Form-finding of Tensegrity Structures via Force Density Matrix Decomposition

This study proposes a form-finding algorithm based on force density matrix decomposition for tensegrity structures. The only information required is node connection and component type. The process is divided into three parts. Firstly, the non-self-stressed tensegrity structure is transformed into a self-stressed tensegrity structure using the virtual component method. In the second part, the solution of force density is transformed into the minimum rank deficit problem of the force density matrix and equilibrium matrix, and the semi-positive qualitative condition is taken as the iteration constraint. The third part specifies a set of independent node coordinate vectors, and the structure is guided to converge quickly. The force density form-finding method avoids the judgment of structural potential energy and stiffness matrix. The numerical example shows that the proposed method can promptly converge and search for new configurations.