Stochastic Structural Dynamics

Application of Finite Element Methods

Cho W. S. To

• Publisher: Wiley
• Year: 2013
• Print ISBN: 9781118342350
• eBook ISBN: 9781118402726
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

One of the first books to provide in-depth and systematic application of finite element methods to the field of stochastic structural dynamics

The parallel developments of the Finite Element Methods in the 1950's and the engineering applications of stochastic processes in the 1940's 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. Aimed at advanced and specialist levels, the author presents and illustrates analytical and direct integration methods for analyzing the statistics of the response of structures to stochastic loads. The analysis methods are based on structural models represented via the Finite Element Method. In addition to linear problems the text also addresses nonlinear problems and non-stationary random excitation with systems having large spatially stochastic property variations.

• A systematic treatment of stochastic structural dynamics applying the finite element methods
• Highly illustrated throughout and aimed at advanced and specialist levels, it focuses on computational aspects instead of theory
• Emphasizes results mainly in the time domain with limited contents in the time-frequency domain
• Presents and illustrates direction integration methods for analyzing the statistics of the response of linear and nonlinear structures to stochastic loads

Under Author Information - one change of word to existing text: He is a Fellow of the American Society of Mechanical Engineers (ASME)........

Table of contents

• Cover
• Half Title page
• Title page
• Copyright page
• Dedication
• Preface
• Acknowledgments
• Chapter 1: Introduction
• Chapter 2: Spectral Analysis and Response Statistics of Linear Structural Systems
• Chapter 3: Direct Integration Methods for Linear Structural Systems
• Chapter 4: Modal Analysis and Response Statistics of Quasi-linear Structural Systems
• Chapter 5: Direct Integration Methods for Response Statistics of Quasi-linear Structural Systems
• Chapter 6: Direct Integration Methods for Temporally Stochastic Nonlinear Structural Systems
• Chapter 7: Direct Integration Methods for Temporally and Spatially Stochastic Nonlinear Structural Systems
• Appendix 1A: Mass and Stiffness Matrices of Higher Order Tapered Beam Element
• Appendix 1B: Consistent Stiffness Matrix of Lower Order Triangular Shell Element
• Appendix 1C: Consistent Mass Matrix of Lower Order Triangular Shell Element
• Appendix 2A: Eigenvalue Solution
• Appendix 2B: Derivation of Evolutionary Spectral Densities and Variances of Displacements
• Appendix 2C: Time-dependent Covariances of Displacements
• Appendix 2D: Covariances of Displacements and Velocities
• Appendix 2E: Time-dependent Covariances of Velocities
• Appendix 2F: Cylindrical Shell Element Matrices
• Appendix 3A: Deterministic Newmark Family of Algorithms
• Index