Chowdhury / Dasgupta Dynamics of Structure and Foundation - A Unified Approach

1. Fundamentals
1. Auflage 2008
ISBN: 978-1-134-02985-3
Verlag: Taylor & Francis
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 882 Seiten

Designed to provide engineers with quick access to current and practical information on the dynamics of structure and foundation, this 2-volume reference work is intended for engineers involved with earthquake or dynamic analysis, or the design of machine foundations in the oil, gas, and energy sector. Volume 1 deals with theories and formulations, covering the full range of topics involved with dynamics of structure and foundation. It specifically focuses on a unified approach in dealing with dynamic soil-structure interaction and geotechnical considerations for dynamic soil-structure interaction. The authors present new insights and theories, such as the computation of Rayleigh damping for structures with a large number of degrees of freedom, and the dynamic analysis of Hammer foundations, considering non-classical soil damping. It addresses detailed themes: elasticity and numerical methods in engineering; lumped parameter vibration; soil-structure systems under static load, and structural and soil dynamics. Vol. 2 (ISBN 9780415492232) focusses on Applications.

Autoren/Hrsg.

Chowdhury, Indrajit

Dasgupta, Shambhu P.

Fachgebiete

• Geowissenschaften Geologie Geophysik
• Naturwissenschaften Physik Angewandte Physik Geophysik

Inhaltsverzeichnis

1 Introduction

- 1.1 Why this book

- 1.2 Why the topic of dynamics?

- 1.3 The demography of the book

2 Theory of elasticity and numerical methods in engineering

- 2.1 Mechanics of continua: Stress and strain

- 2.2 Concept of strain

- 2.2.1 Displacement field

- 2.2.2 Concept of small domain

- 2.2.3 Body undergoing small deformation

- 2.2.4 Strain tensor

- 2.2.5 Derivative of a vector fixed in a moving reference

- 2.2.6 Physical interpretation of strain tensor

- 2.2.7 Cubical dilatation

- 2.2.8 Transformation of strains

- 2.2.9 Equations of compatibility

- 2.3 Stresses

- 2.3.1 Concept of stress

- 2.3.2 Principal stresses and strains, invariants

- 2.3.3 Cauchy’s stress quadric and Mohr diagram

- 2.3.4 Plane stress conditions

- 2.3.5 Plane strain conditions

- 2.3.6 Octahedral stresses and strains

- 2.3.7 Spherical and deviatoric stress components

- 2.4 Constitutive relations

- 2.5 Equations of equilibrium

- 2.5.1 Some useful expressions

- 2.5.2 Differential equations at a point (general)

- 2.5.3 Differential equations at a point (in terms of stresses)

- 2.5.4 Differential equations at a point (in terms of displacements)

- 2.5.5 General solution

- 2.5.6 Two-dimensional cases

- 2.6 Theorems of elasticity

- 2.6.1 Principles of superposition

- 2.6.2 Strain energy

- 2.6.3 Virtual work

- 2.7 Mechanics of homogeneous isotropic elastic bodies

- 2.7.1 Material derivative of volume integral

- 2.7.2 The equations of continuity

- 2.7.3 The equations of motion

- 2.7.4 Moment of momentum

- 2.7.5 Basic equation of motion of an elastic body

- 2.7.6 Various strain measures

- 2.7.7 Solution of the three-dimensional equation

- 2.7.8 Static solutions with no body forces

- 2.8 Some basics

- 2.8.1 Summary of governing equations/relations

- 2.8.2 Lame’s equations [combining all equations, governing differential equation in terms

- of u, v, w]

- 2.9 Some classical solutions of elastostatics

- 2.9.1 Kelvin (1848) problem – A single force acting in the interior of an infinite solid.

- (Malvern 1969, Fung 1965)

- 2.9.2 Boussinesq (1878) problem – A normal force acting on the surface of a semi-infinite solid

- 2.9.3 Cerruti (1882) problem – A tangential force acting on the surface of a semi-infinite solid

- (Mindlin 1936, Love 1944), [same as Boussinesq’s problem, only the load acting on the surface is horizontal]

- 2.9.4 Mindlin’s (1936) solution

- 2.9.5 Theories of Elastodynamics

- 2.10 Numerical methods in engineering: Basics and applications

- 2.10.1 Introduction

- 2.10.2 Approximate methods applied to boundary value problems

- 2.11 The Finite Difference Method (FDM)

- 2.11.1 Application to ordinary differential equations (ode)

- 2.11.2 Application to partial differential equations

- 2.11.3 Laplace and Biharmonic equations

- 2.11.4 Irregular meshes or grids

- 2.11.5 Laplace operator with irregular mesh

- 2.11.6 Bi-harmonic equations with irregular meshes

- 2.11.7 Refined finite difference analysis

- 2.11.8 Free edged plates with different boundary conditions

- 2.11.9 Finite difference in polar co-ordinate

- 2.11.10 Finite difference solution for initial value problem

- 2.11.11 Finite difference solution for initialboundary value problem

- 2.11.12 Finite difference application in dynamics

- 2.12 The finite element method

- 2.12.1 The finite element club and its members

- 2.12.2 Brief history on the development of finite element method

- 2.12.3 The basic philosophy

- 2.12.4 Displacement based derivation of stiffness matrix

- 2.12.5 Plane strain CST element

- 2.12.6 Why constant strain and how effective is the element?

- 2.12.7 Why convergence improve with refined meshes

- 2.12.8 The constitutional laws which bound the developers

- 2.12.9 The rule of polynomial – the entry rule to developers club

- 2.12.10 How do we select the polynomial function correctly?

- 2.12.11 The law of convergence – the three commandments

- 2.12.12 Non-conforming elements an exception to the law

- 2.12.13 Natural coordinates: the gateway to numerical analysis through computer

- 2.12.14 Numerical integration technique used for FEM

- 2.12.15 Gauss quadrature scheme for numerical integration

- 2.12.16 Stiffness matrix for 4-nodded rectangular element under plane strain condition

- 2.12.17 Iso-parametric formulation for elements with arbitrary shape

- 2.12.18 Other form of isoparametric elements

- 2.12.19 Iso-parametric formulation of CST element

- 2.12.20 Condensation – The Houdini trick of vanishing nodes

- 2.12.21 Alternative method of deriving a quadrilateral element

- 2.12.22 The Reverse Logic – How correct it is?

- 2.12.23 Incompatible or Non-conforming element – Where two wrongs make one right

- 2.12.24 How tough is this lawbreaker?

- 2.12.25 Taylor’s improved incompatible quadrilateral

- 2.12.26 Higher order finite elements – The second generation members of the FEM family

- 2.12.27 Lagrange’s interpolation function – An extension to school co-ordinate geometry

- 2.12.28 Elements of Serendipidity family – named after Princes of Serendip

- 2.12.29 Other type of higher order elements

- 2.12.30 Plate element – the problem child of FEM family

- 2.12.31 Triangular plate element in bending – the Catch-22 element

- 2.12.32 DKT Plate element

- 2.12.33 Rectangular plate element in bending mode

- 2.12.34 Four-nodded quadrilateral plate element in bending

- 2.12.35 Three Dimensional Hexahedral Element – One last to bore you

- 2.12.36 Twenty-nodded hexahedral element

- 2.12.37 The patch and eigenvalue test – The performance warranty certificates

- 2.12.38 A retrospection on what we presented so far

- 2.12.39 The assemblers – the tailors who stitches the pieces to give final shape

- 2.12.40 Formulation of the global stiffness matrix

- 2.12.41 Transformation in space for 3D analysis

- 2.12.42 Members vertical in space – a special case

- 2.12.43 Global stiffness matrix and transformation of finite element continuum

- 2.12.44 Implementing the boundary condition

- 2.12.45 Formulating specified support displacement

- 2.12.46 Calculation of element stress and displacements

- 2.12.47 Solution of equilibrium equation

- 2.12.48 Gaussian elimination – The technique of back substitution

- 2.12.49 The LDLT decomposition technique

- 2.12.50 Frontal wave solution – Iron’s technique reflecting present consumer market

- 2.12.51 The World of Boris Galerkin – A look at finite element beyond stress analysis

- 2.12.52 Thermal analysis of composite wall in one dimension

- 2.12.53 The user domain-rookies, fakes, control freaks and clever Ivans

- 2.12.54 Finite element model of table top centrifugal compressor with dynamic soil-structure interaction

- 2.12.55 Static soil-structure interaction analysis of a pedestrian subway below ground

3 Basics of lumped parameter vibration

- 3.1 Introduction

- 3.2 Single-degree-of freedom

- 3.2.1 Free vibration: Undamped case

- 3.2.2 Forced vibration

- 3.2.3 Steady-state analysis: Mechanical impedance method

- 3.2.4 Q-values and their interpretation

- 3.2.5 Power absorption

- 3.2.6 Heavy damping

- 3.2.7 Frequency dependent loading

- 3.2.8 Dissipation of energy

- 3.2.9 Velocity squared damping

- 3.2.10 Solid damping

- 3.2.11 Analysis of friction forces (Coulomb friction, dry friction)

- 3.2.12 Response under impulsive loading

- 3.2.13 General solution for any arbitrary forcing system

- 3.2.14 Response spectra

- 3.2.15 Earthquake type of excitation

- 3.3 Stability of dynamic solutions

- 3.3.1 Phase planes and stability of solution

- 3.3.2 Basics of differential equation

- 3.3.3 Homogeneous Systems with Constant Coefficients, Phase Plane, Critical Points

- 3.3.4 Phase plane method for SDOF system

- 3.3.5 Self-excited oscillations

- 3.3.6 Autonomous system

- 3.3.7 State space method

- 3.3.8 State speed

- 3.3.9 Stability of the solution

- 3.4 Multiple-degrees-of-freedom systems

- 3.4.1 Free vibration: Undamped system

- 3.4.2 Steady-state analysis: Mechanical impedance method

- 3.4.3 Coupled translation and rotation

- 3.4.4 Forced vibration

- 3.4.5 Semi-definite systems

- 3.5 Nonlinear systems

- 3.5.1 Free vibrations

- 3.5.2 Forced vibrations

- 3.5.3 Large amplitudes in response: Order and chaos

4 An introduction to soil-structure systems under statical condition

- 4.1 Introduction

- 4.1.1 What we did twenty years ago

- 4.1.2 The Present Scenario.

- 4.2 Soil-structure interaction

- 4.3 Static soil-structure interaction

- 4.4 Non uniform contact pressure

- 4.5 Various soil models–the tools in the toolkit

- 4.5.1 Winkler springs

- 4.5.2 Estimation of sub-grade modulus

- 4.6 Evaluation of nodal springs

- 4.6.1 So the ground rule is

- 4.7 Limitations/advantages of Winkler spring model

- 4.8 Finite element models

- 4.8.1 Plate element

- 4.9 Finite element analysis of plate with soil stiffness based on isotropic elastic half space theory

- 4.9.1 Displacement profile of soil under a foundation based on half space theory

- 4.10 Finite grid method/equivalent beam element, the unsung work horse

- 4.11 FEM application for problems of class 2D

- 4.12 Plane stress and plane strain condition

- 4.12.1 Plane stress condition

- 4.12.2 Plane strain condition

- 4.13 FEM model for the vertical cut problem

- 4.14 Infinite finite element a logical paradox

- 4.15 Basis of formulation of the infinite element

- 4.15.1 What does it really mean?

- 4.15.2 Why did we transform the co-ordinate and what did we gain out of it?

- 4.16 Material property affecting the model

- 4.17 Relation between sub-grade modulus and modulus of elasticity

- 4.18 Selection of Poisson’s ratio

- 4.19 Limitation and advantages of finite element method in static soil structure interaction problem

5 Concepts in structural and soil dynamics

- 5.1 Introduction

- 5.2 A brief history of dynamic analysis of structure and foundation in civil engineering

- 5.2.1 Basic concepts

- 5.2.2 Orthogonal transformation or the transformation basis

- 5.2.3 Direct integration technique, the alternate approach

- 5.2.4 Wilson-Theta method

- 5.3 Eigen value analysis

- 5.3.1 Some techniques for eigen value analysis

- 5.3.2 Standard Jacobi’s technique

- 5.3.3 Generalized Jacobi technique

- 5.3.4 Dynamic analysis based on finite element method

- 5.4 Introduction to soil and elasto-dynamics

- 5.4.1 Development of soil dynamics to the present state of art

- 5.4.2 One-dimensional propagation of wave through an elastic medium

- 5.4.3 Three-dimensional propagation of waves in an infinite elastic medium

- 5.4.4 Propagation of waves in polar co-ordinates

- 5.4.5 Reflection/Refraction

- 5.4.6 Where does this all lead to?

- 5.4.7 Some background on integral transforms and other mathematical theorems

- 5.5 Halfspace elastodynamic solution

- 5.5.1 Lamb’s solution for two-dimensional problem

- 5.5.2 Pekeris’ solution for surface pulse

- 5.5.3 Pekeris’ solution for buried pulse

- 5.5.4 Interpretation of Pekeris’ solution

- 5.5.5 Chang’s Solution to dynamic response for horizontal surface loading

- 5.6 Geotechnical earthquake analysis

- 5.6.1 Soil dynamics and earthquake

- 5.6.2 Waves induced by underground blast

- 5.7 Geotechnical analysis of machine foundations

- 5.7.1 Soil dynamics and machine foundation

- 5.7.2 Reissner’s method

- 5.7.3 Sung and Quinlan’s method

- 5.7.4 Bycroft’s solution for dynamic response of foundation

- 5.7.5 Reissner and Sagoci’s method of torsional oscillation

- 5.7.6 Hseih’s method for dynamic response of foundation

- 5.7.7 Lysmer and Richart’s model for dynamic response of foundation

- 5.7.8 Hall’s analog for sliding and rocking vibration

- 5.7.9 Vibration of rectangular footings resting on elastic half-space

- 5.7.10 Rigid strip footing

- 5.7.11 Luco and Westmann solution for rigid strip footing

- 5.7.12 Dynamic response of circular footings

- 5.7.13 Vibration of an elastic half space under rectangular loading

- 5.8 Vibration of embedded footings

- 5.8.1 Embedment effect on foundation

- 5.8.2 Research carried out in India

- 5.8.3 Energy transmitted from a circular area

- 5.9 Finite element solution for foundation dynamics

- 5.9.1 Soil dynamics and finite element analysis

- 5.9.2 Use of structural boundary conditions

- 5.9.3 Use of spring or boundary elements

- 5.9.4 Use of transmitting/silent boundaries with finite elements

- 5.9.5 Standard viscous and Rayleigh boundary elements

- 5.9.6 Paraxial boundaries

- 5.9.7 Infinite finite elements

- 5.9.8 Epilogue

References
Subject index