Add the Two-Dimensional Highly Non-Linear Limit State Function (Example 5) from Grandhi and Wang (1999)

[damar-wicaksono]

The two-dimensional reliabity test function from Grandhi and Wang (1999)¹ is defined as follows (see Example 5):

$$ \mathcal{M}(\boldsymbol{x}) = 2.5 + 0.00463 (x_1 + x_2 - 20)^4 - 0.2357 (x_1 - x_2), $$

where $\boldsymbol{x} = \{ x_1, x_2 \}$ is the vector of input variables modeled as two independent normal random variables with mean $10$ and standard deviation $3$.
The function features a highly-nonlinear limit state function.

Footnotes

1. R. V. Grandhi and L. Wang, “Higher-order failure probability calculation using nonlinear approximations,” Computer Methods in Applied Mechanics and Engineering, vol. 168, no. 1–4, pp. 185–206, Jan. 1999, doi: 10.1016/S0045-7825(98)00140-6. ↩