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Nonlinear Finite Element Analysis of Solids and Structures 2nd edition [Hardback]

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, (T U Eindhoven), , (Imperial College, London)
  • Formāts: Hardback, 544 pages, height x width x depth: 252x175x30 mm, weight: 948 g
  • Sērija : Wiley Series in Computational Mechanics
  • Izdošanas datums: 17-Aug-2012
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 0470666447
  • ISBN-13: 9780470666449
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Nonlinear Finite Element Analysis of Solids and Structures 2nd editionPalielināt
  • Formāts: Hardback, 544 pages, height x width x depth: 252x175x30 mm, weight: 948 g
  • Sērija : Wiley Series in Computational Mechanics
  • Izdošanas datums: 17-Aug-2012
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 0470666447
  • ISBN-13: 9780470666449
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780470666449.html
Keywords:
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.
Preface xi
Series Preface xiii
Notation xv
About the Code xxi
PART I BASIC CONCEPTS AND SOLUTION TECHNIQUES
1 Preliminaries
3(28)
1.1 A Simple Example of Non-linear Behaviour
3(2)
1.2 A Review of Concepts from Linear Algebra
5(7)
1.3 Vectors and Tensors
12(5)
1.4 Stress and Strain Tensors
17(6)
1.5 Elasticity
23(2)
1.6 The PyFEM Finite Element Library
25(6)
References
29(2)
2 Non-linear Finite Element Analysis
31(32)
2.1 Equilibrium and Virtual Work
31(2)
2.2 Spatial Discretisation by Finite Elements
33(5)
2.3 PyFEM: Shape Function Utilities
38(3)
2.4 Incremental-iterative Analysis
41(9)
2.5 Load versus Displacement Control
50(3)
2.6 PyFEM: A Linear Finite Element Code with Displacement Control
53(10)
References
62(1)
3 Geometrically Non-linear Analysis
63(50)
3.1 Truss Elements
64(12)
3.1.1 Total Lagrange Formulation
67(3)
3.1.2 Updated Lagrange Formulation
70(2)
3.1.3 Co rotational Formulation
72(4)
3.2 PyFEM: The Shallow Truss Problem
76(9)
3.3 Stress and Deformation Measures in Continua
85(6)
3.4 Geometrically Non-linear Formulation of Continuum Elements
91(9)
3.4.1 Total and Updated Lagrange Formulations
91(5)
3.4.2 Corotational Formulation
96(4)
3.5 Linear Buckling Analysis
100(3)
3.6 PyFEM: A Geometrically Non-linear Continuum Element
103(10)
References
110(3)
4 Solution Techniques in Quasi-static Analysis
113(30)
4.1 Line Searches
113(3)
4.2 Path-following or Arc-length Methods
116(8)
4.3 PyFEM: Implementation of Riks' Arc-length Solver
124(5)
4.4 Stability and Uniqueness in Discretised Systems
129(5)
4.4.1 Stability of a Discrete System
129(1)
4.4.2 Uniqueness and Bifurcation in a Discrete System
130(4)
4.4.3 Branch Switching
134(1)
4.5 Load Stepping and Convergence Criteria
134(4)
4.6 Quasi-Newton Methods
138(5)
References
141(2)
5 Solution Techniques for Non-linear Dynamics
143(26)
5.1 The Semi-discrete Equations
143(1)
5.2 Explicit Time Integration
144(5)
5.3 PyFEM: Implementation of an Explicit Solver
149(3)
5.4 Implicit Time Integration
152(4)
5.4.1 The Newmark Family
153(1)
5.4.2 The HHT α-method
154(1)
5.4.3 Alternative Implicit Methods for Time Integration
155(1)
5.5 Stability and Accuracy in the Presence of Non-linearities
156(5)
5.6 Energy-conserving Algorithms
161(3)
5.7 Time Step Size Control and Element Technology
164(5)
References
165(4)
PART II MATERIAL NON-LINEARITIES
6 Damage Mechanics
169(50)
6.1 The Concept of Damage
169(2)
6.2 Isotropic Elasticity-based Damage
171(4)
6.3 PyFEM: A Plane-strain Damage Model
175(4)
6.4 Stability, Ellipticity and Mesh Sensitivity
179(6)
6.4.1 Stability and Ellipticity
179(3)
6.4.2 Mesh Sensitivity
182(3)
6.5 Cohesive-zone Models
185(5)
6.6 Element Technology: Embedded Discontinuities
190(8)
6.7 Complex Damage Models
198(3)
6.7.1 Anisotropic Damage Models
198(1)
6.7.2 Microplane Models
199(2)
6.8 Crack Models for Concrete and Other Quasi-brittle Materials
201(9)
6.8.1 Elasticity-based Smeared Crack Models
201(5)
6.8.2 Reinforcement and Tension Stiffening
206(4)
6.9 Regularised Damage Models
210(9)
6.9.1 Non-local Damage Models
210(1)
6.9.2 Gradient Damage Models
211(4)
References
215(4)
7 Plasticity
219(62)
7.1 A Simple Slip Model
219(4)
7.2 Flow Theory of Plasticity
223(16)
7.2.7 Yield Function
223(5)
7.2.2 Flow Rule
228(4)
7.2.3 Hardening Behaviour
232(7)
7.3 Integration of the Stress--strain Relation
239(10)
7.4 Tangent Stiffness Operators
249(3)
7.5 Multi-surface Plasticity
252(15)
7.5.1 Koiter's Generalisation
252(2)
7.5.2 Rankine Plasticity for Concrete
254(6)
7.5.3 Tresca and Mohr--Coulomb Plasticity
260(7)
7.6 Soil Plasticity: Cam-clay Model
267(3)
7.7 Coupled Damage--Plasticity Models
270(1)
7.8 Element Technology: Volumetric Locking
271(10)
References
277(4)
8 Time-dependent Material Models
281(26)
8.1 Linear Visco-elasticity
281(6)
8.1.1 One-dimensional Linear Visco-elasticity
282(2)
8.7.2 Three-dimensional Visco-elasticity
284(1)
8.1.3 Algorithmic Aspects
285(2)
8.2 Creep Models
287(2)
8.3 Visco-plasticity
289(18)
8.3.1 One-dimensional Visco-plasticity
289(2)
8.3.2 Integration of the Rate Equations
291(1)
8.3.3 Perzyna Visco-plasticity
292(2)
8.3.4 Duvaut--Lions Visco-plasticity
294(2)
8.3.5 Consistency Model
296(2)
8.3.6 Propagative or Dynamic Instabilities
298(5)
References
303(4)
PART III STRUCTURAL ELEMENTS
9 Beams and Arches
307(36)
9.1 A Shallow Arch
307(10)
9.1.1 Kirchhoff Formulation
307(7)
9.1.2 Including Shear Deformation: Timoshenko Beam
314(3)
9.2 PyFEM: A Kirchhoff Beam Element
317(4)
9.3 Corotational Elements
321(7)
9.3.1 Kirchhoff Theory
321(5)
9.3.2 Timoshenko Beam Theory
326(2)
9.4 A Two-dimensional Isoparametric Degenerate Continuum Beam Element
328(5)
9.5 A Three-dimensional Isoparametric Degenerate Continuum Beam Element
333(10)
References
341(2)
10 Plates and Shells
343(22)
10.1 Shallow-shell Formulations
344(7)
10.2 An Isoparametric Degenerate Continuum Shell Element
351(5)
10.3 Solid-like Shell Elements
356(1)
10.4 Shell Plasticity: Ilyushin's Criterion
357(8)
References
361(4)
PART IV LARGE STRAINS
11 Hyperelasticity
365(36)
11.1 More Continuum Mechanics
365(9)
11.1.1 Momentum Balance and Stress Tensors
365(3)
11.1.2 Objective Stress Rates
368(4)
11.1.3 Principal Stretches and Invariants
372(2)
11.2 Strain Energy Functions
374(15)
11.2.7 Incompressibility and Near-incompressibility
376(2)
11.2.2 Strain Energy as a Function of Stretch Invariants
378(4)
11.2.3 Strain Energy as a Function of Principal Stretches
382(4)
11.2.4 Logarithmic Extension of Linear Elasticity: Hencky Model
386(3)
11.3 Element Technology
389(12)
11.3.1 u/p Formulation
389(3)
11.3.2 Enhanced Assumed Strain Elements
392(3)
11.3.3 F-bar Approach
395(1)
11.3.4 Corotational Approach
396(2)
References
398(3)
12 Large-strain Elasto-plasticity
401(26)
12.1 Eulerian Formulations
402(5)
12.2 Multiplicative Elasto-plasticity
407(4)
12.3 Multiplicative Elasto-plasticity versus Rate Formulations
411(3)
12.4 Integration of the Rate Equations
414(4)
12.5 Exponential Return-mapping Algorithms
418(9)
References
422(5)
PART V ADVANCED DISCRETISATION CONCEPTS
13 Interfaces and Discontinuities
427(14)
13.1 Interface Elements
428(8)
13.2 Discontinuous Galerkin Methods
436(5)
References
439(2)
14 Meshless and Partition-of-unity Methods
441(32)
14.1 Meshless Methods
442(9)
14.1.1 The Element-free Galerkin Method
442(4)
14.1.2 Application to Fracture
446(2)
14.1.3 Higher-order Damage Mechanics
448(2)
14.1.4 Volumetric Locking
450(1)
14.2 Partition-of-unity Approaches
451(22)
14.2.1 Application to Fracture
455(5)
14.2.2 Extension to Large Deformations
460(5)
14.2.3 Dynamic Fracture
465(3)
14.2.4 Weak Discontinuities
468(2)
References
470(3)
15 Isogeometric Finite Element Analysis
473(36)
15.1 Basis Functions in Computer Aided Geometric Design
473(10)
15.1.1 Univariate B-splines
474(4)
15.1.2 Univariate NURBS
478(1)
15.1.3 Multivariate B-splines and NURBS Patches
478(2)
15.1.4 T-splines
480(3)
15.2 Isogeometric Finite Elements
483(4)
15.2.1 Bezier Element Representation
483(2)
75.2.2 Bezier Extraction
485(2)
15.3 PyFEM: Shape Functions for Isogeometric Analysis
487(3)
15.4 Isogeometric Analysis in Non-linear Solid Mechanics
490(19)
15.4.1 Design-through-analysis of Shell Structures
491(5)
15.4.2 Higher-order Damage Models
496(4)
15.4.3 Cohesive Zone Models
500(6)
References
506(3)
Index 509
Mike Crisfield (deceased), Imperial College, London; René de Borst, Joris Remmers & Clemens Verhoosel, TU Eindhoven, Netherlands

Professor Mike Crisfield (deceased) joined the Transport & Road Research Laboratory (TRRL) in 1971, where he rose to the rank of Deputy Chief Scientific Officer. In 1989 he was appointed as first holder of the FEA Chair in Computational Mechanics in the aeronautics department at Imperial College, London, the department that had pioneered FEA in the 1950s and 1960s. Shortly before he died, a list of the most cited engineering researchers in the UK was published included Mike in the top 20, and he received an IACM Research Achievement Award in recognition of his extraordinary achievements in the field of non-linear computational mechanics. An eminent researcher and a scholar, he was reputed as an innovative thinker who adopted a 'hands-on' approach.

René de Borst was appointed Dean and Distinguished University Professor of the Faculty of Mechanical Engineering of TU Eindhoven in May 2007 after a long tenure as Professor and deputy Dean at TU Delft. He is Editor for the International Journal for Numerical Methods in Engineering and International Journal for Numerical and Analytical Methods in Geomechanics and Editor for the Encyclopedia of Computational Mechanics. His many awards and the outstanding assessment of his work by the scientific community attest to his reputation as a world leading scientist and researcher within the field of computational mechanics.

Joris Remmers is an assistant professor within René de Borst's group at TU Eindhoven.

Clemens Verhoosel is an assistant professor within René de Borst's group at TU Eindhoven.