The parallel developments of the Finite Element Methods (FEM) and the engineering applications of stochastic processes in the mid-20th century provided a combined numerical analysis tool for the studies of dynamics of structures and structural systems under random loadings. In the open literature, there are books on statistical dynamics of structures and books on structural dynamics with chapters dealing with random response analysis. However, a systematic treatment of stochastic structural dynamics applying the finite element methods seems to be lacking, and this book redresses the balance.
Aimed at advanced and specialist levels, the author presents and illustrates closed form solutions and the stochastic central difference methods for the computation of response statistics of linear and quasi-linear structures to nonstationary random loads. In addition to the linear and quasi-linear problems, the text also addresses highly nonlinear systems with uncertain parameters of large variations. The systems considered in the text include beam, plate and shell structures which are represented by the FEM.
Key features:
- Fully illustrated throughout and aimed at advanced and specialist levels, the focus is on closed form solutions and computational approaches
- Emphasizes results of time-dependent response statistics of beam, plate and shell structures represented by the FEM
- Presents and illustrates computed results of highly nonlinear deformations of finite rotations and finite strains with large uncertain variations
- Presents efficient methods for large-scale computation of time-dependent linear and nonlinear response statistics of structural systems approximated by the FEM
