Probability Distribution of von Mises Stress in the Presence of Pre-load

Random vibration under preload is important in multiple endeavors, including those involving launch and re-entry. In these days of increasing reliance on predictive simulation, it is important to address this problem in a probabilistic manner - this is the appropriate flavor of quantification of margin and uncertainty in the context of random vibration. One of the quantities of particular interest in design is the probability distribution of von Mises stress. There are some methods in the literature that begin to address this problem, but they generally are extremely restricted and astonishingly, the most common restriction of these techniques is that they assume zero mean loads. The work presented here employs modal tools to suggest an approach for estimating the probability distributions for von Mises stress of a linear structure for the case of multiple independent Gaussian random loadings combined with a nonzero pre-load.