Tensegrity is a unique class of structural morphology which is a combination of disconnected compression members with connected tension members. The structure can maintain the stabilization in its self-equilibrium state and can deform by itself without the application of external force. Therefore, it is basically important to find out the equilibrium configurations to design the tensegrity structures. In this study, the tangent stiffness method is applied to conduct the form-finding analysis since it is quite effective in the geometrical nonlinear analysis due to its strict rigid body displacement of elements. Taking the advantage of the tangent stiffness method, it is possible to set the element behavior freely, even real or virtual, by defining the measure potential. In this study, we proposed the power function whose differential calculus gives the corresponding element force equation. In this geometrical nonlinear analysis, tangent stiffness method gives strict equilibrium solutions in form-finding analysis, but it also tends to produce flat or deployed shape, and in some cases, it cannot catch the equilibrium solutions accidentally. Therefore, this study is to analyze the possibility of obtaining equilibrium solutions and shape formation.

A triple-layered hexagonal tensegrity with 18 struts and 78 cables is proposed to conduct the analysis with variation of coefficients. The strut is designated as a truss behavior with a real constant stiffness of steel. For the virtual coefficients of cables, we set 5 different values of C, 10 different values for n, and 21 sets of non-stressed length ratio. Total 562 equilibrium solutions out of 1050 trials are obtained in which 244 equilibrium solutions are in three-dimensional (3D) configuration. Emphasizing only on 3D solutions, it is found that varying amount of C does not give much difference while n with odd number has typical tendency to give the higher percent of 3D shapes. It is found that the non-stressed length ratio has much influence on the 3D shape formation. Based on this analysis, it is expected to give the insight for selecting coefficients and utilizing them in more efficient way in the further related studies.

Keywords: Tensegrity structures, measure potential, influential coefficients