Randomly Excited Structures Reliability by Means of the Von Mises Stress Response

The paper presents a complete analysis of the probabilistic structure for the von Mises stress. Von Mises stresses are a nonlinear function of the stress vector components, so the form of their probability distribution is not known a priori. The resulting probability distribution is not gaussian, nor it is centered about zero, even when the stress vector components are gaussian with zero mean. The derivation of a simple analytical form for the cumulative probability distribution is presented first. The effective computation of the probability distribution can be performed either by a Monte Carlo Simulation or by means of a direct numerical integration. For a fast preliminary analysis of the von Mises stress range around the high-probability tail of the cumulative probability distribution, a simplified interpolation approach can be effectively used. The information gained by means of any of the methods presented might then be used for a reliability analysis of the structure under investigation.