Estimating the probability distribution of von Mises stress for structuresundergoing random excitation

The von Mises stress is often used as the metric for evaluating design marg ins, particularly for structures made of ductile materials. For determinist ic loads, both static and dynamic, the calculation of von Mises stress is s traightforward, as is the resulting calculation of reliability. For loads m odeled as random processes, the task is different; the response to such loa ds is itself a random process and its properties must be determined in term s of those of both the loads and the system. This has been done in the past by Monte Carlo sampling of numerical realizations that reproduce the secon d order statistics of the problem. Here, we present a method that provides analytic expressions for the probability distributions of von Mises stress which can be evaluated efficiently and with good numerical precision. Furth er, this new approach has the important advantage of providing the asymptot ic properties of the probability distribution.