Morphogenesis analysis of icosahedral and prismatic tensegrity modules

Abstract

Morphogenesis is a critical aspect of tensegrity system design. This paper explores icosahedral and prismatic tensegrity modules' pattern formation and foundational theories. First, a material consumption functional and self-strain energy functional are introduced from an engineering perspective, along with a variational principle involving independent dual-variable in the morphogenesis process of tensegrity structures. Next, a Symbol Parsing Method is proposed and successfully applied to the optimal morphology analysis of the icosahedral tensegrity module. Due to memory limitations in personal computers, the Singular Value Decomposition of the symbolic equilibrium matrix for the prismatic tensegrity module is constrained. As an alternative, a discrete numerical solution, the semi-symbolic parsing method, is obtained by directly utilizing a numerical equilibrium matrix. This method was recently employed to analyze and optimize a practical tensegrity footbridge designed by the authors. Lastly, the paper delves into the stability of self-equilibrium states in icosahedral and classical prismatic tensegrity modules by employing a second-order variational analysis of the self-strain energy functional. The findings presented are expected to contribute to future research on the morphogenesis of tensegrity structures.