Modified scheme based on semi-analytic approach for computing non-probabilistic reliability index

A new computation scheme proposed to tackle commensurate problems is developed by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.