A robust approximation method for nonlinear cases of structural reliability analysis. (November 2017) - Roudak, Mohammad Amin; Shayanfar, Mohsen Ali; Barkhordari, Mohammad Ali; Karamloo, Mohammad
Highlights: A reliability algorithm in the category of approximation methods is proposed. The algorithm is a generalization of HL-RF method in computing reliability index. Two adjusting parameters are included in HL-RF method. The parameters help to control the instability of HL-RF in highly nonlinear cases. The algorithm is robust and efficient while keeping the simplicity of HL-RF. Abstract: The Hasofer–Lind and Rackwitz–Fiessler (HL-RF) method is a popular iterative approximation method in structural reliability analysis. However, it may pose numerical instability and result in divergence in the face of high nonlinearity. In the present paper, two adjusting parameters are included in this method and a generalization of HL-RF is proposed. The represented parameters are to control the convergence of the sequence especially when nonlinearity increases. The proposed algorithm actually improves the performance of HL-RF in convergence, while it remains as simple as HL-RF to implement without any need to merit functions or line search processes, needed in many approximation methods. Through various numerical examples, the robustness and efficiency of the proposed algorithm in highly nonlinear cases have been shown. Graphical abstract: