A fast hybrid algorithm for nonlinear analysis of structures

The efficiency of the Newton-Raphson iteration method for solving nonlinear equations has made it popular, although the time required to achieve convergence inspires aspirations to find a more efficient alternative. In the current study a hybrid iterative algorithm is employed for solving nonlinear problems. To that effect, an alternative to the Newton- Raphson method, and related classical methods in numerical computing based on a Homotopy Perturbation Method (HPM) is introduced. In perturbation methods, perturbation quantities are used to replace a nonlinear problem by a number of manageable linear subproblems. Then, an approximate solution is reached by summing up the results of these subproblems. In this paper three global methods belonging to this family are discussed and then it is shown how to combine a global method with Newton-Raphson method into a hybrid algorithm as a possible way to reduce computational cost. Several well-known and difficult applications are considered for testing the performance of the new approach. The results reveal that using 2nd HPM coupled with two-point method requires less time to achieve convergence and reduces the total number of iterations.