AN EFFICIENT FORMULATION FOR LIMIT STATE FUNCTION GRADIENT CALCULATION

In the first-order second moment (FOSM) reliability analysis, the grad ients of the limit state function with respect to the basic random var iables need to be calculated. For complex structures, these calculatio ns can often be performed with the use of the probabilistic finite ele ment (PFE) routines. However, for practical problems with a large numb er of basic random variables, the computation of the gradients is usua lly very expensive. This is particularly true in the FOSM analysis sin ce the computation of the gradient vector is required to be repeated a t each iteration step in the optimization algorithm. A new formulation , which reduces CPU time in computing the gradient vector without affe cting the accuracy, is developed in this paper. For a simple example, direct comparison of the new technique with other methods that it is a ble to significantly reduce the CPU time and storage space requirement s.