A new method to solve the structural reliability index based on homotopy analysis

In this paper, we introduce a homotopy analysis method into the structural reliability analysis and propose a different algorithm from the traditional Hasofer–Lind–Rackwitz–Fiessler type of iterations to solve the reliability index. Due to the powerful function of homotopy analysis in solving nonlinear equations, the method presented in this paper yields high efficiency and strong convergence of the reliability analysis. We first establish the Karush–Kuhn–Tucker (KKT) condition of the optimization problem for reliability index in the first-order reliability method. Next, we construct the corresponding combined homotopy equations for the KKT condition and apply the path-tracking algorithm to efficiently solve the equations. Finally, several numerical examples and an engineering application are provided to validate the effectiveness of the present method.