دانلود کتاب Computational Statics and Dynamics: An Introduction Based on the Finite Element Method

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Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Acknowledgements
Contents
Symbols and Abbreviations
Latin Symbols (Capital Letters)
Latin Symbols (Small Letters)
Greek Symbols (Capital Letters)
Greek Symbols (Small Letters)
Mathematical Symbols
Indices, Superscripted
Indices, Subscripted
Abbreviations
Some Standard Abbreviations
1 Introduction to the Finite Element Method
References
2 Rods and Trusses
2.1 Introduction
2.2 Derivation of the Governing Differential Equation
2.2.1 Kinematics
2.2.2 Constitutive Equation
2.2.3 Equilibrium
2.2.4 Differential Equation
2.3 Finite Element Solution
2.3.1 Derivation of the Principal Finite Element Equation
2.3.2 Derivation of Interpolation Functions
2.3.3 Assembly of Elements and Consideration of Boundary Conditions
2.3.4 Post-computation: Determination of Strain, Stress and Further Quantities
2.3.5 Analogies to Other Field Problems
2.3.6 Solved Rod Problems
2.4 Assembly of Elements to Plane Truss Structures
2.4.1 Rotational Transformation in a Plane
2.4.2 Solved Truss Problems
2.5 Supplementary Problems
References
3 Euler-Bernoulli Beams and Frames
3.1 Introduction
3.2 Derivation of the Governing Differential Equation
3.2.1 Kinematics
3.2.2 Constitutive Equation
3.2.3 Equilibrium
3.2.4 Differential Equation
3.3 Finite Element Solution
3.3.1 Derivation of the Principal Finite Element Equation
3.3.2 Derivation of Interpolation Functions
3.3.3 Assembly of Elements and Consideration of Boundary Conditions
3.3.4 Post-computation: Determination of Strain, Stress and Further Quantities
3.3.5 Solved Beam Problems
3.4 Assembly of Elements to Plane Frame Structures
3.4.1 Rotation of a Beam Element
3.4.2 Generalized Beam Element
3.4.3 Solved Problems
3.5 Supplementary Problems
References
4 Timoshenko Beams
4.1 Introduction
4.2 Derivation of the Governing Differential Equation
4.2.1 Kinematics
4.2.2 Equilibrium
4.2.3 Constitutive Equation
4.2.4 Differential Equation
4.3 Finite Element Solution
4.3.1 Derivation of the Principal Finite Element Equation
4.3.2 Linear Interpolation Functions for the Displacement and Rotational Field
4.3.3 Higher-Order Interpolation Functions for the Beam with Shear Contribution
4.3.4 Solved Problems
4.4 Supplementary Problems
References
5 Plane Elements
5.1 Introduction
5.2 Derivation of the Governing Differential Equation
5.2.1 Kinematics
5.2.2 Constitutive Equation
5.2.3 Equilibrium
5.2.4 Differential Equation
5.3 Finite Element Solution
5.3.1 Derivation of the Principal Finite Element Equation
5.3.2 Four-Node Planar Element
5.3.3 Solved Plane Elasticity Problems
5.4 Supplementary Problems
References
6 Classical Plate Elements
6.1 Introduction
6.2 Derivation of the Governing Differential Equation
6.2.1 Kinematics
6.2.2 Constitutive Equation
6.2.3 Equilibrium
6.2.4 Differential Equation
6.3 Finite Element Solution
6.3.1 Derivation of the Principal Finite Element Equation
6.3.2 Rectangular Four-Node Plate Element
6.3.3 Distorted Four-Node Plate Element
6.3.4 Solved Classical Plate Element Problems
6.4 Supplementary Problems
References
7 Shear Deformable Plate Elements
7.1 Introduction
7.2 Derivation of the Governing Differential Equation
7.2.1 Kinematics
7.2.2 Constitutive Equation
7.2.3 Equilibrium
7.2.4 Differential Equation
7.3 Finite Element Solution
7.3.1 Derivation of the Principal Finite Element Equation
7.3.2 Rectangular Four-Node Plate Element
7.3.3 Solved Thick Plate Element Problems
7.4 Supplementary Problems
References
8 Three-Dimensional Elements
8.1 Derivation of the Governing Differential Equation
8.1.1 Kinematics
8.1.2 Constitutive Equation
8.1.3 Equilibrium
8.1.4 Differential Equation
8.2 Finite Element Solution
8.2.1 Derivation of the Principal Finite Element Equation
8.2.2 Hexahedron Solid Elements
8.2.3 Solved Three-Dimensional Element Problems
8.3 Supplementary Problems
References
9 Principles of Linear Dynamics
9.1 Newton\'s Laws of Motion
9.2 Relationship Between Displacement, Velocity and Acceleration
9.3 Solved Problems
9.4 Supplementary Problems
References
10 Integration Methods for Transient Problems
10.1 Introduction
10.2 Derivation of the Governing Differential Equation
10.2.1 Kinematics
10.2.2 Constitutive Equation
10.2.3 Equilibrium
10.2.4 Differential Equation
10.3 Finite Element Solution
10.3.1 Derivation of the Principal Finite Element Equation
10.3.2 Consideration of Damping
10.3.3 Transient Solution Schemes
10.3.4 Solved Problems
10.4 Supplementary Problems
References
Appendix A Mathematics
A.1 Greek Alphabet
A.2 Frequently Used Constants
A.3 Special Products
A.4 Trigonometric Functions
A.5 Derivatives
A.6 Integrals
A.7 Integration by Parts
A.8 Integration and Coordinate Transformation
A.9 Numerical Integration
A.9.1 Simpson\'s Rule
A.9.2 Gauss-Legendre Quadrature
A.10 Taylor\'s Series Expansion
A.11 Matrix Operations
A.11.1 Matrix Multiplication
A.11.2 Scalar Product
A.11.3 Dyadic Product
A.11.4 Inverse of Matrices
A.12 Solution of Linear Systems of Equations
A.12.1 Elimination of Variables
A.12.2 Matrix Solution
A.13 Elementary Geometry
A.14 Analytical Geometry
A.14.1 Straight-Line Equations
A.14.2 Sign of Second Derivative of a Curve
A.14.3 Area of a Polygon
Appendix B Mechanics
B.1 Centroids
B.2 Second Moment of Area
B.3 Parallel-Axis Theorem
Appendix C Units and Conversion
C.1 SI Base Units
C.2 Coherent SI Derived Units
C.3 Consistent Units
C.4 Conversion of Important English Units to The Metric System
Appendix D Triangular Elements
D.1 Plane Elements
D.2 Classical Plate Elements
Appendix E Summary of Stiffness Matrices
E.1 One-Dimensional Elements
E.2 Two-Dimensional Elements
E.3 Three-Dimensional Elements
Appendix F Extrapolation from Integration Points to Nodes
Appendix G Answers to Supplementary Problems
G.1 Problems from Chap. 2摥映數爠eflinkchap:RodsandTrusses22
G.2 Problems from Chap. 3摥映數爠eflinkchap:EBspsBeamsspsFrames33
G.3 Problems from Chap. 4摥映數爠eflinkchap:Timoshenkospsbeams44
G.4 Problems from Chap. 5摥映數爠eflinkchapspsPlaneElements55
G.5 Problems from Chap. 6摥映數爠eflinkchap:FEspsclassicalspsplate66
G.6 Problems from Chapter 7摥映數爠eflinkchap:ShearDeformablePlateElements77
G.7 Problems from Chap. 8摥映數爠eflinkchap:ThreespsDimensionalspsElements88
G.8 Problems from Chapter 9摥映數爠eflinkchap:LinspsDyn99
G.9 Problems from Chap. 10摥映數爠eflinkchap:IntegrationspsTrans1010
Index