Structural reliability assessment based on directional vector approximation method

A new numerical integration method for calculating structural failure probabilities based on a directional vector approximation is proposed. The approach is based on a division method of the surface of the unit hypersphere, in which the directional vectors are determined by relating to the finite element meshes allocated on the surface of the unit hypersphere. The failure probability is calculated by using the values of area of the finite element meshes and the upper probabilities of the chi square distribution. Numerical examples are provided to show the validity of the proposed method, which gives efficiently good approximate values of structural failure probabilities.