Chapter
1.6 The Scope and Layout of the Book
2.3 Special Types of Matrices
2.4 Determinant of a Square Matrix
2.6 Eigenvalues and Eigenvectors
2.7 Positive Definite Matrix
2.9 Inverse of a Square Matrix
Chapter 3 Some Explicit and Iterative Solvers
3.1 The Central Difference Solver
3.2 Generalized Direction Methods
3.3 The Method of Conjugate DirectionsConjugate Directions
Chapter 4 Numerical Integration
4.1 Newton-Cotes Numerical Integration
4.2 Gaussian Numerical Integration
4.3 Gaussian Integration in 2D
4.4 Gaussian Integration in 3DGaussian Integration in 3D
Chapter 5 Work of Internal Forces on Virtual Displacements
5.1 The Principle of Virtual Work
Part Two Physical Quantities
6.2 Scalar FunctionsScalar Functions
6.3 Scalar GraphsScalar Graphs
6.7 Base and Derived Scalar Variables
7.3 Matrix Representation of Vectors
7.5 General Vector Base in 2D
7.8 Self-duality of the Orthonormal Base
Chapter 9 Vectors in n-Dimensional Space
9.1 Extension from 3D to 4-Dimensional Space
9.3 Changing the Base in 4D
9.4 Generalization to n-Dimensional Space
9.5 Changing the Base in n-Dimensional Space
Chapter 10 First Order Tensors
10.1 The Slope TensorSlope Tensor
10.2 First Order Tensors in 2D
10.3 Using First Order Tensors
10.4 Using Different Vector Bases in 2D
10.5 Differential of a 2D Scalar Field as the First Order Tensor
10.6 First Order Tensors in 3D
10.7 Changing the Vector Base in 3D
10.8 First Order Tensor in 4D
10.9 First Order Tensor in n-Dimensions
10.10 Differential of a 3D Scalar Field as the First Order Tensor
10.11 Scalar Field in n-Dimensional Space
Chapter 11 Second Order Tensors in 2D
11.2 Second Order Tensor in 2D
11.3 Physical Meaning of Tensor Matrix in 2D
11.5 Using Two Different Bases in 2D
11.6 Some Special Cases of Stress Tensor Matrices in 2D
11.7 The First Piola-Kirchhoff Stress Tensor Matrix
11.8 The Second Piola-Kirchhoff Stress Tensor Matrix
Chapter 12 Second Order Tensors in 3D
12.2 General Base for Surfaces
12.3 General Base for Forces
12.4 General Base for Forces and Surfaces
12.5 The Cauchy Stress Tensor Matrix in 3D
12.6 The First Piola-Kirchhoff Stress Tensor Matrix in 3D
12.7 The Second Piola-Kirchhoff Stress Tensor Matrix in 3D
Chapter 13 Second Order Tensors in nD
13.1 Second Order Tensor in n-Dimensions
Part Three Deformability and Material Modeling
Chapter 14 Kinematics of Deformation in 1D
14.1 Geometric Nonlinearity in General
14.3 Material Element and Continuum Assumption
Chapter 15 Kinematics of Deformation in 2D
15.3 Homogeneous and Isotropic Solid
15.4 Nonhomogeneous and Anisotropic Solids
15.5 Material Element Deformation
15.6 Cauchy Stress Matrix for the Solid Element
15.7 Coordinate Systems in 2D
15.8 The Solid- and the Material-Embedded Vector Bases
15.9 Kinematics of 2D Deformation
15.10 2D Equilibrium Using the Virtual Work of Internal Forces
Chapter 16 Kinematics of Deformation in 3D
16.1 The Cartesian Coordinate System in 3D
16.2 The Solid-Embedded Coordinate System
16.3 The Global and the Solid-Embedded Vector Bases
16.4 Deformation of the Solid
16.5 Generalized Material Element
16.6 Kinematic of Deformation in 3D
16.7 The Virtual Work of Internal Forces
Chapter 17 The Unified Constitutive Approach in 2D
17.3 Micromechanical Aspects and Homogenization
17.4 Generalized Homogenization
17.5 The Material Package
17.6 Hyper-Elastic Constitutive Law
17.7 Hypo-Elastic Constitutive Law
17.8 A Unified Framework for Developing Anisotropic Material Models in 2D
17.9 Generalized Hyper-Elastic Material
17.10 Converting the Munjiza Stress Matrix to the Cauchy Stress Matrix
17.11 Developing Constitutive Laws
17.12 Generalized Hypo-Elastic Material
17.13 Unified Constitutive Approach for Strain Rate and Viscosity
Chapter 18 The Unified Constitutive Approach in 3D
18.1 Material Package Framework
18.2 Generalized Hyper-Elastic Material
18.3 Generalized Hypo-Elastic Material
18.4 Developing Material Models
18.5 Calculation of the Cauchy Stress Tensor Matrix
Part Four The Finite Element Method in 2D
Chapter 19 2D Finite Element: Deformation Kinematics Using the Homogeneous Deformation Triangle
19.1 The Finite Element MeshMesh
19.2 The Homogeneous Deformation Finite Element
Chapter 20 2D Finite Element: Deformation Kinematics Using Iso-Parametric Finite Elements
20.1 The Finite Element LibraryFinite Element Library
20.4 Positions of Material Points inside a Single Finite Element
20.5 The Solid-Embedded Vector Base
20.6 The Material-Embedded Vector Base
20.7 Some Examples of 2D Finite Elements
Chapter 21 Integration of Nodal Forces over Volume of 2D Finite Elements
21.1 The Principle of Virtual Work in the 2D Finite Element Method
21.2 Nodal Forces for the Homogeneous Deformation Triangle
21.3 Nodal Forces for the Six-Noded Triangle
21.4 Nodal Forces for the Four-Noded Quadrilateral
Chapter 22 Reduced and Selective Integration of Nodal Forces over Volume of 2D Finite Elements
22.3 Selective Integration
Part Five The Finite Element Method in 3D
Chapter 23 3D Deformation Kinematics Using the Homogeneous Deformation Tetrahedron Finite Element
23.2 The Homogeneous Deformation Four-Noded Tetrahedron Finite Element
Chapter 24 3D Deformation Kinematics Using Iso-Parametric Finite Elements
24.1 The Finite Element Library
24.4 Positions of Material Points inside a Single Finite Element
24.5 The Solid-Embedded Infinitesimal Vector Base
24.6 The Material-Embedded Infinitesimal Vector Base
24.7 Examples of Deformation Kinematics
Chapter 25 Integration of Nodal Forces over Volume of 3D Finite Elements
25.1 Nodal Forces Using Virtual Work
25.2 Four-Noded Tetrahedron Finite Element
25.3 Reduce Integration for Eight-Noded 3D Solid
25.4 Selective Stretch Sampling-Based Integration for the Eight-Noded Solid Finite Element
Chapter 26 Integration of Nodal Forces over Boundaries of Finite Elements
26.1 Stress at Element Boundaries
26.2 Integration of the Equivalent Nodal Forces over the Triangle Finite Element
26.3 Integration over the Boundary of the Composite Triangle
26.4 Integration over the Boundary of the Six-Noded Triangle
26.5 Integration of the Equivalent Internal Nodal Forces over the Tetrahedron Boundaries
Part Six The Finite Element Method in 2.5D
Chapter 27 Deformation in 2.5D Using Membrane Finite Elements
27.2 The Homogeneous Deformation Three-Noded Triangular Membrane Finite Element
Chapter 28 Deformation in 2.5D Using Shell Finite Elements
28.2 The Six-Noded Triangular Shell Finite Element
28.3 The Solid-Embedded Coordinate System
28.5 The Coordinates of the Finite Element´s Material Points
28.6 The Solid-Embedded Infinitesimal Vector Base
28.7 The Solid-Embedded Vector Base versus the Material-Embedded Vector Base
28.8 The Constitutive Law
28.9 Selective Stretch Sampling Based Integration of the Equivalent Nodal Forces
28.10 Multi-Layered Shell as an Assembly of Single Layer Shells
28.11 Improving the CPU Performance of the Shell Element
Large Strain Finite Element Method
：A Practical Course
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