An efficient formulation for limit state function gradient calculation

In the first-order second moment (FOSM) reliability analysis, the gradients of the limit state function with respect to the basic random variables need to be calculated. For complex structures, these calculations can often be performed with the use of the probabilistic finite element (PFE) routines. However, for practical problems with a large number of basic random variables, the computation of the gradients is usually very expensive. This is particularly true in the FOSM analysis since the computation of the gradient vector is required to be repeated at each iteration step in the optimization algorithm. A new formulation, which reduces CPU time in computing the gradient vector without affecting the accuracy, is developed in this paper. For a simple example, direct comparison of the new technique with other methods that it is able to significantly reduce the CPU time and storage space requirements.