An efficient Newton-Raphson based form-finding method for tensegrity structures with given strut forces and cable force density

Tensegrity structures are geometric nonlinear systems and statically and kinematically indeterminate structures that require an initial shape-finding procedure to establish a self-equilibrium state. This paper presents a shape-finding algorithm requiring structure topology, strut force, cable force density, and a random initial estimate of node coordinates as input. The equilibrium of the structure is achieved by zeroing the nonlinear static equilibrium in which the generalized nodal coordinates are chosen as variables. The modified Newton-Raphson method is used to solve the nonlinear equilibrium system by decreasing the nonlinear least square function to ensure global convergence. The stability of the self-balancing structure was evaluated using the properties of the geometric and tangent stiffness matrix. Various numerical examples are presented to illustrate the method's effectiveness for 2-d and 3-d tensegrity structures with multiple states of self-stress.