An iterative method for the analysis of geometric nonlinear cable nets

Abstract

Generally, cable structures possess geometric nonlinearity: in which an iterative procedure is inevitably needed. An iterative scheme frequently used for solving geometric nonlinear problems is the Newton-Raphson method. Many variants of the Newton-Raphson schemes have been developed which are designed.to accelerate the rate of convergence of the numerical solution. However, such iterative methods (e.g. the Kar method) may not even converge in some highly geometric nonlinear problem and an incremental load procedure must be employed A simple iterative technique is presented for improving the convergence of the solution of strong geometric nonlinear problems. The proposed iterative technique features a simple procedure to assess a good trial equilibrium state at the first cycle of iteration since a poor estimate of the state may lead to slow convergence or even numerical overflow in highly geometric nonlinear problems. Numerical examples are presented to demonstrate the effectiveness of the proposed technique in view of stability and rate of convergence in comparison with the Newton-Raphson and Kar methods. Results of analyses reveal clearly the superiority of the new scheme over the others for cables with zero to moderate level of priestess.