Active Control of Stiffness of Tensegrity Plate-like Structures Built with Simplex Modules

Abstract

The aim of this study is to prove that it is possible to control the static behavior of tensegrity plate-like structures. This possibility is very important, particularly in the case of deployable structures. Here, we analyze the impact the support conditions of the structure have on the existence of specific characteristics, such as self-stress states and infinitesimal mechanisms, and, consequently, on the active control. Plates built with Simplex modules are considered. Firstly, the presence of the specific characteristics is examined, and a classification is carried out. Next, the influence of the level of self-stress state on the behavior of structures is analyzed. A geometrically non-linear model, implemented in an original program, written in the Mathematica environment, is used. The results confirm the feasibility of the active control of stiffness of tensegrity plate-like structures characterized by the presence of infinitesimal mechanisms. In the case when mechanisms do not exist, structures are insensitive to the initial prestress level. It is possible to control the occurrence of mechanisms by changing the support conditions of the structure. Based on the obtained results, tensegrity is very promising structural concept, applicable in many areas, when conventional solutions are insufficient.

Qualitative and quantitative analysis of tensegrity domes

“…It is the parametric analysis leading to the determination of the impact of the self-stress state (initial prestress) on the behavior of the structure under static load. To assess this behavior, a geometrically non-linear model (thirdorder theory) is used [29,31,37]:…”

Dynamic Stability of Tensegrity Structures—Part I: The Time-Independent External Load

“…The existence of these features depends only on the expansion matrix , so the geometrical and mechanical characteristics do not affect them (the elasticity matrix is an identity matrix ). The self-stress state is considered as an eigenvector related to the zero eigenvalue of the compatibility matrix , whereas the mechanism is an eigenvector related to the zero eigenvalue of the stiffness matrix [ 18 , 19 , 21 , 22 , 32 ].…”

“…From the beginning of the idea of tensegrity, i.e., the 1960s, to the present day, the most popular subject of papers is the search for geometrical configuration (form-finding)—a few sample papers from the last two years [ 1 , 2 , 3 , 4 ]. Other popular applications can be divided into three main areas: algorithms changing the shape of the structure—optimization algorithms aimed at generating new topologies; the new topology aims to achieve the desired performance criteria, such as stiffness level [ 5 , 6 , 7 , 8 ], shape control methods—methods examining the change of the shape of the structure under the influence of external forces [ 7 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ], parametric analysis taking into account the impact of the initial prestress on the static and dynamic behavior of structures [ 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ]. …”

“…parametric analysis taking into account the impact of the initial prestress on the static and dynamic behavior of structures [ 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ].…”

“…The static parametrical analysis of structures build with tensegrity modules, i.e., Simplex and Quartex, was performed, among others, in [ 19 , 20 , 21 ]. In turn, in [ 22 , 23 , 24 ], the influence of the initial prestress on the dynamic properties of the Simplex module was analyzed. In [ 25 ], the impact of the initial prestress on the dynamic properties of a six-strut spherical module and a two-module cylindrical tensegrity model was considered.…”