Stiffness formulations and necessary and sufficient conditions for exponential stability of prestressable structures

Prestressable structures composed of elastic tendons and rigid bars are investigated for their stiffness and stability properties. Two analytical formulations of the tangent stiffness matrix are analyzed, the first using tendon lengths and forces, and the second using tendon lengths squared and force densities. Several necessary and sufficient conditions for the exponential stability of prestressable configurations are proved using both formulations. Advantages of these conditions, primarily with respect to the traditional test which uses the matrix of the first order system, are discussed and illustrated via examples. Advantages of the second formulation of the tangent stiffness matrix in analytical manipulations and computations are also revealed.