A state-of-the-art report on computational stochastic mechanics

This state-of-the-art report assesses the current state of development of computational procedures as utilized in stochastic mechanics. The theoretical developments and aspects of practical applications are discussed in this report, which is structured in four sections. The first section is concerned with the latest developments in Monte Carlo simulation (MCS)--including parallel processing and various types of variance reduction techniques. In the second section, various possibilities for representing stochastic processes and random fields (including discrete and conditional representations) and wavelets are reviewed. The third section is concerned with various methods for prediction of the response of structural systems under stochastic excitation, e.g. by using the FEM method to solve the Fokker-Planck equation (FPE), path integral method, moment closure schemes, maximum entropy considerations, etc. This section also includes a brief subsection on computational aspects of stochastic stability. The final section is concerned with the treatment of stochastic uncertainties of system properties, such as material and geometric variation, by applying stochastic finite element methods (SFEMs). All sections include statements on the current limitations and also of the future potential of the discussed procedures.