On computational stochastic structural dynamics applying finite elements

This article presents a review of the state of the art of techniques on computational stochastic structural dynamics applying the finite elements. Linear systems under random excitations, quasi-linear systems, nonlinear systems excited by stochastic disturbances, and spatially stochastic nonlinear systems are included. For spatially stochastic linear and nonlinear systems under stochastic and deterministic excitations, alternative approaches, proposed by the author, to the so-called stochastic finite element method are introduced. The introduced approaches are free from the limitations of the: (a) normal mode analysis for linear and quasi-linear systems, (b) normal mode with statistical linearization for nonlinear systems, and (c) perturbation approximation techniques for spatially stochastic systems. The introduced approaches for nonlinear systems are applicable to systems undergoing large deformations of finite strains and finite rotations. Selected computed results are included to demonstrate their simplicity and efficiency.[PUBLICATION ABSTRACT]