Reliability Assessment of Structural Systems Based on A Directional Vector Approximation Method.

Abstract

This paper describes a new method for evaluating the probability of structural failure based on a directional vector approximation. Since failure probability is defined by a directional integration of the conditional failure probability evaluated as the upper probability of a chi square distribution in the specified direction, it is evaluated by the summation of the product of the area of the finite element mesh and the upper probability of the chi square distribution corresponding to each element mesh. The directional vectors are detemined by adopting the unit centerline vectors related to finite element meshes allocated regularly on the surface of the unit sphere, which is divided analytically into a specified number of finite element meshes. The proposed method gives good estimates of the structural failure probability. Numerical examples are provided to show the validity of the proposed method.