# Genetic Algorithm as a Tool for the Determination of the Self-Stress States of Tensegrity Domes
## 1 Introduction  
Tensegrity is a term derived from the English language as a compound of two words: \"tension\"--stretching, and \"integrity\"--stability. The idea of tensegrity structures has been around for over 60 years. During this period, many researchers dealt with this unique type of structure, each of them trying to define the essence of this idea in their own way. The first attempts to describe tensegrity structures come from the creators of the idea. The concept of tensegrity systems was conceived in 1962 by [PERSON] [1], which reflected his idea as \"islands of compression in a sea of tension\". In 1964, [PERSON] [2] added the condition of the self-stress state. In 1965, [PERSON] [3] patented a system called \"Continuous Tension, Discontinuous Compression Structures\". The definition provided in 1976 by [PERSON] [4] is the most widely accepted: \"A tensegrity system is established when a set of discontinuous compression components interacts with a set of continuous tensile components to define a stable volume in space\". This definition was narrowed in 1992 by [PERSON] [5]: \"A tensegrity system is a system in a stable self-equilibrated state comprising a discontinuous set of compressed components inside a continuum of tensioned components\". In general, tensegrity systems are structures whose integrity is based on a balance between tension and compression. Thus far, neither a precise nor a general definition has been agreed upon. Moreover, there are several definitions and classifications that take into account the different features of tensegrity [6]. However, from a mechanical point of view, the most important features are closely related to the advantages of the tensegrity structures. The first step to understand the unique properties is the qualitative analysis, which includes the identification of self-stress state (or states) and infinitesimalmechanism (or mechanisms) [7, 8]. The self-stress state is understood as a system of self-equilibrated internal forces, which satisfies homogeneous equations of equilibrium, while the infinitesimal mechanism means the geometrical variability that is stabilized by the self-stress states. Additionally, the modification of self-equilibrated internal forces allows the behavior of the structure to be controlled; i.e., stiffness and frequency can be influenced. Such structures are characterized by stabilization through tension, efficiency, deployability and easy tunability, the possibility of reliable modeling and more precise controllability [9, 10]. Tensegrity as a structural system offers many advantages over conventional structural systems. Over the years, this concept has evolved, finding a wider audience in engineering, mathematics and biology [11]. In civil engineering, the idea of tensegrity relates to specific self-balancing trusses consisting of continuous tensioned cables and individual compression struts. The self-equilibrium, called the self-stress state, means that there is an equilibrium stress state between struts and cables under zero external loads. An example of tensegrity systems is a cable dome. A typical cable dome consists of the load-bearing girders (built with ridge cables, diagonal cables and vertical struts) connected by a circumferential cable system. The girders are connected by an outer compression ring. To ensure the structural feasibility, continuous cables are often subjected to tension and individual struts subjected to compression. The rigidity of the dome is a result of self-equilibrium between cables and struts. However, opinions are divided as to whether cable domes can be regarded as tensegrity systems. Those in favor regard the outer compression ring as a curved strut. The others insist that the tensegrity system should be self-supporting, which means that it should not be stabilized with a compression ring. However, most people agree that cable domes are a successful extension of the concept of tensegrity [12, 13, 14, 15, 16] due to the mechanical and mathematical properties that distinguish them from conventional systems.