Self-equilibrium and super-stability of truncated regular polyhedral tensegrity structures: a unified analytical solution

Abstract

In spite of their great importance and numerous applications in many civil, aerospace and biological systems, our understanding of tensegrity structures is still quite preliminary, fragmented and incomplete. Here we establish a unified closed-form analytical solution for the necessary and sufficient condition that ensures the existence of self-equilibrated and super-stable states for truncated regular polyhedral tensegrity structures, including truncated tetrahedral, cubic, octahedral, dodecahedral and icosahedral tensegrities.

A Numerical Method for Simulating Nonlinear Mechanical Responses of Tensegrity Structures Under Large Deformations

“…For a linear elastic element, ^^(y) remains constant and can be solved from [29] ?<•((/•) = • (y) (14) where A is the cross-sectional area of the element, and E is the Young's modulus of the material. Then, Eq.…”

“…where I e R^"^ denotes the three-dimensional identity matrix, and ® the Kronecker product symbol [30]; D is the reduced stress matrix [12], also referred to as the force density matrix [31,32], which can be obtained as [14] -qe(ij) if i 7^ j and / is connected with j by element e 0 if / 7^ j and i does not connect with j (8)…”

“…Invoking the following definition of element stress (also referred to as force density or tension coefficient) [14] (4)…”

“…In most previous studies, the main attention has been focused on infinitesimal mechanisms for which the first-order elongations of all elements are zero [6,12] or prestressed states in which the structures are self-equilibrated without external loads [13,14]. The tensegrities were often assumed to be subjected to infinitesimal disturbances and undergo relatively small deformations from their original configuration.…”

Geometrically nonlinear elasto-plastic analysis of clustered tensegrity based on the co-rotational approach

“…A lot of previous studies of tensegrity structures involved in theoretical research [8,9], experimental study [10][11][12] and numerical analysis [13][14][15][16][17][18][19]. Almost of the numerical analyses focused on the classical tensegrity structure at the beginning of the study.…”