عنوان

Nonlinear finite elements for continua and structures

Title Proper

Nonlinear finite elements for continua and structures

Place of Publication, Distribution, etc.

Chichester, West Sussex

Name of Publisher, Distributor, etc.

Wiley

Date of Publication, Distribution, etc.

c2014

Specific Material Designation and Extent of Item

804 p.

Text of Note

Includes bibliographical references and index

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Ted Belytschko, Wing Kam Liu, Brian Moran, Khalil I. Elkhodary

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Machine generated contents note: Preface xi List of Boxes xv 1 Introduction 1 1.1 Nonlinear finite elements in design 1 1.2 Related books and a brief history of nonlinear finite elements 4 1.3 Notation 7 1.4 Mesh descriptions 9 1.5 Classification of partial differential equations 31 1.6 Exercises 81 2 Lagrangian and Eulerian finite elements in one dimension 91 2.1 Introduction 91 2.2 Governing equations for total Lagrangian formulation 02 2.3 Weak form for total Lagrangian formulation 72 2.4 Finite element discretization in total Lagrangian formulation 33 2.5 Element and global matrices 83 2.6 Governing equations for updated Lagrangian formulation 84 2.7 Weak form for updated Lagrangian formulation 15 2.8 Element equations for updated Lagrangian formulation 25 2.9 Governing equations for Eulerian formulation 46 2.01 Weak forms for Eulerian mesh equations 56 2.11 Finite element equations 66 2.21 Solution methods 07 2.31 Summary 27 2.41 Exercises 27 3 Continuum mechanics 57 3.1 Introduction 57 3.2 Deformation and motion 67 3.3 Strain measures 29 3.4 Stress measures 101 3.5 Conservation equations 801 3.6 Lagrangian conservation equations 911 3.7 Polar decomposition and frame-invariance 521 3.8 Exercises 731 4 Lagrangian meshes 141 4.1 Introduction 141 4.2 Governing equations 241 4.3 Weak form: principle of virtual power 541 4.4 Updated Lagrangian finite element discretization 251 4.5 Implementation 261 4.6 Corotational formulations 581 4.7 Total Lagrangian formulation 391 4.8 Total Lagrangian weak form 691 4.9 Finite element semidiscretization 891 4.01 Exercise 312 5 Constitutive models 512 5.1 Introduction 512 5.2 The stress-strain curve 612 5.3 One-dimensional elasticity 122 5.4 Nonlinear elasticity 522 5.5 One-dimensional plasticity 042 5.6 Multiaxial plasticity 742 5.7 Hyperelastic-plastic models 462 5.8 Viscoelasticity 472 5.9 Stress update algorithms 772 5.01 Continuum mechanics and constitutive models 492 5.11 Exercises 803 6 Solution methods and stability 903 6.1 Introduction 903 6.2 Explicit methods 013 6.3 Equilibrium solutions and implicit time integration 713 6.4 Linearization 733 6.5 Stability and continuation methods 353 6.6 Numerical stability 963 6.7 Material stability 483 6.8 Exercises 293 7 Arbitrary Lagrangian Eulerian formulations 393 7.1 Introduction 393 7.2 ALE continuum mechanics 593 7.3 Conservation laws in ALE description 204 7.4 ALE governing equations 304 7.5 Weak forms 404 7.6 Introduction to the Petrov-Galerkin method 804 7.7 Petrov-Galerkin formulation of momentum equation 714 7.8 Path-dependent materials 024 7.9 Linearization of the discrete equations 234 7.01 Mesh update equations 534 7.11 Numerical example: an elastic-plastic wave propagation problem 244 7.21 Total ALE formulations 344 8 Element technology 154 8.1 Introduction 154 8.2 Element performance 354 8.3 Element properties and patch tests 164 8.4 Q4 and volumetric locking 964 8.5 Multi-field weak forms and elements 474 8.6 Multi-field quadrilaterals 784 8.7 One-point quadrature elements 194 8.8 Examples 005 8.9 Stability 405 8.01 Exercises 705 9 Beams and shells 905 9.1 Introduction 905 9.2 Beam theories 115 9.3 Continuum-based beam 415 9.4 Analysis of CB beam 425 9.5 Continuum-based shell implementation 635 9.6 CB shell theory 055 9.7 Shear and membrane locking 555 9.8 Assumed strain elements 065 9.9 One-point quadrature elements 365 9.01 Exercises 665 01 Contact-impact 965 01.1 Introduction 965 01.2 Contact interface equations 075 01.3 Friction models 085 01.4 Weak forms 585 01.5 Finite element discretization 595 01.6 On explicit methods 906 11 XFEM 11.1. INTRODUCTION 11.2. PARTITION OF UNITY AND ENRICHMENTS 11.3. ONE DIMENSIONAL XFEM 11.4. MULTI-DIMENSION XFEM 11.5. WEAK AND STRONG FORMS 11.6. DISCRETE EQUATIONS 11.7. LEVEL SET METHOD 11.8. XFEM IMPLEMENTATION STRATEGY 11.9. INTEGRATION 11.01. AN EXAMPLE OF XFEM SIMULATION 11.11. EXERCISE 21 Introduction to multiresolution theory 21.1 MOTIVATION: MATERIALS ARE STRUCTURED CONTINUA 21.2 BULK DEFORMATION OF MICROSTRUCTURED CONTINUA 21.3 GENERALIZING MECHANICS TO BULK MICROSTRUCTURED CONTINUA 21.4 MULTISCALE MICROSTRUCTURES AND THE MULTIRESOLUTION CONTINUUM THEORY 21.5 GOVERNING EQUATIONS FOR MCT 21.6 CONSTRUCTING MCT CONSTITUTIVE RELATIONSHIPS 21.7 BASIC GUIDELINES FOR RVE MODELS 21.8 FINITE ELEMENT IMPLEMENTATION OF MCT 21.9 NUMERICAL EXAMPLE 21.01 FUTURE RESEARCH DIRECTION OF MCT MODELING 21.11 EXERCISES 31 Single-crystal plasticity 31.1 Introduction 31.2 Crystallographic description of cubic and non-cubic crystals 31.3 Atomic origins of plasticity and the burgers vector in single crystals 31.4 Defining slip planes and directions in general single crystals 31.5 Kinematics of single crystal plasticity 31.6 Dislocation density evolution 31.7 Stress required for dislocation motion. 31.8 Stress update in rate-dependent single-crystal plasticity 31.9 Algorithm for rate-dependent dislocation-density based crystal plasticity 31.01 Numerical example 31.11 Exercises Appendix 1 Voigt notation 516 Appendix 2 Norms 916 Appendix 3 Element shape functions 226 Appendix 4 Euler angles from pole figures Appendix 5 Example of dislocation density evolutionary equations Glossary 726 References 136 Index 146

Entry Element

، Finite element method

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، Continuum mechanics

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، Structural analysis )Engineering(

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، SCIENCE / Mechanics / General

Class number

Dates

3491-

Entry Element

Belytschko, Ted

Relator Code

AU

AU Liu, Wing Kam

AU Moran, Brian 1958-

AU Elkhodary, Khalil I.

TI