Cover -- Title Page -- Copyright Page -- Table of Contents -- Dedication -- Preface -- Acknowledgements -- 1. Introduction -- 1.1 Displacement Formulation Based Finite Element Method -- 1.1.1 Derivation of element equation of motion -- 1.1.2 Mass and stiffness matrices of uniform beam element -- 1.1.3 Mass and stiffness matrices of tapered beam element -- 1.2 Element Equations of Motion for Temporally and Spatially Stochastic Systems -- 1.3 Hybrid Stress Based Element Equations of Motion -- 1.3.1 Derivation of element equation of motion -- 1.3.2 Mass and stiffness matrices of uniform beam element -- 1.4 Incremental Variational Principle and Mixed Formulation Based Nonlinear Element Matrices -- 1.4.1 Incremental variational principle and linearization -- 1.4.2 Linear and nonlinear element stiffness matrices -- 1.5 Constitutive Relations and Updating of Configurations and Stresses -- 1.5.1 Elastic materials -- 1.5.2 Elasto-plastic materials with isotropic strain hardening -- 1.5.3 Configuration and stress updatings -- 1.6 Concluding Remarks -- References -- 2. Spectral Analysis and Response Statistics of Linear Structural Systems -- 2.1 Spectral Analysis -- 2.1.1 Theory of spectral analysis -- 2.1.2 Remarks -- 2.2 Evolutionary Spectral Analysis -- 2.2.1 Theory of evolutionary spectra -- 2.2.2 Modal analysis and evolutionary spectra -- 2.3 Evolutionary Spectra of Engineering Structures -- 2.3.1 Evolutionary spectra of mast antenna structure -- 2.3.2 Evolutionary spectra of cantilever beam structure -- 2.3.3 Evolutionary spectra of plate structure -- 2.3.4 Remarks -- 2.4 Modal Analysis and Time-Dependent Response Statistics -- 2.4.1 Time-dependent covariances of displacements -- 2.4.2 Time-dependent covariances of displacements and velocities -- 2.4.3 Time-dependent covariances of velocities -- 2.4.4 Remarks.

2.5 Response Statistics of Engineering Structures -- 2.5.1 Mast antenna structure -- 2.5.2 Truncated conical shell structures -- 2.5.3 Laminated composite plate and shell structures -- References -- 3. Direct Integration Methods for Linear Structural Systems -- 3.1 Stochastic Central Difference Method -- 3.2 Stochastic Central Difference Method with Time Co-ordinate Transformation -- 3.3 Applications -- 3.3.1 Beam structures under base random excitations -- 3.3.2 Plate structures -- 3.3.3 Remarks -- 3.4 Extended Stochastic Central Difference Method and Narrow-band Force Vector -- 3.4.1 Extended stochastic central difference method -- 3.4.2 Beam structure under a narrow-band excitations -- 3.4.3 Concluding remarks -- 3.5 Stochastic Newmark Family of Algorithms -- 3.5.1 Deterministic Newmark family of algorithms -- 3.5.2 Stochastic version of Newmark algorithms -- 3.5.3 Responses of square plates under transverse random forces -- References -- 4. Modal Analysis and Response Statistics of Quasi-linear Structural Systems -- 4.1 Modal Analysis of Temporally Stochastic Quasi-linear Systems -- 4.1.1 Modal analysis and bi-modal approach -- 4.1.2 Response statistics by Cumming's approach -- 4.2 Response Analysis Based on Melosh-Zienkiewicz-Cheung Bending Plate Finite Element -- 4.2.1 Simply-supported plate structure -- 4.2.2 Square plate clamped at all sides -- 4.2.3 Remarks -- 4.3 Response Analysis Based on High Precision Triangular Plate Finite Element -- 4.3.1 Simply-supported plate structures -- 4.3.2 Square plate clamped at all sides -- 4.4 Concluding Remarks -- References -- 5. Direct Integration Methods for Response Statistics of Quasi-linear Structural Systems -- 5.1 Stochastic Central Difference Method for Quasi-linear Structural Systems -- 5.1.1 Derivation of covariance matrix of displacements.

5.1.2 Column under external and parametric random excitations -- 5.2 Recursive Covariance Matrix of Displacements of Cantilever Pipe Containing Turbulent Fluid -- 5.2.1 Recursive covariance matrix of displacements -- 5.2.2 Cantilever pipe containing turbulent fluid -- 5.3 Quasi-linear Systems under Narrow-band Random Excitations -- 5.3.1 Recursive covariance matrix of pipe with mean flow and under narrow-band random excitation -- 5.3.2 Responses of pinned pipe with mean flow and under narrow-band random excitation -- 5.4 Concluding Remarks -- References -- 6. Direct Integration Methods for Temporally Stochastic Nonlinear Structural Systems -- 6.1 Statistical Linearization Techniques -- 6.2 Symplectic Algorithms of Newmark Family of Integration Schemes -- 6.2.1 Deterministic symplectic algorithms -- 6.2.2 Symplectic members of stochastic version of Newmark family of algorithms -- 6.2.3 Remarks -- 6.3 Stochastic Central Difference Method with Time Co-ordinate Transformation and Adaptive Time Schemes -- 6.3.1 Issues in general nonlinear analysis of shells -- 6.3.2 Time-dependent variances and mean squares of responses -- 6.3.3 Time co-ordinate transformation and adaptive time schemes -- 6.4 Outline of steps in computer program -- 6.5 Large Deformations of Plate and Shell Structures -- 6.5.1 Responses of cantilever plate structure -- 6.5.2 Responses of clamped spherical cap -- 6.6 Concluding Remarks -- References -- 7. Direct Integration Methods for Temporally and Spatially Stochastic Nonlinear Structural Systems -- 7.1 Perturbation Approximation Techniques and Stochastic Finite Element Methods -- 7.1.1 Stochastic finite element method -- 7.1.2 Statistical moments of responses -- 7.1.3 Solution procedure and computational steps -- 7.1.4 Concluding remarks.

7.2 Stochastic Central Difference Methods for Temporally and Spatially Stochastic Nonlinear Systems -- 7.2.1 Temporally and spatially homogeneous stochastic nonlinear systems -- 7.2.2 Temporally and spatially non-homogeneous stochastic nonlinear systems -- 7.3 Finite Deformations of Spherical Shells with Large Spatially Stochastic Parameters -- 7.3.1 Spherical cap with spatially homogeneous properties -- 7.3.2 Spherical cap with spatially non-homogeneous properties -- 7.4 Closing Remarks -- References -- Appendices -- 1A Mass and Stiffness Matrices of Higher Order Tapered Beam Element -- 1B Consistent Stiffness Matrix of Lower Order Triangular Shell Element -- 1B.1 Inverse of Element Generalized Stiffness Matrix -- 1B.2 Element Leverage Matrices -- 1B.3 Element Component Stiffness Matrix Associated with Torsion -- References -- 1C Consistent Mass Matrix of Lower Order Triangular Shell Element -- Reference -- 2A Eigenvalue Solution -- References -- 2B Derivation of Evolutionary Spectral Densities and Variances of Displacements -- 2B.1 Evolutionary Spectral Densities Due to Exponentially Decaying Random Excitations -- 2B.2 Evolutionary Spectral Densities Due to Uniformly Modulated Random Excitations -- 2B.3 Variances of Displacements -- References -- 2C Time-dependent Covariances of Displacements -- 2D Covariances of Displacements and Velocities -- 2E Time-dependent Covariances of Velocities -- 2F Cylindrical Shell Element Matrices -- 3A Deterministic Newmark Family of Algorithms -- Reference -- Index.