Figure 2
The scatter plot presents x 1 on the horizontal axis and x 2 on the vertical axis, ranging approximately from negative 6 to positive 8 on both axes. A dense cloud of Monte Carlo simulation samples fills the central region. Discrete initial samples are distributed around and within this cloud at regular intervals. A closed, irregular boundary labelled theoretical G of x equals 0 encloses a central feasible region with curved and straight segments. The boundary intersects near x 1 around negative 1 and positive 2 at x 2 around 5, and near x 2 around negative 5 at x 1 around negative 1. The figure illustrates the relationship between sampled points and the theoretical limit state surface.The theoretical LSS and MCS samples in Example 1