Study on structural non-probabilistic reliability index under convex models and its solution methods

In the circumstances of hardly defining precise probability distributions of uncertainties when only a limited number of sample information is available, the non-probabilistic reliability based on convex models serves as an effective approach for structural safety assessment. Based on the multi-ellipsoid model description for bounds of uncertainties in material properties, geometric dimensions and loading conditions, a min-max mathematical definition of the non-probabilistic reliability index is presented by using the normalized transformation and the generalized infinity norm measurement. The presented non-probabilistic reliability index can be regarded as the relative "length" ratio of the structural allowable variation range to the reference variation range. By approximating the limit-state function with linear expansion, an explicit iterative algorithm is presented for solving the non-probabilistic reliability index conveniently. Numerical examples are given to illustrate the validity and efficiency of the present iterative approach.