (2017) in order to prove the feasibility of footbridges composed of a succession of elementary tensegrity modules of the types simplex, quadruplex, hexaplex, and pentaplex , with a suspended deck situated inside the main Class 2 tensegrity structures. In other words, the study focuses on selection of the types of tensegrity modules, their number S, and the ratios L=H (span over height) that lead to the lightest and=or stiffest structures.…”

“…As detailed in Latteur et al (2017), a way to numerically create a prestress scenarioP is to numerically apply to some element i of the structure an external axial force F pre;i at its extremities.…”