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Nonlinear Finite Elements for Continua and Structures


Nonlinear Finite Elements for Continua and Structures


2. Aufl.

von: Ted Belytschko, Wing Kam Liu, Brian Moran, Khalil Elkhodary

81,99 €

Verlag: Wiley
Format: EPUB
Veröffentl.: 25.11.2013
ISBN/EAN: 9781118700082
Sprache: englisch
Anzahl Seiten: 832

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Beschreibungen

<b>Nonlinear Finite Elements for Continua and Structures</b> p><b>Nonlinear Finite Elements for Continua and Structures</b> <p>This updated and expanded edition of the bestselling textbook provides a comprehensive introduction to the methods and theory of nonlinear finite element analysis. New material provides a concise introduction to some of the cutting-edge methods that have evolved in recent years in the field of nonlinear finite element modeling, and includes the eXtended Finite Element Method (XFEM), multiresolution continuum theory for multiscale microstructures, and dislocation- density-based crystalline plasticity. <p><i>Nonlinear Finite Elements for Continua and Structures, Second Edition</i> focuses on the formulation and solution of discrete equations for various classes of problems that are of principal interest in applications to solid and structural mechanics. Topics covered include the discretization by finite elements of continua in one dimension and in multi-dimensions; the formulation of constitutive equations for nonlinear materials and large deformations; procedures for the solution of the discrete equations, including considerations of both numerical and multiscale physical instabilities; and the treatment of structural and contact-impact problems. <p><b>Key features:</b> <ul><li>Presents a detailed and rigorous treatment of nonlinear solid mechanics and how it can be implemented in finite element analysis</li> <li>Covers many of the material laws used in today’s software and research</li> <li>Introduces advanced topics in nonlinear finite element modelling of continua</li> <li>Introduction of multiresolution continuum theory and XFEM</li> <li>Accompanied by a website hosting a solution manual and MATLAB<sup>®</sup> and FORTRAN code</li></ul> <p><i>Nonlinear Finite Elements for Continua and Structures, Second Edition</i> is a must-have textbook for graduate students in mechanical engineering, civil engineering, applied mathematics, engineering mechanics, and materials science, and is also an excellent source of information for researchers and practitioners.
<p><i>Foreword xxi</i></p> <p><i>Preface xxiii</i></p> <p><i>List of Boxes xxvii</i></p> <p><b>1 Introduction 1</b></p> <p>1.1 Nonlinear Finite Elements in Design 1</p> <p>1.2 Related Books and a Brief History of Nonlinear Finite Elements 4</p> <p>1.3 Notation 7</p> <p>1.4 Mesh Descriptions 9</p> <p>1.5 Classification of Partial Differential Equations 13</p> <p>1.6 Exercises 17</p> <p><b>2 Lagrangian and Eulerian Finite Elements in One Dimension 19</b></p> <p>2.1 Introduction 19</p> <p>2.2 Governing Equations for Total Lagrangian Formulation 21</p> <p>2.3 Weak Form for Total Lagrangian Formulation 28</p> <p>2.4 Finite Element Discretization in Total Lagrangian Formulation 34</p> <p>2.5 Element and Global Matrices 40</p> <p>2.6 Governing Equations for Updated Lagrangian Formulation 51</p> <p>2.7 Weak Form for Updated Lagrangian Formulation 53</p> <p>2.8 Element Equations for Updated Lagrangian Formulation 55</p> <p>2.10 Weak Forms for Eulerian Mesh Equations 68</p> <p>2.11 Finite Element Equations 69</p> <p>2.12 Solution Methods 72</p> <p>2.13 Summary 74</p> <p>2.14 Exercises 75</p> <p><b>3 Continuum Mechanics 77</b></p> <p>3.1 Introduction 77</p> <p>3.2 Deformation and Motion 78</p> <p>3.3 Strain Measures 95</p> <p>3.4 Stress Measures 104</p> <p>3.5 Conservation Equations 111</p> <p>3.6 Lagrangian Conservation Equations 123</p> <p>3.7 Polar Decomposition and Frame-Invariance 130</p> <p>3.8 Exercises 143</p> <p><b>4 Lagrangian Meshes 147</b></p> <p>4.1 Introduction 147</p> <p>4.2 Governing Equations 148</p> <p>4.3 Weak Form: Principle of Virtual Power 152</p> <p>4.4 Updated Lagrangian Finite Element Discretization 158</p> <p>4.5 Implementation 168</p> <p>4.6 Corotational Formulations 194</p> <p>4.7 Total Lagrangian Formulation 203</p> <p>4.8 Total Lagrangian Weak Form 206</p> <p>4.9 Finite Element Semidiscretization 209</p> <p>4.10 Exercises 225</p> <p><b>5 Constitutive Models 227</b></p> <p>5.1 Introduction 227</p> <p>5.2 The Stress–Strain Curve 228</p> <p>5.3 One-Dimensional Elasticity 233</p> <p>5.4 Nonlinear Elasticity 237</p> <p>5.5 One-Dimensional Plasticity 254</p> <p>5.6 Multiaxial Plasticity 262</p> <p>5.7 Hyperelastic–Plastic Models 281</p> <p>5.8 Viscoelasticity 292</p> <p>5.9 Stress Update Algorithms 294</p> <p>5.10 Continuum Mechanics and Constitutive Models 314</p> <p>5.11 Exercises 328</p> <p><b>6 Solution Methods and Stability 329</b></p> <p>6.1 Introduction 329</p> <p>6.2 Explicit Methods 330</p> <p>6.3 Equilibrium Solutions and Implicit Time Integration 337</p> <p>6.4 Linearization 358</p> <p>6.5 Stability and Continuation Methods 375</p> <p>6.6 Numerical Stability 391</p> <p>6.7 Material Stability 407</p> <p>6.8 Exercises 415</p> <p><b>7 Arbitrary Lagrangian Eulerian Formulations 417</b></p> <p>7.1 Introduction 417</p> <p>7.2 ALE Continuum Mechanics 419</p> <p>7.3 Conservation Laws in ALE Description 426</p> <p>7.4 ALE Governing Equations 428</p> <p>7.5 Weak Forms 429</p> <p>7.6 Introduction to the Petrov–Galerkin Method 433</p> <p>7.7 Petrov–Galerkin Formulation of Momentum Equation 442</p> <p>7.8 Path-Dependent Materials 445</p> <p>7.9 Linearization of the Discrete Equations 457</p> <p>7.10 Mesh Update Equations 460</p> <p>7.11 Numerical Example: An Elastic–Plastic Wave Propagation Problem 468</p> <p>7.12 Total ALE Formulations 471</p> <p>7.13 Exercises 475</p> <p><b>8 Element Technology 477</b></p> <p>8.1 Introduction 477</p> <p>8.2 Element Performance 479</p> <p>8.3 Element Properties and Patch Tests 487</p> <p>8.4 Q4 and Volumetric Locking 496</p> <p>8.5 Multi-Field Weak Forms and Elements 501</p> <p>8.6 Multi-Field Quadrilaterals 514</p> <p>8.7 One-Point Quadrature Elements 518</p> <p>8.8 Examples 527</p> <p>8.9 Stability 531</p> <p>8.10 Exercises 533</p> <p><b>9 Beams and Shells 535</b></p> <p>9.1 Introduction 535</p> <p>9.2 Beam Theories 537</p> <p>9.3 Continuum-Based Beam 540</p> <p>9.4 Analysis of the CB Beam 551</p> <p>9.5 Continuum-Based Shell Implementation 563</p> <p>9.6 CB Shell Theory 578</p> <p>9.7 Shear and Membrane Locking 584</p> <p>9.8 Assumed Strain Elements 589</p> <p>9.9 One-Point Quadrature Elements 592</p> <p>9.10 Exercises 595</p> <p><b>10 Contact-Impact 597</b></p> <p>10.1 Introduction 597</p> <p>10.2 Contact Interface Equations 598</p> <p>10.3 Friction Models 609</p> <p>10.4 Weak Forms 614</p> <p>10.5 Finite Element Discretization 624</p> <p>10.6 On Explicit Methods 638</p> <p><b>11 EXtended Finite Element Method (XFEM) 643</b></p> <p>11.1 Introduction 643</p> <p>11.2 Partition of Unity and Enrichments 647</p> <p>11.3 One-Dimensional XFEM 648</p> <p>11.4 Multi-Dimension XFEM 656</p> <p>11.5 Weak and Strong Forms 660</p> <p>11.6 Discrete Equations 662</p> <p>11.7 Level Set Method 668</p> <p>11.8 The Phantom Node Method 670</p> <p>11.9 Integration 673</p> <p>11.10 An Example of XFEM Simulation 675</p> <p>11.11 Exercise 678</p> <p><b>12 Introduction to Multiresolution Theory 681</b></p> <p>12.1 Motivation: Materials are Structured Continua 681</p> <p>12.2 Bulk Deformation of Microstructured Continua 685</p> <p>12.3 Generalizing Mechanics to Bulk Microstructured Continua 686</p> <p>12.4 Multiscale Microstructures and the Multiresolution Continuum Theory 696</p> <p>12.5 Governing Equations for MCT 699</p> <p>12.6 Constructing MCT Constitutive Relationships 701</p> <p>12.7 Basic Guidelines for RVE Modeling 705</p> <p>12.8 Finite Element Implementation of MCT 710</p> <p>12.9 Numerical Example 712</p> <p>12.10 Future Research Directions of MCT Modeling 718</p> <p>12.11 Exercises 719</p> <p><b>13 Single-Crystal Plasticity 721</b></p> <p>13.1 Introduction 721</p> <p>13.2 Crystallographic Description of Cubic and Non-Cubic Crystals 723</p> <p>13.3 Atomic Origins of Plasticity and the Burgers Vector in Single Crystals 726</p> <p>13.4 Defining Slip Planes and Directions in General Single Crystals 729</p> <p>13.5 Kinematics of Single Crystal Plasticity 735</p> <p>13.6 Dislocation Density Evolution 740</p> <p>13.7 Stress Required for Dislocation Motion 742</p> <p>13.8 Stress Update in Rate-Dependent Single-Crystal Plasticity 743</p> <p>13.9 Algorithm for Rate-Dependent Dislocation-Density Based Crystal Plasticity 745</p> <p>13.10 Numerical Example: Localized Shear and Inhomogeneous Deformation 747</p> <p>13.11 Exercises 750</p> <p>Appendix 1 Voigt Notation 751</p> <p>Appendix 2 Norms 757</p> <p>Appendix 3 Element Shape Functions 761</p> <p>Appendix 4 Euler Angles From Pole Figures 767</p> <p>Appendix 5 Example of Dislocation-Density Evolutionary Equations 771</p> <p><i>Glossary 777</i></p> <p><i>References 781</i></p> <p><i>Index 795</i></p>
<p><b>Ted Belytschko,</b> <i>Northwestern University, USA</i><br> <b>Wing Kam Liu,</b> <i>Northwestern University, USA</i><br> <b>Brian Moran,</b> <i>King Abdullah University of Science and Technology, The Kingdom of Saudi Arabia</i><br> <b>Khalil I. Elkhodary,</b> <i>The American University in Cairo, Egypt</i>
<p><b>Nonlinear Finite Elements for Continua and Structures</b></p> <p>This updated and expanded edition of the bestselling textbook provides a comprehensive introduction to the methods and theory of nonlinear finite element analysis. New material provides a concise introduction to some of the cutting-edge methods that have evolved in recent years in the field of nonlinear finite element modeling, and includes the eXtended Finite Element Method (XFEM), multiresolution continuum theory for multiscale microstructures, and dislocation- density-based crystalline plasticity. <p><i>Nonlinear Finite Elements for Continua and Structures, Second Edition</i> focuses on the formulation and solution of discrete equations for various classes of problems that are of principal interest in applications to solid and structural mechanics. Topics covered include the discretization by finite elements of continua in one dimension and in multi-dimensions; the formulation of constitutive equations for nonlinear materials and large deformations; procedures for the solution of the discrete equations, including considerations of both numerical and multiscale physical instabilities; and the treatment of structural and contact-impact problems. <p><b>Key features:</b> <ul><li>Presents a detailed and rigorous treatment of nonlinear solid mechanics and how it can be implemented in finite element analysis</li> <li>Covers many of the material laws used in today’s software and research</li> <li>Introduces advanced topics in nonlinear finite element modelling of continua</li> <li>Introduction of multiresolution continuum theory and XFEM</li> <li>Accompanied by a website hosting a solution manual and MATLAB<sup>®</sup> and FORTRAN code</li></ul> <p><i>Nonlinear Finite Elements for Continua and Structures, Second Edition</i> is a must-have textbook for graduate students in mechanical engineering, civil engineering, applied mathematics, engineering mechanics, and materials science, and is also an excellent source of information for researchers and practitioners.

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