Abstract
The new method is presented for computing engineering structure reliability by direct searching the next checking point and accelerating convergence based on the analysis of errors in the center point method and borrowing ideas form the merits of the other First-Order Second Moment (FOSM) methods. The idea of the direct searching method is constructing a new explicit searching formula to make the new checking point being more closed to the failure surface based on the results of the center point method. The new checking point has steepest descent character because the searching path is the gradient of the approximate surface. An example shows that the method presented in this article has well precision. Although the direct searching formula may not reach the globally optimal point, the error can be controlled owing to the locally optimal plan at each searching step.
Highlights
There are a lot of uncertainties in the analysis of engineering structure [1], the distribution type of the random variable is various, the functions of the member do not follow the normal distribution, which are generally nonlinear, it is hard to calculate the reliability index of the structure directly
The new method is presented for computing engineering structure reliability by direct searching the checking point and accelerating convergence based on the analysis of errors in the center point method and borrowing ideas form the merits of the other First-Order Second Moment (FOSM) methods
Big for the nonlinear limit state equation, as a result, reliability indexes which obtained from different format of nonlinear limit state equation with the same mechanical meaning differ greatly, it is inconvenient in the real application and could not meet the requirement of engineering accuracy
Summary
There are a lot of uncertainties in the analysis of engineering structure [1], the distribution type of the random variable is various, the functions of the member do not follow the normal distribution, which are generally nonlinear, it is hard to calculate the reliability index of the structure directly. Big for the nonlinear limit state equation, as a result, reliability indexes which obtained from different format of nonlinear limit state equation with the same mechanical meaning differ greatly, it is inconvenient in the real application and could not meet the requirement of engineering accuracy Both the checking point method and mapping transformation method select the design checking point as the linearization point of the nonlinear function, which could get reliability index with higher accuracy and ensure the uniqueness of reliability index for the same member, but the two methods are implicit and the calculation process are complex, which need several double iteration and the selection of initial values have impact on the iteration process, they are not easy to be applied in the real engineering. Based on the analysis of the defect of center point method and advantage of other methods, a new approximate calculation method which is suitable for engineering application and with high calculation accuracy is proposed in the paper
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