Mechanical and Civil Engineering Seminar

Monte Carlo Simulation (MCS) techniques were introduced in the field of Engineering & Applied Mechanics in the 1970's to deal with excitation as well as system uncertainties. Subsequently, MCS techniques enabled the accurate solution of complex stochastic nonlinear problems whose solutions were unavailable through analytical methods. One of the most critical parts of MCS techniques in Probabilistic Mechanics is the simulation of stochastic processes and fields involved in the problem under consideration. Usually, stochastic processes are used to model stochastic system excitations and stochastic fields to model stochastic system properties. These processes and fields can be scalar or vector, one-dimensional or multi-dimensional, Gaussian or non-Gaussian, stationary or non-stationary, homogeneous or non-homogeneous, or any combination of the above. Extensive work has been done in the last three decades in developing simulation algorithms for this purpose. This presentation will focus on two recent developments in this area: (1) simulation of non-Gaussian scalar and vector processes and fields, and (2) simulation of stochastic waves in lieu of stochastic vector processes of large size. Theoretical development of the algorithms will be provided as well as a number of numerical examples demonstrating their capabilities.