Study of Computation for Structural Reliability Index Based on Penalty Function Method

According to the geometric meaning of the structural reliability index, an unconstrained optimization model with structural reliability index and design point is obtained by exterior penalty function method. The Powell method, golden section method and extrapolation method are used to solve the unconstrained optimization problem. The proposed method not has to deal with the any derivative of the limited state function, and can been used to obtain structural reliability index and design point of the strong nonlinear limit state function, which first-order reliability method (FORM) may fail to converge. Three examples are given to compare penalty function method with the difference methods. The results show that the given method is simply, effective and precise enough.