Tensegrity structures are frameworks in a stable self-equilibrated prestress state that have been applied in various fields in science and engineering. Research into tensegrity structures has resulted in reliable techniques for their form finding and analysis. However, most techniques address topology and form separately. This paper presents a bio-inspired approach for the combined topology identification and form finding of planar tensegrity structures. Tensegrity structures are generated using tensegrity cells (elementary stable self-stressed units that have been proven to compose any tensegrity structure) according to two multiplication mechanisms: cellular adhesion and fusion. Changes in the dimension of the self-stress space of the structure are found to depend on the number of adhesion and fusion steps conducted as well as on the interaction among the cells composing the system. A methodology for defining a basis of the self-stress space is also provided. Through the definition of the equilibrium shape, the number of nodes and members as well as the number of self-stress states, the cellular multiplication method can integrate design considerations, providing great flexibility and control over the tensegrity structure designed and opening the door to the development of a whole new realm of planar tensegrity systems with controllable characteristics.

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Tensegrity structures are systems composed of elements in compression and tension in a stable self-equilibrium state that provides stability and stiffness to the structure. Tensegrity finds its root in contemporary art with Kenneth Snelson's sculptures, yet it quickly evolved into a structural paradigm employed in a wide spectrum of science and engineering applications. Tensegrity structures being lightweight, and capable of combining sensors and actuators with structural elements, they are advantageous for active applications. However, in most active applications, sensor placement is based on engineering judgement and not a systematic approach based on the analysis of tensegrity structures. This paper addresses sensor placement for structural identification and damage detection in tensegrity structures using cellular decomposition. By decomposing tensegrity structures into the minimum number of constitutive unicellular substructures (cells and stable sub-structures resulting from their interaction), the minimum number of sensors required for their self-stress identification can be defined along with a set of edge solutions for sensor placement. Moreover, under the assumptions of a known deformed geometry and loading, it is shown that the resulting sensor configurations can be extended for structural identification as well as damage detection providing a theoretical framework for active and sensory tensegrity structures based on their cellular composition.

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Network equilibrium models represent a versatile tool for the analysis of interconnected objects and their relationships. They have been widely employed in both science and engineering to study the behaviour of complex systems under various conditions, including external perturbations and damage. In this paper, network equilibrium models are revisited through graph-theory laws and attributes with special focus on systems that can sustain equilibrium in the absence of external perturbations (self-equilibrium). A new approach for the analysis of self-equilibrated networks is proposed; they are modelled as a collection of cells, predefined elementary network units that have been mathematically shown to compose any self-equilibrated network. Consequently, the equilibrium state of complex self-equilibrated systems can be obtained through the study of individual cell equilibria and their interactions. A series of examples that highlight the flexibility of network equilibrium models are included in the paper. The examples attest how the proposed approach, which combines topological as well as geometrical considerations, can be used to decipher the state of complex systems.