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Large strain finite element method : a practical course / Antonio Munjiza, Esteban Rougier, Earl E. Knight.

By: Contributor(s): Material type: TextPublication details: West Sussex : Wiley, 2015.Description: xiv, 469 p. : ill. ; 24 cmISBN:
  • 9781118405307
  • 1118405307
Subject(s): DDC classification:
  • 23 620.11230151825  MUN
Contents:
PART ONE FUNDAMENTALS, 1 Introduction : 1.1 Assumption of Small Displacements -- 1.2 Assumption of Small Strains -- 1.3 Geometric Nonlinearity -- 1.4 Stretches -- 1.5 Some Examples of Large Displacement Large Strain Finite Element Formulation -- 1.6 The Scope and Layout of the Book -- 1.7 Summary -- 2 Matrices : 2.1 Matrices in General -- 2.2 Matrix Algebra -- 2.3 Special Types of Matrices -- 2.4 Determinant of a Square Matrix -- 2.5 Quadratic Form -- 2.6 Eigenvalues and Eigenvectors -- 2.7 Positive Definite Matrix -- 2.8 Gaussian Elimination -- 2.9 Inverse of a Square Matrix -- 2.10 Column Matrices -- 2.11 Summary -- 3 Some Explicit and Iterative Solvers : 3.1 The Central Difference Solver -- 3.2 Generalized Direction Methods -- 3.3 The Method of Conjugate Directions -- 3.4 Summary -- 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 3D -- 4.5 Summary -- 5 Work of Internal Forces on Virtual Displacements -- 5.1 The Principle of Virtual Work -- 5.2 Summary -- PART TWO PHYSICAL QUANTITIES, 6 Scalars : 6.1 Scalars in General -- 6.2 Scalar Functions -- 6.3 Scalar Graphs -- 6.4 Empirical Formulas -- 6.5 Fonts -- 6.6 Units -- 6.7 Base and Derived Scalar Variables -- 6.8 Summary -- 7 Vectors in 2D : 7.1 Vectors in General -- 7.2 Vector Notation -- 7.3 Matrix Representation of Vectors -- 7.4 Scalar Product -- 7.5 General Vector Base in 2D -- 7.6 Dual Base -- 7.7 Changing Vector Base -- 7.8 Self-duality of the Orthonormal Base -- 7.9 Combining Bases -- 7.10 Examples -- 7.11 Summary -- 8 Vectors in 3D : 8.1 Vectors in 3D -- 8.2 Vector Bases -- 8.3 Summary -- 9 Vectors in n-Dimensional Space : 9.1 Extension from 3D to 4-Dimensional Space -- 9.2 The Dual Base in 4D -- 9.3 Changing the Base in 4D -- 9.4 Generalization to n-Dimensional Space -- 9.5 Changing the Base in n-Dimensional Space -- 9.6 Summary -- 10 First Order Tensors : 10.1 The Slope 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 -- 10.12 Summary -- 11 Second Order Tensors in 2D : 11.1 Stress Tensor in 2D -- 11.2 Second Order Tensor in 2D -- 11.3 Physical Meaning of Tensor Matrix in 2D -- 11.4 Changing the Base -- 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 -- 11.9 Summary -- 12 Second Order Tensors in 3D : 12.1 Stress Tensor 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 -- 12.8 Summary -- 13 Second Order Tensors in nD : 13.1 Second Order Tensor in n-Dimensions -- 13.2 Summary -- PART THREE DEFORMABILITY AND MATERIAL MODELING, 14 Kinematics of Deformation in 1D -- 14.1 Geometric Nonlinearity in General -- 14.2 Stretch -- 14.3 Material Element and Continuum Assumption -- 14.4 Strain -- 14.5 Stress -- 14.6 Summary -- 15 Kinematics of Deformation in 2D, 15.1 Isotropic Solids -- 15.2 Homogeneous Solids -- 15.3 Homogeneous and Isotropic Solids -- 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 -- 15.11 Examples -- 15.12 Summary -- 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 -- 16.8 Summary -- 17 The Unified Constitutive Approach in 2D : 17.1 Introduction -- 17.2 Material Axes -- 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 -- 17.14 Summary -- 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 -- 18.6 Summary -- PART FOUR THE FINITE ELEMENT METHOD IN 2D, 2D Finite Element: Deformation Kinematics Using the Homogeneous Deformation Triangle : 19.1 The Finite Element Mesh -- 19.2 The Homogeneous Deformation Finite Element -- 19.3 Summary -- 20 2D Finite Element: Deformation Kinematics Using Iso-Parametric Finite Elements : 20.1 The Finite Element Library -- 20.2 The Shape Functions -- 20.3 Nodal Positions -- 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 -- 20.8 Summary -- 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 -- 21.5 Summary -- 22 Reduced and Selective Integration of Nodal Forces over Volume of 2D Finite Elements : 22.1 Volumetric Locking -- 22.2 Reduced Integration -- 22.3 Selective Integration -- 22.4 Shear Locking -- 22.5 Summary -- PART FIVE THE FINITE ELEMENT METHOD IN 3D, 23 3D Deformation Kinematics Using the Homogeneous Deformation Tetrahedron Finite Element : 23.1 Introduction -- 23.2 The Homogeneous Deformation Four-Noded Tetrahedron Finite Element -- 23.3 Summary -- 24 3D Deformation Kinematics Using Iso-Parametric Finite Elements : 24.1 The Finite Element Library -- 24.2 The Shape Functions -- 24.3 Nodal Positions -- 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 -- 24.8 Summary -- 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 -- 25.5 Summary -- 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 -- 26.6 Summary -- PART SIX THE FINITE ELEMENT METHOD IN 2.5D, 27 Deformation in 2.5D Using Membrane Finite Elements : 27.1 Solids in 2.5D -- 27.2 The Homogeneous Deformation Three-Noded Triangular Membrane Finite Element -- 27.3 Summary -- 28 Deformation in 2.5D Using Shell Finite Elements : 28.1 Introduction -- 28.2 The Six-Noded Triangular Shell Finite Element -- 28.3 The Solid-Embedded Coordinate System -- 28.4 Nodal Coordinates -- 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 -- 28.12 Summary
Summary: An introductory approach to the subject of large strains and large displacements in finite elements.
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Cover image Item type Current library Home library Collection Shelving location Call number Materials specified Vol info URL Copy number Status Notes Date due Barcode Item holds Item hold queue priority Course reserves
Book - Borrowing Central Library First floor Academic Bookshop 620.11230151825 MUN (Browse shelf(Opens below)) 9155 Available 000033159
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Index : p. 461-469.

Includes bibliographical references.

PART ONE FUNDAMENTALS, 1 Introduction : 1.1 Assumption of Small Displacements -- 1.2 Assumption of Small Strains -- 1.3 Geometric Nonlinearity -- 1.4 Stretches -- 1.5 Some Examples of Large Displacement Large Strain Finite Element Formulation -- 1.6 The Scope and Layout of the Book -- 1.7 Summary -- 2 Matrices : 2.1 Matrices in General -- 2.2 Matrix Algebra -- 2.3 Special Types of Matrices -- 2.4 Determinant of a Square Matrix -- 2.5 Quadratic Form -- 2.6 Eigenvalues and Eigenvectors -- 2.7 Positive Definite Matrix -- 2.8 Gaussian Elimination -- 2.9 Inverse of a Square Matrix -- 2.10 Column Matrices -- 2.11 Summary -- 3 Some Explicit and Iterative Solvers : 3.1 The Central Difference Solver -- 3.2 Generalized Direction Methods -- 3.3 The Method of Conjugate Directions -- 3.4 Summary -- 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 3D -- 4.5 Summary -- 5 Work of Internal Forces on Virtual Displacements -- 5.1 The Principle of Virtual Work -- 5.2 Summary -- PART TWO PHYSICAL QUANTITIES, 6 Scalars : 6.1 Scalars in General -- 6.2 Scalar Functions -- 6.3 Scalar Graphs -- 6.4 Empirical Formulas -- 6.5 Fonts -- 6.6 Units -- 6.7 Base and Derived Scalar Variables -- 6.8 Summary -- 7 Vectors in 2D : 7.1 Vectors in General -- 7.2 Vector Notation -- 7.3 Matrix Representation of Vectors -- 7.4 Scalar Product -- 7.5 General Vector Base in 2D -- 7.6 Dual Base -- 7.7 Changing Vector Base -- 7.8 Self-duality of the Orthonormal Base -- 7.9 Combining Bases -- 7.10 Examples -- 7.11 Summary -- 8 Vectors in 3D : 8.1 Vectors in 3D -- 8.2 Vector Bases -- 8.3 Summary -- 9 Vectors in n-Dimensional Space : 9.1 Extension from 3D to 4-Dimensional Space -- 9.2 The Dual Base in 4D -- 9.3 Changing the Base in 4D -- 9.4 Generalization to n-Dimensional Space -- 9.5 Changing the Base in n-Dimensional Space -- 9.6 Summary -- 10 First Order Tensors : 10.1 The Slope 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 -- 10.12 Summary -- 11 Second Order Tensors in 2D : 11.1 Stress Tensor in 2D -- 11.2 Second Order Tensor in 2D -- 11.3 Physical Meaning of Tensor Matrix in 2D -- 11.4 Changing the Base -- 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 -- 11.9 Summary -- 12 Second Order Tensors in 3D : 12.1 Stress Tensor 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 -- 12.8 Summary -- 13 Second Order Tensors in nD : 13.1 Second Order Tensor in n-Dimensions -- 13.2 Summary -- PART THREE DEFORMABILITY AND MATERIAL MODELING, 14 Kinematics of Deformation in 1D -- 14.1 Geometric Nonlinearity in General -- 14.2 Stretch -- 14.3 Material Element and Continuum Assumption -- 14.4 Strain -- 14.5 Stress -- 14.6 Summary -- 15 Kinematics of Deformation in 2D, 15.1 Isotropic Solids -- 15.2 Homogeneous Solids -- 15.3 Homogeneous and Isotropic Solids -- 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 -- 15.11 Examples -- 15.12 Summary -- 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 -- 16.8 Summary -- 17 The Unified Constitutive Approach in 2D : 17.1 Introduction -- 17.2 Material Axes -- 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 -- 17.14 Summary -- 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 -- 18.6 Summary -- PART FOUR THE FINITE ELEMENT METHOD IN 2D, 2D Finite Element: Deformation Kinematics Using the Homogeneous Deformation Triangle : 19.1 The Finite Element Mesh -- 19.2 The Homogeneous Deformation Finite Element -- 19.3 Summary -- 20 2D Finite Element: Deformation Kinematics Using Iso-Parametric Finite Elements : 20.1 The Finite Element Library -- 20.2 The Shape Functions -- 20.3 Nodal Positions -- 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 -- 20.8 Summary -- 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 -- 21.5 Summary -- 22 Reduced and Selective Integration of Nodal Forces over Volume of 2D Finite Elements : 22.1 Volumetric Locking -- 22.2 Reduced Integration -- 22.3 Selective Integration -- 22.4 Shear Locking -- 22.5 Summary -- PART FIVE THE FINITE ELEMENT METHOD IN 3D, 23 3D Deformation Kinematics Using the Homogeneous Deformation Tetrahedron Finite Element : 23.1 Introduction -- 23.2 The Homogeneous Deformation Four-Noded Tetrahedron Finite Element -- 23.3 Summary -- 24 3D Deformation Kinematics Using Iso-Parametric Finite Elements : 24.1 The Finite Element Library -- 24.2 The Shape Functions -- 24.3 Nodal Positions -- 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 -- 24.8 Summary -- 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 -- 25.5 Summary -- 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 -- 26.6 Summary -- PART SIX THE FINITE ELEMENT METHOD IN 2.5D, 27 Deformation in 2.5D Using Membrane Finite Elements : 27.1 Solids in 2.5D -- 27.2 The Homogeneous Deformation Three-Noded Triangular Membrane Finite Element -- 27.3 Summary -- 28 Deformation in 2.5D Using Shell Finite Elements : 28.1 Introduction -- 28.2 The Six-Noded Triangular Shell Finite Element -- 28.3 The Solid-Embedded Coordinate System -- 28.4 Nodal Coordinates -- 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 -- 28.12 Summary

An introductory approach to the subject of large strains and large displacements in finite elements.

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