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Nonlinear Solid Mechanics for Finite Element Analysis: Statics [Kietas viršelis]

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(Swansea University), (Swansea University), (Swansea University)
  • Formatas: Hardback, 350 pages, aukštis x plotis x storis: 252x180x23 mm, weight: 760 g, Worked examples or Exercises; 40 Halftones, black and white; 45 Line drawings, black and white
  • Išleidimo metai: 23-Jun-2016
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107115795
  • ISBN-13: 9781107115798
Kitos knygos pagal šią temą:
Nonlinear Solid Mechanics for Finite Element Analysis: StaticsDidesnis paveikslėlis
  • Formatas: Hardback, 350 pages, aukštis x plotis x storis: 252x180x23 mm, weight: 760 g, Worked examples or Exercises; 40 Halftones, black and white; 45 Line drawings, black and white
  • Išleidimo metai: 23-Jun-2016
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107115795
  • ISBN-13: 9781107115798
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781107115798.html
Raktažodžiai:
Designing engineering components that make optimal use of materials requires consideration of the nonlinear static and dynamic characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, which requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both the nonlinear solid mechanics and the associated finite element techniques together, the authors provide, in the first of two books in this series, a complete, clear, and unified treatment of the static aspects of nonlinear solid mechanics. Alongside a range of worked examples and exercises are user instructions, program descriptions, and examples for the FLagSHyP MATLAB computer implementation, for which the source code is available online. While this book is designed to complement postgraduate courses, it is also relevant to those in industry requiring an appreciation of the way their computer simulation programs work.

This book provides a clear and complete postgraduate introduction to the theory and computer programming for the complex simulation of material behavior. It will also appeal to those in industry wishing to appreciate the way their computer simulations work.

Daugiau informacijos

A clear and complete postgraduate introduction to the theory and computer programming for the complex simulation of material behavior.
Preface xiii
1 Introduction 1(20)
1.1 Nonlinear Computational Mechanics
1(1)
1.2 Simple Examples Of Nonlinear Structural Behavior
2(2)
1.2.1 Cantilever
2(1)
1.2.2 Column
3(1)
1.3 Nonlinear Strain Measures
4(8)
1.3.1 One-Dimensional Strain Measures
4(2)
1.3.2 Nonlinear Truss Example
6(4)
1.3.3 Continuum Strain Measures
10(2)
1.4 Directional Derivative, Linearization And Equation Solution
12(7)
1.4.1 Directional Derivative
13(2)
1.4.2 Linearization And Solution Of Nonlinear Algebraic Equations
15(4)
Exercises
19(2)
2 Mathematical Preliminaries 21(38)
2.1 Introduction
21(1)
2.2 Vector And Tensor Algebra
21(24)
2.2.1 Vectors
22(4)
2.2.2 Second-Order Tensors
26(9)
2.2.3 Vector And Tensor Invariants
35(4)
2.2.4 Higher-Order Tensors
39(6)
2.3 Linearization And The Directional Derivative
45(9)
2.3.1 One Degree Of Freedom
45(1)
2.3.2 General Solution To A Nonlinear Problem
46(2)
2.3.3 Properties Of The Directional Derivative
48(1)
2.3.4 Examples Of Linearization
49(5)
2.4 Tensor Analysis
54(3)
2.4.1 The Gradient And Divergence Operators
54(2)
2.4.2 Integration Theorems
56(1)
Exercises
57(2)
3 Analysis Of Three-Dimensional Truss Structures 59(37)
3.1 Introduction
59(2)
3.2 Kinematics
61(3)
3.2.1 Linearization Of Geometrical Descriptors
63(1)
3.3 Internal Forces And Hyperelastic Constitutive Equations
64(2)
3.4 Nonlinear Equilibrium Equations And The Newton-Raphson Solution
66(5)
3.4.1 Equilibrium Equations
66(1)
3.4.2 Newton-Raphson Procedure
67(1)
3.4.3 Tangent Elastic Stiffness Matrix
68(3)
3.5 Total Potential Energy
71(4)
3.5.1 Principle Of Virtual Work
72(3)
3.6 Elasto-Plastic Behavior
75(14)
3.6.1 Multiplicative Decomposition Of The Stretch
76(1)
3.6.2 Rate-Independent Plasticity
77(4)
3.6.3 Incremental Kinematics
81(2)
3.6.4 Time Integration
83(1)
3.6.5 Stress Update And Return Mapping
84(3)
3.6.6 Algorithmic Tangent Modulus
87(1)
3.6.7 Revised Newton-Raphson Procedure
88(1)
3.7 Examples
89(2)
3.7.1 Inclined Axial Rod
89(1)
3.7.2 Trussed Frame
90(1)
Exercises
91(5)
4 Kinematics 96(41)
4.1 Introduction
96(1)
4.2 The Motion
96(1)
4.3 Material And Spatial Descriptions
97(2)
4.4 Deformation Gradient
99(3)
4.5 Strain
102(4)
4.6 Polar Decomposition
106(6)
4.7 Volume Change
112(1)
4.8 Distortional Component Of The Deformation Gradient
113(3)
4.9 Area Change
116(1)
4.10 Linearized Kinematics
117(2)
4.10.1 Linearized Deformation Gradient
117(1)
4.10.2 Linearized Strain
118(1)
4.10.3 Linearized Volume Change
119(1)
4.11 Velocity And Material Time Derivatives
119(4)
4.11.1 Velocity
119(1)
4.11.2 Material Time Derivative
120(1)
4.11.3 Directional Derivative And Time Rates
121(1)
4.11.4 Velocity Gradient
122(1)
4.12 Rate Of Deformation
123(3)
4.13 Spin Tensor
126(3)
4.14 Rate Of Change Of Volume
129(1)
4.15 Superimposed Rigid Body Motions And Objectivity
130(2)
Exercises
132(5)
5 Stress And Equilibrium 137(21)
5.1 Introduction
137(1)
5.2 Cauchy Stress Tensor
137(5)
5.2.1 Definition
137(4)
5.2.2 Stress Objectivity
141(1)
5.3 Equilibrium
142(3)
5.3.1 Translational Equilibrium
142(2)
5.3.2 Rotational Equilibrium
144(1)
5.4 Principle Of Virtual Work
145(1)
5.5 Work Conjugacy And Alternative Stress Representations
146(8)
5.5.1 The Kirchhoff Stress Tensor
146(1)
5.5.2 The First Piola-Kirchhoff Stress Tensor
147(3)
5.5.3 The Second Piola-Kirchhoff Stress Tensor
150(3)
5.5.4 Deviatoric And Pressure Components
153(1)
5.6 Stress Rates
154(2)
Exercises
156(2)
6 Hyperelasticity 158(30)
6.1 Introduction
158(1)
6.2 Hyperelasticity
158(2)
6.3 Elasticity Tensor
160(2)
6.3.1 The Material Or Lagrangian Elasticity Tensor
160(1)
6.3.2 The Spatial Or Eulerian Elasticity Tensor
161(1)
6.4 Isotropic Hyperelasticity
162(6)
6.4.1 Material Description
162(1)
6.4.2 Spatial Description
163(2)
6.4.3 Compressible Neo-Hookean Material
165(3)
6.5 Incompressible And Nearly Incompressible Materials
168(7)
6.5.1 Incompressible Elasticity
168(2)
6.5.2 Incompressible Neo-Hookean Material
170(2)
6.5.3 Nearly Incompressible Hyperelastic Materials
172(3)
6.6 Isotropic Elasticity In Principal Directions
175(11)
6.6.1 Material Description
175(1)
6.6.2 Spatial Description
176(1)
6.6.3 Material Elasticity Tensor
177(2)
6.6.4 Spatial Elasticity Tensor
179(1)
6.6.5 A Simple Stretch-Based Hyperelastic Material
180(1)
6.6.6 Nearly Incompressible Material In Principal Directions
181(3)
6.6.7 Plane Strain And Plane Stress Cases
184(1)
6.6.8 Uniaxial Rod Case
185(1)
Exercises
186(2)
7 Large Elasto-Plastic Deformations 188(26)
7.1 Introduction
188(1)
7.2 The Multiplicative Decomposition
188(5)
7.3 Rate Kinematics
193(4)
7.4 Rate-Independent Plasticity
197(2)
7.5 Principal Directions
199(4)
7.6 Incremental Kinematics
203(6)
7.6.1 The Radial Return Mapping
206(2)
7.6.2 Algorithmic Tangent Modulus
208(1)
7.7 Two-Dimensional Cases
209(3)
Exercises
212(2)
8 Linearized Equilibrium Equations 214(20)
8.1 Introduction
214(1)
8.2 Linearization And The Newton-Raphson Process
214(2)
8.3 Lagrangian Linearized Internal Virtual Work
216(1)
8.4 Eulerian Linearized Internal Virtual Work
217(2)
8.5 Linearized External Virtual Work
219(2)
8.5.1 Body Forces
219(1)
8.5.2 Surface Forces
219(2)
8.6 Variational Methods And Incompressibility
221(11)
8.6.1 Total Potential Energy And Equilibrium
222(1)
8.6.2 Lagrange Multiplier Approach To Incompressibility
223(3)
8.6.3 Penalty Methods For Incompressibility
226(1)
8.6.4 Hu-Washizu Variational Principle For Incompressibility
227(2)
8.6.5 Mean Dilatation Procedure
229(3)
Exercises
232(2)
9 Discretization And Solution 234(26)
9.1 Introduction
234(1)
9.2 Discretized Kinematics
234(5)
9.3 Discretized Equilibrium Equations
239(3)
9.3.1 General Derivation
239(2)
9.3.2 Derivation In Matrix Notation
241(1)
9.4 Discretization Of The Linearized Equilibrium Equations
242(9)
9.4.1 Constitutive Component: Indicial Form
244(1)
9.4.2 Constitutive Component: Matrix Form
245(1)
9.4.3 Initial Stress Component
246(1)
9.4.4 External Force Component
247(2)
9.4.5 Tangent Matrix
249(2)
9.5 Mean Dilatation Method For Incompressibility
251(2)
9.5.1 Implementation Of The Mean Dilatation Method
251(2)
9.6 Newton-Raphson Iteration And Solution Procedure
253(5)
9.6.1 Newton-Raphson Solution Algorithm
253(1)
9.6.2 Line Search Method
254(2)
9.6.3 Arc Length Method
256(2)
Exercises
258(2)
10 Computer Implementation 260(56)
10.1 Introduction
260(3)
10.2 User Instructions
263(6)
10.3 Output File Description
269(3)
10.4 Element Types
272(2)
10.5 Solver Details
274(2)
10.6 Program Structure
276(2)
10.7 Master M-File Flagshyp
278(7)
10.8 Function residual_and_stiffness_assembly
285(9)
10.9 Function constitutive_matrix
294(1)
10.10 Function geometric_matrix
295(1)
10.11 Function pressure_load_and_stiffness_assembly
296(2)
10.12 Examples
298(8)
10.12.1 Simple Patch Test
298(1)
10.12.2 Nonlinear Truss
299(1)
10.12.3 Strip With A Hole
300(1)
10.12.4 Plane Strain Nearly Incompressible Strip
300(2)
10.12.5 Twisting Column
302(1)
10.12.6 Elasto-Plastic Cantilever
303(3)
10.13 Appendix: Dictionary Of Main Variables
306(3)
10.14 Appendix: Constitutive Equation Summary
309(7)
Bibliography 316(2)
Index 318
Javier Bonet is a Professor of Engineering and Head of the College of Engineering at Swansea University, Director of the Welsh 'Sźr Cymru' National Research Network in Advanced Engineering and Materials, 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, with contributions in modeling superplastic forming, large strain dynamic analysis, membrane modeling, and finite element technology, including error estimation and meshless methods (smooth particle hydrodynamics). Since the book was completed, he has been appointed as Deputy Vice-Chancellor, Research and Enterprise, at the University of Greenwich. Antonio J. Gil is an Associate Professor in the Zienkiewicz Centre for Computational Engineering at Swansea University. He has numerous publications in various areas of computational mechanics with specific experience in the field of large strain nonlinear mechanics. His work covers the areas of computational simulation of nanomembranes, biomembranes (heart valves) and superplastic forming of medical prostheses, fluid-structure interaction, modeling of smart electro-magneto-mechanical devices, and numerical analysis of fast transient dynamical phenomena. He has received a number of prizes for his contributions to the field of computational mechanics. Richard D. Wood is an Honorary Research Fellow in the Zienkiewicz Centre for Computational Engineering 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. Wood's academic career has focused on finite element analysis. He has written numerous papers in international journals, and many chapter contributions, on topics related to nonlinear finite element analysis.