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E-raamat: Nonlinear Continuum Mechanics for Finite Element Analysis

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(Swansea University), (Swansea University)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 13-Mar-2008
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9780511389139
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Nonlinear Continuum Mechanics for Finite Element AnalysisSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 13-Mar-2008
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9780511389139
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Designing engineering components that make optimal use of materials requires consideration of the nonlinear characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, and this requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both nonlinear continuum analysis and associated finite element techniques under one roof, Bonet and Wood provide, in this edition of this successful text, a complete, clear, and unified treatment of these important subjects. New chapters dealing with hyperelastic plastic behavior are included, and the authors have thoroughly updated the FLagSHyP program, freely accessible at www.flagshyp.com. Worked examples and exercises complete each chapter, making the text an essential resource for postgraduates studying nonlinear continuum mechanics. It is also ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.

Arvustused

' a unified introduction - can be recommended to postgraduate students and to researchers from mechanical, aerospace and civil engineering areas.' Zentralblatt für Mathematik und ihre Grenzgebiete 'The authors have succeeded in writing an excellent textbook - the book is absolutely recommended directly to students and scientists in the field of solid mechanics at universities.' K. Schweizerhof, ZAMM

Muu info

This edition of this successful text includes chapters on hyperelastic plastic behaviour and updates to FLagSHyP web program.
Preface xv
Introduction
1(21)
Nonlinear Computational Mechanics
1(1)
Simple Examples of Nonlinear Structural Behavior
2(2)
Cantilever
2(1)
Column
3(1)
Nonlinear Strain Measures
4(9)
One-Dimensional Strain Measures
5(1)
Nonlinear Truss Example
6(4)
Continuum Strain Measures
10(3)
Directional Derivative, Linearization and Equation Solution
13(9)
Directional Derivative
14(2)
Linearization and Solution of Nonlinear Algebraic Equations
16(6)
Mathematical Preliminaries
22(41)
Introduction
22(1)
Vector and Tensor Algebra
22(25)
Vectors
23(5)
Second-Order Tensors
28(9)
Vector and Tensor Invariants
37(4)
Higher-Order Tensors
41(6)
Linearization and the Directional Derivative
47(10)
One Degree of Freedom
48(1)
General Solution to a Nonlinear Problem
49(3)
Properties of the Directional Derivative
52(1)
Examples of Linearization
53(4)
Tensor Analysis
57(6)
The Gradient and Divergence Operators
58(2)
Integration Theorems
60(3)
Analysis of Three-Dimensional Truss Structures
63(31)
Introduction
63(2)
Kinematics
65(3)
Linearization of Geometrical Descriptors
67(1)
Internal Forces and Hyperelastic Constitutive Equations
68(2)
Nonlinear Equilibrium Equations and the Newton-Raphson Solution
70(4)
Equilibrium Equations
70(1)
Newton--Raphson Procedure
71(1)
Tangent Elastic Stiffness Matrix
72(2)
Elasto-Plastic Behavior
74(15)
Multiplicative Decomposition of the Stretch
74(2)
Rate-independent Plasticity
76(4)
Incremental Kinematics
80(3)
Time Integration
83(1)
Stress Update and Return Mapping
83(3)
Algorithmic Tangent Modulus
86(2)
Revised Newton--Raphson Procedure
88(1)
Examples
89(5)
Inclined Axial Rod
89(1)
Trussed Frame
89(5)
Kinematics
94(40)
Introduction
94(1)
The Motion
94(1)
Material and Spatial Descriptions
95(2)
Deformation Gradient
97(4)
Strain
101(4)
Polar Decomposition
105(5)
Volume Change
110(2)
Distortional Component of the Deformation Gradient
112(3)
Area Change
115(1)
Linearized Kinematics
116(2)
Linearized Deformation Gradient
116(1)
Linearized Strain
117(1)
Linearized Volume Change
118(1)
Velocity and Material Time Derivatives
118(4)
Velocity
118(1)
Material Time Derivative
119(1)
Directional Derivative and Time Rates
120(2)
Velocity Gradient
122(1)
Rate of Deformation
122(3)
Spin Tensor
125(3)
Rate of Change of Volume
128(2)
Superimposed Rigid Body Motions and Objectivity
130(4)
Stress and Equilibrium
134(21)
Introduction
134(1)
Cauchy Stress Tensor
134(5)
Definition
134(4)
Stress Objectivity
138(1)
Equilibrium
139(3)
Translational Equilibrium
139(2)
Rotational Equilibrium
141(1)
Principle of Virtual Work
142(2)
Work Conjugacy and Alternative Stress Representations
144(8)
The Kirchhoff Stress Tensor
144(1)
The First Piola--Kirchhoff Stress Tensor
145(3)
The Second Piola--Kirchhoff Stress Tensor
148(3)
Deviatoric and Pressure Components
151(1)
Stress Rates
152(3)
Hyperelasticity
155(33)
Introduction
155(1)
Hyperelasticity
155(2)
Elasticity Tensor
157(3)
The Material or Lagrangian Elasticity Tensor
157(1)
The Spatial or Eulerian Elasticity Tensor
158(2)
Isotropic Hyperelasticity
160(6)
Material Description
160(1)
Spatial Description
161(1)
Compressible Neo-Hookean Material
162(4)
Incompressible and Nearly Incompressible Materials
166(8)
Incompressible Elasticity
166(3)
Incompressible Neo-Hookean Material
169(2)
Nearly Incompressible Hyperelastic Materials
171(3)
Isotropic Elasticity in Principal Directions
174(14)
Material Description
174(1)
Spatial Description
175(1)
Material Elasticity Tensor
176(2)
Spatial Elasticity Tensor
178(1)
A Simple Stretch-based Hyperelastic Material
179(1)
Nearly Incompressible Material in Principal Directions
180(3)
Plane Strain and Plane Stress Cases
183(1)
Uniaxial Rod Case
184(4)
Large Elasto-Plastic Deformations
188(28)
Introduction
188(1)
The Multiplicative Decomposition
189(4)
Rate Kinematics
193(4)
Rate-Independent Plasticity
197(3)
Principal Directions
200(4)
Incremental Kinematics
204(7)
The Radial Return Mapping
207(2)
Algorithmic Tangent Modulus
209(2)
Two-Dimensional Cases
211(5)
Linearized Equilibrium Equations
216(21)
Introduction
216(1)
Linearization and Newton--Raphson Process
216(2)
Lagrangian Linearized Internal Virtual Work
218(1)
Eulerian Linearized Internal Virtual Work
219(2)
Linearized External Virtual Work
221(3)
Body Forces
221(1)
Surface Forces
222(2)
Variational Methods and Incompressibility
224(13)
Total Potential Energy and Equilibrium
225(1)
Lagrange Multiplier Approach to Incompressibility
225(3)
Penalty Methods for Incompressibility
228(1)
Hu-Washizu Variational Principle for Incompressibility
229(2)
Mean Dilatation Procedure
231(6)
Discretization and Solution
237(29)
Introduction
237(1)
Discretized Kinematics
237(5)
Discretized Equilibrium Equations
242(5)
General Derivation
242(3)
Derivation in Matrix Notation
245(2)
Discretization of the Linearized Equilibrium Equations
247(9)
Constitutive Component: Indicial Form
248(1)
Constitutive Component: Matrix Form
249(2)
Initial Stress Component
251(1)
External Force Component
252(2)
Tangent Matrix
254(2)
Mean Dilatation Method for Incompressibility
256(2)
Implementation of the Mean Dilatation Method
256(2)
Newton--Raphson Iteration and Solution Procedure
258(8)
Newton--Raphson Solution Algorithm
258(1)
Line Search Method
259(2)
Arc-Length Method
261(5)
Computer Implementation
266(46)
Introduction
266(1)
User Instructions
267(6)
Output File Description
273(3)
Element Types
276(1)
Solver Details
277(1)
Constitutive Equation Summary
277(7)
Program Structure
284(1)
Main Routine flagshyp
284(8)
Routine elemtk
292(6)
Routine radialrtn
298(1)
Routine ksigma
299(2)
Routine bpress
301(1)
Examples
302(6)
Simple Patch Test
302(1)
Nonlinear Truss
303(1)
Strip With a Hole
304(1)
Plane Strain Nearly Incompressible Strip
305(1)
Elasto-plastic Cantilever
306(2)
Appendix: Dictionary of Main Variables
308(4)
Bibliography 312(2)
Index 314
Javier Bonet is a Professor of Engineering and the Deputy Head of the School of Engineering at Swansea University, and a visiting professor at the Universitat Politecnica de Catalunya in Spain. He has extensive experience of teaching topics in structural mechanics, including large strain nonlinear solid mechanics, to undergraduate and graduate engineering students. He has been active in research in the area of computational mechanics for over 25 years and has written over 60 papers and over 70 conference contributions on many topics within the subject and given invited, keynote and plenary lectures at numerous international conferences. Richard D. Wood is an Honorary Research Fellow in the Civil and Computational Engineering Centre at Swansea University. He has over 20 years experience of teaching the course Nonlinear Continuum Mechanics for Finite Element Analysis at Swansea University, which he originally developed at the University of Arizona and also taught at IIT Roorkee, India and the Institute of Structural Engineering at the Technical University in Graz. Dr Wood's academic career has focused on finite element analysis, and he has written over 60 papers in international journals, and many chapter contributions, on topics related to nonlinear finite element analysis.
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