Several methods are currently available to solve a large number of problems in mechanics involving uncertain quantities described by stochastic processes, fields or waves. At this time, however, Monte Carlo simulation appears to be the only universal method that can provide accurate solutions for certain problems in stochastic mechanics involving nonlinearity, system stochasticity, stochastic stability, parametric excitations, large variations of uncertain parameters, etc., and that can assess the accuracy of other approximate methods such as perturbation, statistical linearization, closure techniques, stochastic averaging, etc. The major advantage of Monte Carlo simulation is that accurate solutions can be obtained for any problem whose deterministic solution (either analytical or numerical) is known. The only disadvantage of Monte Carlo simulation is that it is usually time-consuming. It is the author’s belief, however, that in the years to come, the continued evolution of digital computers will further enhance the usefulness of Monte Carlo simulation techniques in the area of engineering mechanics and structural engineering.
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- Simulation of Stochastic Processes and Fields to Model Loading and Material Uncertainties
- Springer Netherlands