Elasto–plastic analysis of steel plane frames using Homotopy Perturbation Method

In this research a new nonlinear method is developed based on Homotopy Perturbation Method (HPM) and is applied to elasto-plastic analysis of steel plane frames. The Homotopy algorithm can be considered as an advancement into classical methods of numerical computation such as Newton–Raphson method. In perturbation methods, perturbation quantities are used to transfer a nonlinear problem into a number of manageable linear sub-problems. Then an approximate solution is reached by summing up the results of first several sub-problems. The HPM developed here is applied to plane frames in which elastic–perfectly plastic behavior is assumed for structural material while conventional plastic hinges of zero length are used to model plasticity effect. Numerical examples are presented in this paper to show the accuracy and effectiveness of the proposed approach. Results obtained showed that when developed HPM is used for elasto-plastic analysis of structures, using various yield criteria for steel elements, less iteration is required to reach solution, and convergence is achieved very fast compared with conventional Newton–Raphson method.

► Homotopy Perturbation Method is applied to elasto-plastic analysis of frames.
► Both geometric and material nonlinearities are considered in this study.
► The proposed method can reduce number of iterations and the computational time.