Nonlinear Finite Element Analysis of Solids and Structures [NOOK Book]

Overview

Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist René de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield’s first edition is acclaimed. 

Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved ...

See more details below
Nonlinear Finite Element Analysis of Solids and Structures

Available on NOOK devices and apps  
  • NOOK Devices
  • Samsung Galaxy Tab 4 NOOK
  • NOOK HD/HD+ Tablet
  • NOOK
  • NOOK Color
  • NOOK Tablet
  • Tablet/Phone
  • NOOK for Windows 8 Tablet
  • NOOK for iOS
  • NOOK for Android
  • NOOK Kids for iPad
  • PC/Mac
  • NOOK for Windows 8
  • NOOK for PC
  • NOOK for Mac
  • NOOK for Web

Want a NOOK? Explore Now

NOOK Book (eBook)
$62.99
BN.com price
(Save 42%)$110.00 List Price
Note: This NOOK Book can be purchased in bulk. Please email us for more information.

Overview

Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist René de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield’s first edition is acclaimed. 

Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. 

The authors’ integrated and consistent style and unrivalled engineering approach assures this book’s unique position within the computational mechanics literature.

 Key features: 

  • Combines the two previous volumes into one heavily revised text with obsolete material removed, an improved layout and updated references and notations
  • Extensive new material on more recent developments in computational mechanics
  • Easily readable, engineering oriented, with no more details in the main text than necessary to understand the concepts.
  • Pseudo-code throughout makes the link between theory and algorithms, and the actual implementation.
  • Accompanied by a website (www.wiley.com/go/deborst) with a Python code, based on the pseudo-code within the book and suitable for solving small-size problems. 

Non-linear Finite Element Analysis of Solids and Structures, 2nd Edition is an essential reference for practising engineers and researchers that can also be used as a text for undergraduate and graduate students within computational mechanics.

Read More Show Less

Product Details

Table of Contents

Preface xi

Series Preface xiii

Notation xv

About the Code xxi

PART I BASIC CONCEPTS AND SOLUTION TECHNIQUES

1 Preliminaries 3

1.1 A Simple Example of Non-linear Behaviour 3

1.2 A Review of Concepts from Linear Algebra 5

1.3 Vectors and Tensors 12

1.4 Stress and Strain Tensors 17

1.5 Elasticity 23

1.6 The PyFEM Finite Element Library 25

References 29

2 Non-linear Finite Element Analysis 31

2.1 Equilibrium and Virtual Work 31

2.2 Spatial Discretisation by Finite Elements 33

2.3 PyFEM: Shape Function Utilities 38

2.4 Incremental-iterative Analysis 41

2.5 Load versus Displacement Control 50

2.6 PyFEM: A Linear Finite Element Code with Displacement Control 53

References 62

3 Geometrically Non-linear Analysis 63

3.1 Truss Elements 64

3.2 PyFEM: The Shallow Truss Problem 76

3.3 Stress and Deformation Measures in Continua 85

3.4 Geometrically Non-linear Formulation of Continuum Elements 91

3.5 Linear Buckling Analysis 100

3.6 PyFEM: A Geometrically Non-linear Continuum Element 103

References 110

4 Solution Techniques in Quasi-static Analysis 113

4.1 Line Searches 113

4.2 Path-following or Arc-length Methods 116

4.3 PyFEM: Implementation of Riks’ Arc-length Solver 124

4.4 Stability and Uniqueness in Discretised Systems 129

4.5 Load Stepping and Convergence Criteria 134

4.6 Quasi-Newton Methods 138

References 141

5 Solution Techniques for Non-linear Dynamics 143

5.1 The Semi-discrete Equations 143

5.2 Explicit Time Integration 144

5.3 PyFEM: Implementation of an Explicit Solver 149

5.4 Implicit Time Integration 152

5.5 Stability and Accuracy in the Presence of Non-linearities 156

5.6 Energy-conserving Algorithms 161

5.7 Time Step Size Control and Element Technology 164

References 165

PART II MATERIAL NON-LINEARITIES

6 Damage Mechanics 169

6.1 The Concept of Damage 169

6.2 Isotropic Elasticity-based Damage 171

6.3 PyFEM: A Plane-strain Damage Model 175

6.4 Stability, Ellipticity and Mesh Sensitivity 179

6.5 Cohesive-zone Models 185

6.6 Element Technology: Embedded Discontinuities 190

6.7 Complex Damage Models 198

6.8 Crack Models for Concrete and Other Quasi-brittle Materials 201

6.8.1 Elasticity-based Smeared Crack Models 201

6.8.2 Reinforcement and Tension Stiffening 206

6.9 Regularised Damage Models 210

References 215

7 Plasticity 219

7.1 A Simple Slip Model 219

7.2 Flow Theory of Plasticity 223

7.3 Integration of the Stress–strain Relation 239

7.4 Tangent Stiffness Operators 249

7.5 Multi-surface Plasticity 252

7.6 Soil Plasticity: Cam-clay Model 267

7.7 Coupled Damage–Plasticity Models 270

7.8 Element Technology: Volumetric Locking 271

References 277

8 Time-dependent Material Models 281

8.1 Linear Visco-elasticity 281

8.2 Creep Models 287

8.3 Visco-plasticity 289

References 303

PART III STRUCTURAL ELEMENTS

9 Beams and Arches 307

9.1 A Shallow Arch 307

9.2 PyFEM: A Kirchhoff Beam Element 317

9.3 Corotational Elements 321

9.4 A Two-dimensional Isoparametric Degenerate Continuum Beam Element 328

9.5 A Three-dimensional Isoparametric Degenerate Continuum Beam Element 333

References 341

10 Plates and Shells 343

10.1 Shallow-shell Formulations 344

10.2 An Isoparametric Degenerate Continuum Shell Element 351

10.3 Solid-like Shell Elements 356

10.4 Shell Plasticity: Ilyushin’s Criterion 357

References 361

PART IV LARGE STRAINS

11 Hyperelasticity 365

11.1 More Continuum Mechanics 365

11.2 Strain Energy Functions 374

11.3 Element Technology 389

References 398

12 Large-strain Elasto-plasticity 401

12.1 Eulerian Formulations 402

12.2 Multiplicative Elasto-plasticity 407

12.3 Multiplicative Elasto-plasticity versus Rate Formulations 411

12.4 Integration of the Rate Equations 414

12.5 Exponential Return-mapping Algorithms 418

References 422

PART V ADVANCED DISCRETISATION CONCEPTS

13 Interfaces and Discontinuities 427

13.1 Interface Elements 428

13.2 Discontinuous Galerkin Methods 436

References 439

14 Meshless and Partition-of-unity Methods 441

14.1 Meshless Methods 442

14.2 Partition-of-unity Approaches 451

References 470

15 Isogeometric Finite Element Analysis 473

15.1 Basis Functions in Computer Aided Geometric Design 473

15.2 Isogeometric Finite Elements 483

15.3 PyFEM: Shape Functions for Isogeometric Analysis 487

15.4 Isogeometric Analysis in Non-linear Solid Mechanics 490

References 506

Index 509

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)