Nonlinear continuum mechanics for finite element analysis bonet, wood

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Đây là bộ sách tiếng anh về chuyên ngành vật lý gồm các lý thuyết căn bản và lý liên quan đến công nghệ nano ,công nghệ vật liệu ,công nghệ vi điện tử,vật lý bán dẫn. Bộ sách này thích hợp cho những ai đam mê theo đuổi ngành vật lý và muốn tìm hiểu thế giới vũ trụ và hoạt độn ra sao. NONLINEAR CONTINUUMMECHANICS FOR FINITEELEMENT ANALYSISJavier Bonet Richard D. WoodUniversity of Wales Swansea University of Wales SwanseaP U B L I S H E D B Y T H E P R E S S SYND I C A T E O F THE U N I V E R S I T Y O F C A M B R I D G EThe Pitt Building, Trumpington Street, Cambridge CB2 1RP, United KingdomC A M B R I D G E U N I V E R S I T Y P R E S SThe Edinburgh Building, Cambridge CB2 2RU, United Kingdom40 West 20th Street, New York, NY 10011-4211, USA10 Stamford Road, Oakleigh, Melbourne 3166, Australiac Cambridge University Press 1997This book is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.First published 1997Printed in the United States of AmericaTypeset in Times and UniversLibrary of Congress Cataloging-in-Publication DataBonet, Javier, 1961–Nonlinear continuum mechanics for finite element analysis / JavierBonet, Richard D. Wood.p. cm.ISBN 0-521-57272-X1. Materials – Mathematical models. 2. Continuum mechanics.3. Nonlinear mechanics. 4. Finite element method. I. Wood.Richard D. II. Title.TA405.B645 1997620.11015118 – dc21 97-11366CIPA catalog record for this book is available fromthe British Library.ISBN 0 521 57272 X hardbackivTo Catherine, Doreen and our childrenvviCONTENTSPreface xiii1 INTRODUCTION 11.1 NONLINEAR COMPUTATIONAL MECHANICS 11.2 SIMPLE EXAMPLES OF NONLINEAR STRUCTURAL BEHAVIOR 21.2.1 Cantilever 21.2.2 Column 31.3 NONLINEAR STRAIN MEASURES 41.3.1 One-Dimensional Strain Measures 51.3.2 Nonlinear Truss Example 61.3.3 Continuum Strain Measures 101.4 DIRECTIONAL DERIVATIVE, LINEARIZATION ANDEQUATION SOLUTION 131.4.1 Directional Derivative 141.4.2 Linearization and Solution of NonlinearAlgebraic Equations 162 MATHEMATICAL PRELIMINARIES 212.1 INTRODUCTION 212.2 VECTOR AND TENSOR ALGEBRA 212.2.1 Vectors 222.2.2 Second-Order Tensors 262.2.3 Vector and Tensor Invariants 33viiviii2.2.4 Higher-Order Tensors 372.3 LINEARIZATION AND THE DIRECTIONAL DERIVATIVE 432.3.1 One Degree of Freedom 432.3.2 General Solution to a Nonlinear Problem 442.3.3 Properties of the Directional Derivative 472.3.4 Examples of Linearization 482.4 TENSOR ANALYSIS 522.4.1 The Gradient and Divergence Operators 522.4.2 Integration Theorems 543 KINEMATICS 573.1 INTRODUCTION 573.2 THE MOTION 573.3 MATERIAL AND SPATIAL DESCRIPTIONS 593.4 DEFORMATION GRADIENT 613.5 STRAIN 643.6 POLAR DECOMPOSITION 683.7 VOLUME CHANGE 733.8 DISTORTIONAL COMPONENT OF THE DEFORMATIONGRADIENT 743.9 AREA CHANGE 773.10 LINEARIZED KINEMATICS 783.10.1 Linearized Deformation Gradient 783.10.2 Linearized Strain 793.10.3 Linearized Volume Change 803.11 VELOCITY AND MATERIAL TIME DERIVATIVES 803.11.1 Velocity 803.11.2 Material Time Derivative 813.11.3 Directional Derivative and Time Rates 823.11.4 Velocity Gradient 833.12 RATE OF DEFORMATION 843.13 SPIN TENSOR 87ix3.14 RATE OF CHANGE OF VOLUME 903.15 SUPERIMPOSED RIGID BODY MOTIONS AND OBJECTIVITY 924 STRESS AND EQUILIBRIUM 964.1 INTRODUCTION 964.2 CAUCHY STRESS TENSOR 964.2.1 Definition 964.2.2 Stress Objectivity 1014.3 EQUILIBRIUM 1014.3.1 Translational Equilibrium 1014.3.2 Rotational Equilibrium 1034.4 PRINCIPLE OF VIRTUAL WORK 1044.5 WORK CONJUGACY AND STRESS REPRESENTATIONS 1064.5.1 The Kirchhoff Stress Tensor 1064.5.2 The First Piola–Kirchhoff Stress Tensor 1074.5.3 The Second Piola–Kirchhoff Stress Tensor 1094.5.4 Deviatoric and Pressure Components 1124.6 STRESS RATES 1135 HYPERELASTICITY 1175.1 INTRODUCTION 1175.2 HYPERELASTICITY 1175.3 ELASTICITY TENSOR 1195.3.1 The Material or Lagrangian Elasticity Tensor 1195.3.2 The Spatial or Eulerian Elasticity Tensor 1205.4 ISOTROPIC HYPERELASTICITY 1215.4.1 Material Description 1215.4.2 Spatial Description 1225.4.3 Compressible Neo-Hookean Material 1245.5 INCOMPRESSIBLE AND NEARLYINCOMPRESSIBLE MATERIALS 1265.5.1 Incompressible Elasticity 1265.5.2 Incompressible Neo-Hookean Material 1295.5.3 Nearly Incompressible Hyperelastic Materials 131x5.6 ISOTROPIC ELASTICITY IN PRINCIPAL DIRECTIONS 1345.6.1 Material Description 1345.6.2 Spatial Description 1355.6.3 Material Elasticity Tensor 1365.6.4 Spatial Elasticity Tensor 1375.6.5 A Simple Stretch-Based Hyperelastic Material 1385.6.6 Nearly Incompressible Material in Principal Directions 1395.6.7 Plane Strain and Plane Stress Cases 1425.6.8 Uniaxial Rod Case 1436 LINEARIZED EQUILIBRIUM EQUATIONS 1466.1 INTRODUCTION 1466.2 LINEARIZATION AND NEWTON–RAPHSON PROCESS 1466.3 LAGRANGIAN LINEARIZED INTERNAL VIRTUAL WORK 1486.4 EULERIAN LINEARIZED INTERNAL VIRTUAL WORK 1496.5 LINEARIZED EXTERNAL VIRTUAL WORK 1506.5.1 Body Forces 1516.5.2 Surface Forces 1516.6 VARIATIONAL METHODS AND INCOMPRESSIBILITY 1536.6.1 Total Potential Energy and Equilibrium 1546.6.2 Lagrange Multiplier Approach to Incompressibility 1546.6.3 Penalty Methods for Incompressibility 1576.6.4 Hu-Washizu Variational Principle for Incompressibility 1586.6.5 Mean Dilatation Procedure 1607 DISCRETIZATION AND SOLUTION 1657.1 INTRODUCTION 1657.2 DISCRETIZED KINEMATICS 1657.3 DISCRETIZED EQUILIBRIUM EQUATIONS 1707.3.1 General Derivation 1707.3.2 Derivation in Matrix Notation 1727.4 DISCRETIZATION OF THE LINEARIZEDEQUILIBRIUM EQUATIONS 1737.4.1 Constitutive Component – Indicial Form 174xi7.4.2 Constitutive Component – Matrix Form 1767.4.3 Initial Stress Component 1777.4.4 External Force Component 1787.4.5 Tangent Matrix 1807.5 MEAN DILATATION METHOD FOR INCOMPRESSIBILITY 1827.5.1 Implementation of the Mean Dilatation Method 1827.6 NEWTON–RAPHSON ITERATION AND SOLUTIONPROCEDURE 1847.6.1 Newton–Raphson Solution Algorithm 1847.6.2 Line Search Method 1857.6.3 Arc Length Method 1878 COMPUTER IMPLEMENTATION 1918.1 INTRODUCTION 1918.2 USER INSTRUCTIONS 1928.3 OUTPUT FILE DESCRIPTION 1968.4 ELEMENT TYPES 1978.5 SOLVER DETAILS 2008.6 CONSTITUTIVE EQUATION SUMMARY 2018.7 PROGRAM STRUCTURE 2068.8 MAIN ROUTINE flagshyp 2068.9 ROUTINE elemtk 2148.10 ROUTINE ksigma 2208.11 ROUTINE bpress 2218.12 EXAMPLES 2238.12.1 Simple Patch Test 2238.12.2 Nonlinear Truss 2248.12.3 Strip With a Hole 2258.12.4 Plane Strain Nearly Incompressible Strip 2258.13 APPENDIX : Dictionary of Main Variables 227APPENDIX LARGE INELASTIC DEFORMATIONS 231A.1 INTRODUCTION 231A.2 THE MULTIPLICATIVE DECOMPOSITION 232xiiA.3 PRINCIPAL DIRECTIONS 234A.4 INCREMENTAL KINEMATICS 236A.5 VON MISES PLASTICITY 238A.5.1 Stress Evaluation 238A.5.2 The Radial Return Mapping 239A.5.3 Tangent Modulus 240Bibliography 243Index 245[...]... geometric nonlinearity, and any metal-forming analysis such as forging or crash-worthiness must include both aspects of nonlinearity Structural instability is inherently a geometric nonlinear phenomenon, as is the behavior of tension structures Indeed the mechanical behavior of the human body itself, say in impact analysis, involves both types of nonlinearity Nonlinear and linear continuum mechanics. .. of the numerical analysis of nonlinear continua using a computer is called nonlinear computational mechanics, which, when applied specifically to the investigation of solid continua, comprises nonlinear continuum mechanics together with the numerical schemes for solving the resulting governing equations The finite element method may be summarized as follows It is a procedure whereby the continuum behavior... INTRODUCTION 1.1 NONLINEAR COMPUTATIONAL MECHANICS Two sources of nonlinearity exist in the analysis of solid continua, namely, material and geometric nonlinearity The former occurs when, for whatever reason, the stress strain behavior given by the constitutive relation is nonlinear, whereas the latter is important when changes in geometry, however large or small, have a significant effect on the load deformation... be suitable for someone starting to use a nonlinear computer program Alternatively, the requirements of a research project may necessitate a deeper understanding of the concepts discussed To assist in this latter endeavour the book includes a computer program for the nonlinear finite deformation finite element analysis of two- and three-dimensional solids Such a program provides the basis for a contemporary... Material nonlinearity can be considered to encompass contact friction, whereas geometric nonlinearity includes deformation-dependent boundary conditions and loading Despite the obvious success of the assumption of linearity in engineering analysis it is equally obvious that many situations demand consideration of nonlinear behavior For example, ultimate load analysis of structures involves material nonlinearity... stated as the exposition of the nonlinear continuum mechanics necessary to develop the governing equations in continuous and discrete form and the formulation of the Jacobian or tangent matrix used in the Newton–Raphson solution of the resulting finite set of nonlinear algebraic equations 1.2 SIMPLE EXAMPLES OF NONLINEAR STRUCTURAL BEHAVIOR It is often the case that nonlinear behavior concurs with one’s... response to working load Currently analysis is most likely to involve a computer simulation of the behavior Because of the availability of commercial finite element computer software, the opportunity for such nonlinear analysis is becoming increasingly realized Such a situation has an immediate educational implication because, for computer programs to be used sensibly and for the results to be interpreted... the deformation is sufficiently small to enable the effect of changes in the geometrical configuration of the solid to be ignored, whereas in the nonlinear case the magnitude of the deformation is unrestricted Practical stress analysis of solids and structures is unlikely to be served by classical methods, and currently numerical analysis, predominately in the 1 2 INTRODUCTION form of the finite element. .. with the fundamentals of nonlinear continuum mechanics, nonlinear finite element formulations, and the solution techniques employed by the software This book seeks to address this problem by providing a unified introduction to these three topics The style and content of the book obviously reflect the attributes and abilities of the authors Both authors have lectured on this material for a number of years... course containing some additional emphasis on maths and numerical analysis A familiarity with statics and elementary stress analysis is assumed, as is some exposure to the principles of the finite element method However, a primary objective of the book is that it be reasonably self-contained, particularly with respect to the nonlinear continuum mechanics chapters, which comprise a large portion of the content . Cataloging-in-Publication Data Bonet, Javier, 1961– Nonlinear continuum mechanics for finite element analysis / Javier Bonet, Richard D. Wood. p. cm.ISBN 0-5 2 1-5 7272-X1 computer program for the nonlinear finite deformationfinite element analysis of two- and three-dimensional solids. Such a pro-gram provides the basis for a contemporary
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