Some Developments in Directional Simulation for Time Variant Structural Systems

Abstract

The mechanical response of a structural system subject to one or more load processes is described in reliability theory by a limit state (hyper-) surface. For complex systems this surface may not be known explicitly. In the formulation presented, a probabilistic structural analysis technique for structural system evaluation is employed to obtain the probabilistic but implicit limit state function as it exists in the load process space. Directional simulation is employed to estimate the outcrossing rate and the initial (zero time) probability of failure and hence to estimate the probability of failure at any subsequent time. Both continuous (Gaussian) and discrete pulse (Poisson) processes are considered. Some discussion of the relationship of the proposed method to importance sampling methods applied to multi-limit state structural systems is also given.