Publications

The von Mises stress is often used as the metric for evaluating design margins, particularly for structures made of ductile materials. While computing the von Mises stress distribution in a structural system due to a deterministic load condition may be straightforward, difficulties arise when considering random vibration environments. As a result, alternate methods are used in practice. One such method involves resolving the random vibration environment to an equivalent static load. This technique, however, is only appropriate for a very small class of problems and can easily be used incorrectly. Monte Carlo sampling of numerical realizations that reproduce the second order statistics of the input is another method used to address this problem. This technique proves computationally inefficient and provides no insight as to the character of the distribution of von Mises stress. This tutorial describes a new methodology to investigate the design reliability of structural systems in a random vibration environment. The method provides analytic expressions for root mean square (RMS) von Mises stress and for the probability distributions of von Mises stress which can be evaluated efficiently and with good numerical precision. Further, this new approach has the important advantage of providing the asymptotic properties of the probability distribution. A brief overview of the theoretical development of the methodology is presented, followed by detailed instructions on how to implement the technique on engineering applications. As an example, the method is applied to a complex finite element model of a Global Positioning Satellite (GPS) system. This tutorial presents an efficient and accurate methodology for correctly applying the von Mises stress criterion to complex computational models. The von Mises criterion is the traditional method for determination of structural reliability issues in industry.

Device penetration into media such as metal and soil is an application of some engineering interest. Often, these devices contain internal components and it is of paramount importance that all significant components survive the severe environment that accompanies the penetration event. In addition, the system must be robust to perturbations in its operating environment, some of which exhibit behavior which can only be quantified to within some level of uncertainty. In the analysis discussed herein, methods to address the reliability of internal components for a specific application system are discussed. The shock response spectrum (SRS) is utilized in conjunction with the Advanced Mean Value (AMV) and Response Surface methods to make probabilistic statements regarding the predicted reliability of internal components. Monte Carlo simulation methods are also explored.