Monte Carlo techniques in computational stochastic mechanics

A state of the art on simulation methods in stochastic structural analysis is presented. The purpose of the paper is to review some of the different methods available for analysing the effects of randomness of models and data in structural analysis. While most of these techniques can be grouped under the general name of Monte Carlo methods, the several published algorithms are more suitable to some objectives of analysis than to others in each case. These objectives have been classified into the foolowing cathegories: (1), The Statistical Description of the structural scattering, a primary analysis in which the uncertain parameters are treated as random variables; (2) The consideration of the spatial variability of the random parameters, that must then be modelled as Random Fields (Stochastic Finite Elements); (3) The advanced Monte Carlo methods for calculating the usually very low failure probabilities (Reliability Analysis) and, (4), a deterministic technique that depart from the random nature of the above methods, but which can be linked with them in some cases, known as the Response Surface Method. All of these techniques are critically examined and discussed. The concluding remarks point out some research needs in the field from the authors' point of view.