An enhanced second-order method in structural reliability analyses

This paper proposes a more sophisticated second-order method for the analysis of structural reliability. The analysis procedures of this new method comprise: (1) Performing the second-order approximation of the limit state surface by the second order Taylor series expansion at the most probable failure point; (2) Obtaining a closed-form expression for a hyperparabolic surface as an approximate failure surface; (3) Breaking down the inner integral as specified in the failure probability equation into two parts; (4) Executing the integration in the failure probability equation and adding four terms so that the analytical result approaches the accurate result in an asymptotically increasing manner. Two calculation examples were utilized in this study to illustrate the accuracy and robustness of our proposed new enhanced second-order method for determining the failure probability in structural reliability analyses. The numerical calculation results showed that for these nonlinear problems the traditional Breitung method can give inaccurate results when compared with the Monte Carlo simulation results. On the contrary, when utilizing our proposed new enhanced second-order method, it is clear that the obtained failure probability results are more accurate when compared with the Monte Carlo simulation results. These computational results in this study convincingly substantiate that our proposed new enhanced second-order method is more accurate and robust than the traditional Breitung method for the nonlinear problems in structural reliability studies.