An Iterative Two-step Lagrangian-based Method for Evaluation of Structural Reliability Index

In structural reliability analysis, Hasofer-Lind and Rackwitz-Fiessler (HL-RF) method is a widely used approximation for evaluating the index. However, by increasing nonlinearity or complexity in limit state function of structure, HL-RF may get trouble convergence. This paper represents an iterative algorithm that tries to minimize Lagrange function, associated with problem. each iteration this method, two steps are followed, satisfy minimization condition existing constraint. first step, movement descent direction followed. second another search contributes approach surface, therefore next can start from vicinity surface. Employing simultaneously proposed two-step Lagrangian-based (TSLB) help control numerical instability highly nonlinear problems. The accuracy robustness shown illustrative examples literature.