Monte Carlo solution of structural dynamics

Abstract

The recent advent of high speed digital computers has made it not only possible but also highly practical to apply the Monte Carlo techniques to a large variety of engineering problems. In this paper a technique of digital simulation of multivariate and/or multidimensional Gaussian random processes (homogeneous or nonhomogeneous) which can represent physical processes germane to structural engineering is presented. The paper also describes a method of digital simulation of envelope functions. Such simulations are accomplished in terms of a sum of cosine functions with random phase angles and used as the basic tool in a general Monte Carlo method of solution of a wide class of problems in structural engineering. Most important problems for which the method is found extremely useful includes (a) numerical analysis of dynamic response of nonlinear structures to random excitations, (b) time domain analysis of linear structures under random excitations performed for the purpose of obtaining a kind of information, such as first excursion probability and time history of a sample function, that is not obtainable from the standard frequency domain analysis, (c) numerical solution of structural problems involving randomly nonhomogeneous material property such as wave propagation through random medium, and (d) dynamic analysis of extremely complex systems such as those involving structure-fluid interaction. Numerical examples of some of these problems are presented.