On the nonlinear mechanics of discrete networks

Summary A formulation of the equilibrium problem for nonlinear elastic networks is presented. Explicit necessary and sufficient conditions for minimum-energy configurations are derived. These are used to generate a relaxed formulation of the theory in which fibre slackening is accounted for automatically. For the relaxed problem, minimum-energy and uniqueness theorems are proved and used as the basis of a numerical method in which equilibrium configurations are recovered asymptotically in the long-time limit of an artificial dynamical problem. Such an approach is particularly useful for networks, as stiffness-based equilibrium formulations are known to suffer from ill-conditioning in a wide variety of applications. Several illustrative examples are discussed. Accepted for publication 22 June 1996