A study of the dimensional invariance of the reliability index in Advanced First-Order Second-Moment Method.

Abstract

The dimensional invariance related to the reliability index is examined. The reliability indices β, based on the Advanced First-Order Second Moment (AFOSM) method by use of the stochastic finite element method, are evaluated in the cases of bars and square plates under tension, whose Young's modulus is regarded as spatial homogeneous stochastic process. The reliability index for the bars is obtained by means of the analytical formulation for continuum. The numerical results show that the reliability indices for several autocorrelation fucitons converge well with the increase of the finite element division, and the index for the bar agrees well with the analytical one. This suggests strongly that the dimensional invariance holds for the reliability index evaluated by the finite element discretization and AFOSM method.