Stochastic structural dynamics. Application of finite element methods (Q2866034)

The present book is an in-depth and systematic treatment of stochastic structural dynamics by applying the finite element method (FEM). First, the author presents and illustrates stochastic methods for the computation of response statistics of linear and quasi-linear structures subjected to non-stationary random loads. In addition to linear and quasi-linear problems, the highly nonlinear systems are described. The systems considered include beam, plate and shell structures studied using the FEM.NEWLINENEWLINEThe book has seven chapters. Chapter 1 introduces the displacement-based FEM and mixed formulation-based nonlinear element matrices together with constitutive relations. Chapter 2 is concerned with the spectral analysis and response statistics of linear structural systems. Direct integration methods for linear structural systems are presented in Chapter 3 by employing the stochastic central difference method. Modal analysis and response statistics of quasi-linear structural systems are covered in Chapter 4. Chapter 5 is concerned with the application of direct integration methods to the response statistics of quasi-linear structural systems. Direct integration methods for temporally stochastic nonlinear structural systems subjected to stationary and non-stationary random excitations are presented in Chapter 6. Chapter 7 is concerned with the presentation of direct integration methods for temporally and spatially stochastic nonlinear structural systems. The stochastic FEM and probabilistic FEM are introduced. Here the author also develops stochastic central difference methods for temporally and spatially stochastic structural systems subjected to stationary and non-stationary random excitations. Finally, some application of the method to spatially homogeneous and non-homogeneous shell structures are given.