Abstract
Random vibration analysis (RVA) of structural systems is a rapidly growing branch of engineering mechanics. The theory of random vibration is central to the analysis and design of structures in a variety of engineering fields. In recent years, RVA in conjunction with finite element methods has been available in several commercial computer-aided-engineering software, such as ANSYS, NASTRAN, etc. The finite element-based RVA is being widely adopted for computing stochastic responses, such as displacements, stresses and strains in terms of statistical quantities, i.e., root-mean-square responses. However, these statistical responses from RVA are limited to Cartesian responses which depend on the coordinate system of use. In structural design, a failure criterion using distortion energy known as the von Mises theory is more appropriate and of interest in this paper. The statistics of von Mises stress can not be obtained in terms of the statistics of Cartesian stresses. Simulation-based von Mises stress responses corresponding to a covariance matrix of Cartesian stresses are used to perform scatter and failure analyses. Based on a sufficient number of stress samples, a probability distribution of von Mises stress response may be obtained. Given a specified design criterion, statistical moments of safety margin as well as a safety index can be computed. In addition, a required design strength corresponding to a desired probability of failure can be provided in this study.