Large strain finite element method : a practical course|RISS 상세보기

목차 (Table of Contents)

CONTENTS
Preface = xiii
Acknowledgements = xv
PART ONE : FUNDAMENTALS = 1
1 Introduction = 3

CONTENTS
Preface = xiii
Acknowledgements = xv
PART ONE : FUNDAMENTALS = 1
1 Introduction = 3
1.1 Assumption of Small Displacements = 3
1.2 Assumption of Small Strains = 6
1.3 Geometric Nonlinearity = 6
1.4 Stretches = 8
1.5 Some Examples of Large Displacement Large Strain Finite Element Formulation = 8
1.6 The Scope and Layout of the Book = 13
1.7 Summary = 13
2 Matrices = 15
2.1 Matrices in General = 15
2.2 Matrix Algebra = 16
2.3 Special Types of Matrices = 21
2.4 Determinant of a Square Matrix = 22
2.5 Quadratic Form = 24
2.6 Eigenvalues and Eigenvectors = 24
2.7 Positive Definite Matrix = 26
2.8 Gaussian Elimination = 26
2.9 Inverse of a Square Matrix = 28
2.10 Column Matrices = 30
2.11 Summary = 32
3 Some Explicit and Iterative Solvers = 35
3.1 The Central Difference Solver = 35
3.2 Generalized Direction Methods = 43
3.3 The Method of Conjugate Directions = 50
3.4 Summary = 63
4 Numerical Integration = 65
4.1 Newton-Cotes Numerical Integration = 65
4.2 Gaussian Numerical Integration = 67
4.3 Gaussian Integration in 2D = 70
4.4 Gaussian Integration in 3D = 71
4.5 Summary = 72
5 Work of Internal Forces on Virtual Displacements = 75
5.1 The Principle of Virtual Work = 75
5.2 Summary = 78
PART TWO : PHYSICAL QUANTITIES = 79
6 Scalars = 81
6.1 Scalars in General = 81
6.2 Scalar Functions = 81
6.3 Scalar Graphs = 82
6.4 Empirical Formulas = 82
6.5 Fonts = 83
6.6 Units = 83
6.7 Base and Derived Scalar Variables = 85
6.8 Summary = 85
7 Vectors in 2D = 87
7.1 Vectors in General = 87
7.2 Vector Notation = 91
7.3 Matrix Representation of Vectors = 91
7.4 Scalar Product = 92
7.5 General Vector Base in 2D = 93
7.6 Dual Base = 94
7.7 Changing Vector Base = 95
7.8 Self-duality of the Orthonormal Base = 97
7.9 Combining Bases = 98
7.10 Examples = 104
7.11 Summary = 108
8 Vectors in 3D = 109
8.1 Vectors in 3D = 109
8.2 Vector Bases = 111
8.3 Summary = 114
9 Vectors in n-Dimensional Space = 117
9.1 Extension from 3D to 4-Dimensional Space = 117
9.2 The Dual Base in 4D = 118
9.3 Changing the Base in 4D = 120
9.4 Generalization to n-Dimensional Space = 121
9.5 Changing the Base in n-Dimensional Space = 124
9.6 Summary = 127
10 First Order Tensors = 129
10.1 The Slope Tensor = 129
10.2 First Order Tensors in 2D = 131
10.3 Using First Order Tensors = 132
10.4 Using Different Vector Bases in 2D = 134
10.5 Differential of a 2D Scalar Field as the First Order Tensor = 137
10.6 First Order Tensors in 3D = 141
10.7 Changing the Vector Base in 3D = 142
10.8 First Order Tensor in 4D = 143
10.9 First Order Tensor in n-Dimensions = 147
10.10 Differential of a 3D Scalar Field as the First Order Tensor = 149
10.11 Scalar Field in n-Dimensional Space = 152
10.12 Summary = 153
11 Second Order Tensors in 2D = 155
11.1 Stress Tensor in 2D = 155
11.2 Second Order Tensor in 2D = 158
11.3 Physical Meaning of Tensor Matrix in 2D = 159
11.4 Changing the Base = 161
11.5 Using Two Different Bases in 2D = 163
11.6 Some Special Cases of Stress Tensor Matrices in 2D = 167
11.7 The First Piola-Kirchhoff Stress Tensor Matrix = 168
11.8 The Second Piola-Kirchhoff Stress Tensor Matrix = 169
11.9 Summary = 174
12 Second Order Tensors in 3D = 175
12.1 Stress Tensor in 3D = 175
12.2 General Base for Surfaces = 179
12.3 General Base for Forces = 182
12.4 General Base for Forces and Surfaces = 184
12.5 The Cauchy Stress Tensor Matrix in 3D = 186
12.6 The First Piola-Kirchhoff Stress Tensor Matrix in 3D = 186
12.7 The Second Piola-Kirchhoff Stress Tensor Matrix in 3D = 188
12.8 Summary = 189
13 Second Order Tensors in nD = 191
13.1 Second Order Tensor in n-Dimensions = 191
13.2 Summary = 200
PART THREE : DEFORMABILITY AND MATERIAL MODELING = 201
14 Kinematics of Deformation in 1D = 203
14.1 Geometric Nonlinearity in General = 203
14.2 Stretch = 205
14.3 Material Element and Continuum Assumption = 208
14.4 Strain = 209
14.5 Stress = 213
14.6 Summary = 214
15 Kinematics of Deformation in 2D = 217
15.1 Isotropic Solids = 217
15.2 Homogeneous Solids = 217
15.3 Homogeneous and Isotropic Solids = 217
15.4 Nonhomogeneous and Anisotropic Solids = 218
15.5 Material Element Deformation = 221
15.6 Cauchy Stress Matrix for the Solid Element = 225
15.7 Coordinate Systems in 2D = 227
15.8 The Solid- and the Material-Embedded Vector Bases = 228
15.9 Kinematics of 2D Deformation = 229
15.10 2D Equilibrium Using the Virtual Work of Internal Forces = 231
15.11 Examples = 235
15.12 Summary = 238
16 Kinematics of Deformation in 3D = 241
16.1 The Cartesian Coordinate System in 3D = 241
16.2 The Solid-Embedded Coordinate System = 241
16.3 The Global and the Solid-Embedded Vector Bases = 243
16.4 Deformation of the Solid = 244
16.5 Generalized Material Element = 246
16.6 Kinematic of Deformation in 3D = 247
16.7 The Virtual Work of Internal Forces = 249
16.8 Summary = 255
17 The Unified Constitutive Approach in 2D = 257
17.1 Introduction = 257
17.2 Material Axes = 259
17.3 Micromechanical Aspects and Homogenization = 260
17.4 Generalized Homogenization = 263
17.5 The Material Package = 264
17.6 Hyper-Elastic Constitutive Law = 265
17.7 Hypo-Elastic Constitutive Law = 266
17.8 A Unified Framework for Developing Anisotropic Material Models in 2D = 267
17.9 Generalized Hyper-Elastic Material = 267
17.10 Converting the Munjiza Stress Matrix to the Cauchy Stress Matrix = 274
17.11 Developing Constitutive Laws = 279
17.12 Generalized Hypo-Elastic Material = 288
17.13 Unified Constitutive Approach for Strain Rate and Viscosity = 292
17.14 Summary = 293
18 The Unified Constitutive Approach in 3D = 295
18.1 Material Package Framework = 295
18.2 Generalized Hyper-Elastic Material = 295
18.3 Generalized Hypo-Elastic Material = 299
18.4 Developing Material Models = 302
18.5 Calculation of the Cauchy Stress Tensor Matrix = 302
18.6 Summary = 312
PART FOUR : THE FINITE ELEMENT METHOD IN 2D = 315
19 2D Finite Element : Deformation Kinematics Using the Homogeneous Deformation Triangle = 317
19.1 The Finite Element Mesh = 317
19.2 The Homogeneous Deformation Finite Element = 317
19.3 Summary = 326
20 2D Finite Element : Deformation Kinematics Using Iso-Parametric Finite Elements = 327
20.1 The Finite Element Library = 327
20.2 The Shape Functions = 327
20.3 Nodal Positions = 330
20.4 Positions of Material Points inside a Single Finite Element = 331
20.5 The Solid-Embedded Vector Base = 332
20.6 The Material-Embedded Vector Base = 334
20.7 Some Examples of 2D Finite Elements = 337
20.8 Summary = 340
21 Integration of Nodal Forces over Volume of 2D Finite Elements = 343
21.1 The Principle of Virtual Work in the 2D Finite Element Method = 343
21.2 Nodal Forces for the Homogeneous Deformation Triangle = 348
21.3 Nodal Forces for the Six-Noded Triangle = 352
21.4 Nodal Forces for the Four-Noded Quadrilateral = 353
21.5 Summary = 355
22 Reduced and Selective Integration of Nodal Forces over Volume of 2D Finite Elements = 357
22.1 Volumetric Locking = 357
22.2 Reduced Integration = 358
22.3 Selective Integration = 359
22.4 Shear Locking = 362
22.5 Summary = 364
PART FIVE : THE FINITE ELEMENT METHOD IN 3D = 365
23 3D Deformation Kinematics Using the Homogeneous Deformation Tetrahedron Finite Element = 367
23.1 Introduction = 367
23.2 The Homogeneous Deformation Four-Noded Tetrahedron Finite Element = 368
23.3 Summary = 377
24 3D Deformation Kinematics Using Iso-Parametric Finite Elements = 379
24.1 The Finite Element Library = 379
24.2 The Shape Functions = 379
24.3 Nodal Positions = 381
24.4 Positions of Material Points inside a Single Finite Element = 382
24.5 The Solid-Embedded Infinitesimal Vector Base = 383
24.6 The Material-Embedded Infinitesimal Vector Base = 386
24.7 Examples of Deformation Kinematics = 387
24.8 Summary = 392
25 Integration of Nodal Forces over Volume of 3D Finite Elements = 393
25.1 Nodal Forces Using Virtual Work = 393
25.2 Four-Noded Tetrahedron Finite Element = 396
25.3 Reduce Integration for Eight-Noded 3D Solid = 399
25.4 Selective Stretch Sampling-Based Integration for the Eight-Noded Solid Finite Element = 400
25.5 Summary = 401
26 Integration of Nodal Forces over Boundaries of Finite Elements = 403
26.1 Stress at Element Boundaries = 403
26.2 Integration of the Equivalent Nodal Forces over the Triangle Finite Element = 404
26.3 Integration over the Boundary of the Composite Triangle = 407
26.4 Integration over the Boundary of the Six-Noded Triangle = 408
26.5 Integration of the Equivalent Internal Nodal Forces over the Tetrahedron Boundaries = 409
26.6 Summary = 412
PART SIX : THE FINITE ELEMENT METHOD IN 2.5D = 415
27 Deformation in 2.5D Using Membrane Finite Elements = 417
27.1 Solids in 2.5D = 417
27.2 The Homogeneous Deformation Three-Noded Triangular Membrane Finite Element = 419
27.3 Summary = 438
28 Deformation in 2.5D Using Shell Finite Elements = 439
28.1 Introduction = 439
28.2 The Six-Noded Triangular Shell Finite Element = 440
28.3 The Solid-Embedded Coordinate System = 441
28.4 Nodal Coordinates = 442
28.5 The Coordinates of the Finite Element's Material Points = 443
28.6 The Solid-Embedded Infinitesimal Vector Base = 444
28.7 The Solid-Embedded Vector Base versus the Material-Embedded Vector Base = 447
28.8 The Constitutive Law = 449
28.9 Selective Stretch Sampling Based Integration of the Equivalent Nodal Forces = 449
28.10 Multi-Layered Shell as an Assembly of Single Layer Shells = 455
28.11 Improving the CPU Performance of the Shell Element = 456
28.12 Summary = 462
Index = 463

서점명	서명	판매현황	종이책			전자책 구매링크
서점명	서명	판매현황	정가	판매가(할인율)	포인트(포인트몰)	전자책 구매링크
	Large Strain Finite Element Method	판매중	247,900원	203,270원 (18%)	10,170포인트 (5%)

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