Numerical and Analytical Approaches to the Self-Equilibrium Problem of Class θ = 1 Tensegrity Metamaterials

Abstract

This study formulates numerical and analytical approaches to the self-equilibrium problem of novel units of tensegrity metamaterials composed of class θ = 1 tensegrity prisms. The freestanding configurations of the examined structures are determined for varying geometries, and it is shown that such configurations exhibit a large number of infinitesimal mechanisms. The latter can be effectively stabilized by applying self-equilibrated systems of internal forces induced by cable prestretching. The equilibrium equations of class θ = 1 tensegrity prisms are studied for varying values of two aspect parameters, and local solutions to the self-equilibrium problem are determined by recourse to Newton-Raphson iterations. Such a numerical approach to the form-finding problem can be easily generalized to arbitrary tensegrity systems. An analytical approach is also proposed for the class θ = 1 units analyzed in the present work. The potential of such structures for development of novel mechanical metamaterials is discussed, in the light of recent findings concerned with structural lattices alternating lumped masses and tensegrity units.

Computational Prediction of the Stability of Tensegrity Structures

“…An approach to the form-finding of the illustrated tensegrity structures is to look for the zero this approach we refer to [16].…”

“…1. The freestanding configuration of the examined structure shows = 120 , = 125 and = 55 [16]. The compressive members are made of grade 8.8, M4 threaded steel bars plated with white zinc, while the strings consist of Spectra ®cables with 0.76 mm diameter [23].…”

“…A new class of tensegrity structures has been recently introduced in the literature, with the name of class theta tensegrity prisms [16]. Such structures are formed by the superimposition of two T3 prisms (i.e., two triangular prisms formed by 3 bars each [Skelton and de Oliveira]), which are connected each other through two different set of cables.…”

“…A first set of cables connects the external nodes of the structure, while the second set connects the inner nodes and provides a connection between the two superimposed prisms. The Greek letter has been introduces by Bieniek to label such systems [16], since it mimics the geometry of a structure formed by external and internal cables.…”

Mathematical analysis of a solution method for finite-strain holonomic plasticity of Cosserat materials

“…So far, physical models of these exciting materials have been fabricated through additive manufacturing (AM) technologies in polymeric materials and have been described through Cosserat elasticity, [3]. The numerical model presented in this work allows for simulating the response of ductile versions of such metamaterials, assuming radial loading and holonomic plasticity, [16,17,18], which are, e.g., fabricated via AM techniques manual assembling methods employing metallic materials, [19,20,21].…”