Static Analysis of Tensegrity Structures

Abstract

Two problems are addressed in this paper. First, the mathematical model to perform the static analysis of an antiprism tensegrity structure subjected to a wide variety of external loads is presented. The virtual work approach is used to deduce the equilibrium equations and a method based on Newton’s Third Law is used to verify the numerical results. Two numerical examples are provided to demonstrate the use of the mathematical model, as well as the verification method. The second problem deals with the development of a mathematical model to perform the static analysis of a prestressed antiprism tensegrity structure subjected to an arbitrary length reduction of its connecting ties. Again, a virtual work approach is used to deduce the equilibrium equations and the numerical results are verified using a Newtonian approach. One example is provided to illustrate the mathematical model.

Geometric and material nonlinear analysis of tensegrity structures

“…Recently, Murakami [21] investigated the elastic behavior of a three-strut tensegrity module under static load at various pre-stress levels by applying the updated Lagrangian formulation. More recently, using a set of well-chosen generalized coordinates and the virtual work approach Crane III et al [22] developed a mathematical model derivation addressing the static analysis problem and found the displacements of the structure under applied external forces. The research was performed for only three-and four-strut tensegrities based on regular prisms.…”

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

“…Establish a Cartesian coordinate system (0-xyi), where the origin O is located at the center of the bottom pentagon, the x axis runs through the node 1, and the z axis is normal to the bottom pentagon. As in Crane et al [23], we assume that the bars are rigid and have a length of 90 mm, and all strings are linear elastic. The top strings, bottom strings, and diagonal strings have the stiffnesses of 0.5 N/mm, 0.3 N/mm, and 0.4 N/mm, and the natural lengths of 35 mm, 45 mm, and 65 mm, respectively.…”

“…By invoking the virtual work principle. Crane et al [23] proposed an analytical method to investigate the responses of cylindrical tensegrities. Recently, Nuhoglu and Korkmaz [24] proposed a point iterative method to analyze the deformation behavior of tensegrities.…”

Kinematic and static analysis of a 3-PUPS spatial tensegrity mechanism

“…Several approaches have been proposed, mostly of numerical nature [8,9,10,11]. However, for simpler architectures [12] or when symmetrical hypotheses are made [13], analytical solutions are possible.…”