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

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(Swansea University), (Swansea University), (University of Greenwich)
  • Formatas: Hardback, 348 pages, aukštis x plotis x storis: 253x177x24 mm, weight: 760 g, Worked examples or Exercises; 1 Tables, black and white; 32 Halftones, black and white; 44 Line drawings, black and white
  • Išleidimo metai: 18-Mar-2021
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107115620
  • ISBN-13: 9781107115620
Kitos knygos pagal šią temą:
Nonlinear Solid Mechanics for Finite Element Analysis: DynamicsDidesnis paveikslėlis
  • Formatas: Hardback, 348 pages, aukštis x plotis x storis: 253x177x24 mm, weight: 760 g, Worked examples or Exercises; 1 Tables, black and white; 32 Halftones, black and white; 44 Line drawings, black and white
  • Išleidimo metai: 18-Mar-2021
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107115620
  • ISBN-13: 9781107115620
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781107115620.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 nonlinear solid mechanics, dynamic conservation laws and principles, and the associated finite element techniques together, the authors provide in this second book a unified treatment of the dynamic simulation of nonlinear solids. Alongside a number of worked examples and exercises are user instructions, program descriptions, and examples for two MATLAB computer implementations for which source codes are 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.

Recenzijos

' the software can be useful to readers in testing different options of the codes, building their own simple examples, and acquiring some additional experience and knowledge about continuum mechanics and numerical methods for their simulations.' Josip Tambaca, Society for Industrial and Applied Mathematics Review

Daugiau informacijos

The perfect introduction to the theory and computer programming for the dynamic simulation of nonlinear solid mechanics.
Preface xiii
1 Introduction
1(26)
1.1 Nonlinear Solid Dynamics
1(2)
1.2 One-Degree-of-Freedom Nonlinear Dynamic Behavior
3(4)
1.2.1 Equation of Motion
4(1)
1.2.2 Leap-Frog Time Integration
4(3)
1.2.3 Column Examples
7(1)
1.3 Two-Degrees-Of-Freedom Example
7(20)
1.3.1 Equations of Motion
9(1)
1.3.2 Leap-Frog Examples
10(1)
1.3.3 Time Integration - Stability
11(3)
1.3.4 Mid-Point Rule
14(4)
1.3.5 Tangent Stiffness Matrix
18(2)
1.3.6 Mid-Point Rule Examples
20(3)
Exercises
23(4)
2 Dynamic Analysis of Three-Dimensional Trusses
27(58)
2.1 Introduction
27(1)
2.2 Dynamic Equilibrium
28(5)
2.2.1 Truss Member -- Kinematics
28(1)
2.2.2 Truss Member -- Forces
29(2)
2.2.3 Dynamic Equilibrium of a Pin-Jointed Truss
31(2)
2.3 Dynamic Variational Principles
33(6)
2.3.1 Kinetic Energy, Potential Energy, and the Lagrangian
33(2)
2.3.2 Lagrange Equations
35(2)
2.3.3 Action Integral and Hamilton's Principle
37(2)
2.4 Time Integration Schemes
39(14)
2.4.1 Discrete Action Integral
40(1)
2.4.2 Leap-Frog Time Integration
41(2)
2.4.3 Mid-Point Time Integration
43(7)
2.4.4 Trapezoidal Time Integration
50(3)
2.5 Global Conservation Laws
53(10)
2.5.1 Conservation of Linear Momentum
54(2)
2.5.2 Conservation of Angular Momentum
56(3)
2.5.3 Conservation of Energy
59(4)
2.6 Hamiltonian Formulations
63(16)
2.6.1 Momentum Variables and the Hamiltonian
64(2)
2.6.2 Phase Space and Hamiltonian Maps
66(3)
2.6.3 The Simplectic Product
69(3)
2.6.4 Discrete Hamiltonian Maps and Simplectic Time Integrators
72(7)
2.7 Examples
79(6)
2.7.1 Swinging Rope
79(2)
2.7.2 L-Shaped Truss
81(2)
Exercises
83(2)
3 Dynamic Equilibrium of Deformable Solids
85(25)
3.1 Introduction
85(1)
3.2 Dynamic Equilibrium
86(7)
3.2.1 Motion, Velocity, and Acceleration
86(1)
3.2.2 External Forces, Inertial Forces, and Global Dynamic Equilibrium in Current and Reference Configurations
87(2)
3.2.3 Local Dynamic Equilibrium
89(4)
3.3 Principle Of Virtual Work And Conservation Of Global Variables
93(9)
3.3.1 Principle of Virtual Work in the Current Configuration
94(1)
3.3.2 Principle of Virtual Work in the Reference Configuration
95(1)
3.3.3 Conservation of Global Momentum Quantities
96(3)
3.3.4 Conservation of Energy
99(3)
3.4 The Action Integral And Hamilton's Principle
102(8)
3.4.1 The Lagrangian
103(1)
3.4.2 The Action Integral and Hamilton's Principle
103(5)
Exercises
108(2)
4 Discretization and Solution
110(47)
4.1 Introduction
110(1)
4.2 Discretized Kinematics
110(3)
4.3 Mass Matrix
113(5)
4.3.1 Lumped Mass Matrix
117(1)
4.4 Discretized Dynamic Equilibrium Equations
118(3)
4.5 Kinetic Energy, Potential Energy, and the Lag Rang Ian
121(2)
4.5.1 Kinetic energy
121(1)
4.5.2 Total Energy and the Lagrangian
122(1)
4.6 Newmark Time Integration Scheme
123(11)
4.6.1 Implementation of the Newmark Acceleration Corrector Method
127(3)
4.6.2 Alpha-Method Time Integration
130(4)
4.7 Variational Integrators
134(9)
4.7.1 Leap-Frog Time Integrator
136(4)
4.7.2 Mid-Point Time Integrator
140(3)
4.8 Global Conservation Laws
143(14)
4.8.1 Conservation of Linear Momentum
144(2)
4.8.2 Conservation of Angular Momentum
146(5)
4.8.3 Conservation of Total Energy
151(4)
Exercises
155(2)
5 Conservation Laws in Solid Dynamics
157(22)
5.1 Introduction
157(1)
5.2 The General Form Of A Conservation Law
158(4)
5.3 Total Lagrangian Conservation Laws In Solid Dynamics
162(6)
5.3.1 Conservation of Mass
164(1)
5.3.2 Conservation of Linear Momentum
164(1)
5.3.3 Conservation of Energy
165(2)
5.3.4 Geometric Conservation Law
167(1)
5.3.5 Summary of the Total Lagrangian Conservation Laws
168(1)
5.4 Updated Lagrangian and Eulerian Conservation Laws
168(11)
5.4.1 Updated Lagrangian Conservation Laws
169(2)
5.4.2 Eulerian Conservation Laws
171(3)
5.4.3 Eulerian Conservation of Mass and Momentum
174(2)
Exercises
176(3)
6 Thermodynamics
179(26)
6.1 Introduction
179(1)
6.2 The First Law of Thermodynamics
180(3)
6.2.1 Internal Energy
180(1)
6.2.2 Temperature and Entropy
181(2)
6.3 The Second Law of Thermodynamics
183(4)
6.3.1 Entropy Production in Thermoelasticity
183(1)
6.3.2 Internal Dissipation and the Clausius-Duhem Inequality
184(3)
6.4 Thermoelasticity
187(18)
6.4.1 The Reference Configuration
187(1)
6.4.2 Energy-Temperature-Entropy Relationships
188(3)
6.4.3 Stress Evaluation in Thermoelasticity
191(1)
6.4.4 Isothermal Processes and the Helmholtz Free Energy
192(3)
6.4.5 Entropic Elasticity
195(2)
6.4.6 Perfect Gas
197(1)
6.4.7 Distortional-Volumetric Energy Decomposition
198(3)
6.4.8 Mie--Gruneisen Equation of State
201(1)
Exercises
202(3)
7 Space And Time Discretization Of Conservation Laws In Solid Dynamics
205(41)
7.1 Introduction
205(1)
7.2 A Simple One-Dimensional System Of Conservation Laws
206(16)
7.2.1 Weak Form Equations and Stabilization
209(6)
7.2.2 Spatial Discretization
215(3)
7.2.3 Time Discretization
218(3)
7.2.4 The One-Dimensional Example
221(1)
7.3 A General Isothermal System Of Conservation Laws
222(17)
7.3.1 Three-Dimensional Weak Form Equations and Stabilization
227(3)
7.3.2 Three-Dimensional Spatial Discretization
230(3)
7.3.3 Time Discretization
233(6)
7.4 A General Thermoelastic System Of Conservation Laws
239(7)
7.4.1 Weak Form Equations and Stabilization
241(1)
7.4.2 Three-Dimensional Spatial Discretization: Entropy
242(2)
Exercises
244(2)
8 Computer Implementation For Displacement-Based Dynamics
246(35)
8.1 Introduction
246(2)
8.2 User Instructions
248(6)
8.3 Solver Details
254(2)
8.4 Program Structure
256(10)
8.5 Examples
266(9)
8.5.1 Two Dimensional Free Oscillating Pulsating Square
266(2)
8.5.2 Two Dimensional Free Oscillating Column
268(3)
8.5.3 Three-Dimensional Free Oscillating Twisting Column
271(2)
8.5.4 Three-Dimensional L-Shape Block
273(2)
8.6 Dictionary Of Main Variables
275(3)
8.7 Constitutive Strain Energy Equation Summary
278(3)
9 Computational Implementation For Conservation-Law-Based Explicit Fast Dynamics
281(25)
9.1 Introduction
281(1)
9.2 User Instructions
282(4)
9.3 Solver Details
286(1)
9.4 Program Structure
287(8)
9.5 Examples
295(9)
9.5.1 Three Dimensional Free Oscillating Bending Column
295(1)
9.5.2 Three-Dimensional Free Oscillating Twisting Column
296(1)
9.5.3 Three-Dimensional L-Shaped Block
297(7)
9.6 Dictionary of Main Variables
304(2)
APPENDIX -- SHOCKS
306(20)
A.1 Introduction
306(1)
A.2 Generic Spatial Jump Condition
307(2)
A.3 Jump Conditions in Total Lagrangian Solid Dynamics
309(2)
A.4 Speed of Propagation Of Volumetric and Shear Shocks
311(3)
A.5 Energy, Temperature, and Entropy Behind the Shock Wave
314(4)
A.6 Constitutive Models Derived from Shock Data
318(3)
A.7 Contact-Impact Conditions
321(5)
Exercises
324(2)
Bibliography 326(3)
Index 329
Javier Bonet is a Professor of Engineering, currently Deputy Vice-chancellor for Research and Enterprise at the University of Greenwich and formerly Head of the College of Engineering at Swansea University. He has extensive experience of teaching topics in structural mechanics and dynamics, 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 30 years with contributions in modeling superplastic forming, large strain solid dynamic analysis, membrane modeling, finite element technology including error estimation and meshless methods (smooth particle hydrodynamics). He has given invited, keynote, and plenary lectures on these topics at numerous international conferences. Antonio J. Gil is a Professor of Engineering 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 computational simulation of nanomembranes, biomembranes (heart valves), and superplastic forming of medical prostheses, 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, including The UK Philip Leverhulme Prize and The O.C. Zienkiewicz Prize awarded by the European Community on Computational Methods in Applied Sciences. 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 Solid Mechanics for Finite Element Analysis at Swansea University, which he originally developed at the University of Arizona. He has also taught at IIT Roorkee, India and the Institute of Structural Engineering at the Technical University in Graz. Dr. Wood's academic career concentrated on finite element analysis, and he has written numerous papers in international journals, and many chapter contributions, on topics related to nonlinear finite element analysis. More recently, his interest has focused on croquet.