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Numerical Methods in Mechanics of Materials: With Applications from Nano to Macro Scales [Kõva köide]

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  • Formaat: Hardback, 340 pages, kõrgus x laius: 254x178 mm, kaal: 800 g, 10 Tables, black and white; 78 Line drawings, black and white
  • Ilmumisaeg: 04-Dec-2017
  • Kirjastus: CRC Press
  • ISBN-10: 1138719161
  • ISBN-13: 9781138719163
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Numerical Methods in Mechanics of Materials: With Applications from Nano to Macro ScalesSuurem pilt
  • Formaat: Hardback, 340 pages, kõrgus x laius: 254x178 mm, kaal: 800 g, 10 Tables, black and white; 78 Line drawings, black and white
  • Ilmumisaeg: 04-Dec-2017
  • Kirjastus: CRC Press
  • ISBN-10: 1138719161
  • ISBN-13: 9781138719163
Teised raamatud teemal:
Teised raamatud sellest sooduspakkumisest: Taylor & Francis teadusraamatud International Student Editions hindadega
Püsilink: https://www.kriso.ee/db/9781138719163.html
Märksõnad:

In the dynamic digital age, the widespread use of computers has transformed engineering and science. A realistic and successful solution of an engineering problem usually begins with an accurate physical model of the problem and a proper understanding of the assumptions employed. With computers and appropriate software we can model and analyze complex physical systems and problems.

However, efficient and accurate use of numerical results obtained from computer programs requires considerable background and advanced working knowledge to avoid blunders and the blind acceptance of computer results. This book provides the background and knowledge necessary to avoid these pitfalls, especially the most commonly used numerical methods employed in the solution of physical problems. It offers an in-depth presentation of the numerical methods for scales from nano to macro in nine self-contained chapters with extensive problems and up-to-date references, covering:

  • Trends and new developments in simulation and computation
  • Weighted residuals methods
  • Finite difference methods
  • Finite element methods
  • Finite strip/layer/prism methods
  • Boundary element methods
  • Meshless methods
  • Molecular dynamics
  • Multiphysics problems
  • Multiscale methods

Arvustused

"The book includes detailed descriptions of trending materials modeling methods such as concurrent multiscale methods and molecular dynamics methods. The authors explain well how these methods can be used to model materials at very fine scales and improve predictions compared to conventional approaches. The description contains enough numerical implementation details to allow students, engineers and researchers interested in high fidelity materials modeling to try the methods presented in the book."

-- Wing Kam Liu, Northwestern University, USA

"This is a one-of-a-kind book and good for numerical methods to solve problems in mechanics of materials, from the nanoscale to the macroscale."

-- Shaofan Li, University of California, Berkeley, USA

"The book would be of greatest use for practicing engineers or graduate students in mechanical engineering, applied mechanics, applied physics, materials science, and related fields."

--J. Lambropoulos, University of Rochester in Choice Connect

Preface xi
Authors xiii
1 The role of numerical methods in engineering
1(10)
1.1 Introduction
1(2)
1.2 Fields of application
3(1)
1.3 Future progress and trends
3(8)
References
5(3)
Bibliography
8(3)
2 Numerical analysis and weighted residuals
11(26)
2.1 Introduction
11(1)
2.2 Approximation problem (Trial functions; Norms or measures of error)
12(1)
2.3 Method of weighted residuals (Ordinary differential equations)
13(6)
2.3.1 Preliminary remarks
13(1)
2.3.2 Method of weighted residuals
14(3)
2.3.3 Boundary methods
17(1)
2.3.4 Convergence theorems
17(2)
2.4 Method of weighted residuals (Partial differential equations)
19(4)
2.4.1 Collocation method
21(1)
2.4.2 Galerkin method
22(1)
2.5 Variation method (Rayleigh--Ritz method)
23(5)
2.5.1 Approximation techniques based on variational methods
25(3)
2.6 Ritz method revisited and Trefftz method
28(9)
2.6.1 Ritz method applied to a rectangular cross-section
29(1)
2.6.2 First approximation
30(2)
2.6.3 Second approximation
32(1)
2.6.4 Trefftz method applied to a rectangular cross-section
32(2)
2.6.5 Bounds on torsion solution
34(1)
References
35(1)
Bibliography
36(1)
3 Finite difference methods
37(36)
3.1 Preliminary remarks and concepts
37(1)
3.1.1 Finite differences, finite elements, and weighted residual methods
38(1)
3.2 Divided differences and interpolation formulas
38(10)
3.2.1 Newton's forward and backward interpolation polynomials
44(1)
3.2.2 Newton--Gauss interpolation polynomial
45(2)
3.2.3 Stirling's central interpretation polynomial
47(1)
3.3 Approximate expressions for derivatives
48(6)
3.4 Two-dimensional harmonic equation, biharmonic equation, and curved boundaries
54(6)
3.4.1 Harmonic equation
57(1)
3.4.2 Biharmonic equation
57(1)
3.4.3 Curved boundaries
58(2)
3.5 Finite difference approximation of the plane stress problem
60(4)
3.6 Torsion problem
64(9)
3.6.1 Square cross-section
65(1)
3.6.2 Bar with elliptical cross-section
66(3)
Appendix 3A Derivation of Equation 3.16
69(1)
Appendix 3B Derivation of Equation 3.38
70(1)
References
71(1)
Bibliography
71(2)
4 The finite element method
73(64)
4.1 Introduction
73(2)
4.1.1 Analytical perspective
73(1)
4.1.2 Sources of error
74(1)
4.2 Formulation for plane elasticity
75(19)
4.2.1 Elasticity concepts
75(3)
4.2.2 Displacement interpolation: Constant-strain triangle
78(3)
4.2.3 Element stiffness matrix: CST
81(3)
4.2.4 Equivalent nodal load vector: CST
84(3)
4.2.5 Assembly of the structure stiffness matrix and load vector
87(3)
4.2.6 Application of constraints
90(3)
4.2.7 Solution of the system of equations
93(1)
4.3 Bilinear rectangle
94(7)
4.4 Linear isoparametric quadrilateral
101(7)
4.4.1 Isoparametric mapping
102(2)
4.4.2 Element stiffness matrix
104(1)
4.4.3 Numerical integration
105(2)
4.4.4 High-order isoparametric elements
107(1)
4.5 Plane frame element
108(9)
4.5.1 Element stiffness matrix
108(5)
4.5.2 Equivalent nodal load vector
113(1)
4.5.3 Coordinate rotations
114(3)
4.6 Generalizations
117(11)
4.6.1 Three-dimensional isoparametric elements
117(1)
4.6.2 Equilibrium equation
118(3)
4.6.3 Viscoelastic solid
121(1)
4.6.4 Nonlocal elasticity
121(2)
4.6.5 Plasticity
123(4)
4.6.6 Finite strain theory
127(1)
4.7 Closing remarks
128(4)
4.7.1 Requirements for accuracy
128(1)
4.7.2 Requirements for convergence
129(1)
4.7.3 Modeling recommendations
130(2)
4.8 Problems
132(5)
4.8.1 Section 4.2
132(1)
4.8.2 Section 4.4
133(1)
4.8.3 Section 4.5
134(1)
References
135(1)
Bibliography
135(2)
5 Specialized methods
137(20)
5.1 Introduction
137(1)
5.2 Finite strip method
137(3)
5.3 Formulation of the FSM
140(3)
5.4 Example of the FSM
143(1)
5.5 Finite layer method
144(3)
5.6 Finite prism method
147(2)
5.7 Applications and developments of FSM, FLM, and FPM
149(8)
References
152(2)
Bibliography
154(3)
6 The boundary element method
157(34)
6.1 Introduction
157(2)
6.2 Integrals in the boundary element method
159(2)
6.3 Equations of elasticity
161(1)
6.4 Fundamental or Kelvin's solution
162(2)
6.5 Boundary element formulation
164(3)
6.6 Displacement and traction interpolation
167(3)
6.7 Element contributions
170(2)
6.8 Assembly of boundary element matrices
172(2)
6.9 Rigid-body motion
174(1)
6.10 Solution of boundary element equations
175(1)
6.11 Displacement at points in the interior
176(1)
6.12 Body forces
177(1)
6.13 Particular integral approach
177(2)
6.14 Evaluation of stresses and strains
179(3)
6.15 Corner problem in the boundary element method
182(3)
6.16 Closing remarks
185(6)
References
186(3)
Bibliography
189(2)
7 Meshless methods of analysis
191(34)
7.1 Introduction
191(1)
7.2 Equations of elasticity
192(1)
7.3 Weak forms of the governing equations
192(2)
7.4 Moving least squares approximations
194(5)
7.5 Characteristics of MLS approximation
199(1)
7.6 MLS weight functions
200(2)
7.7 Discrete EFG formulation
202(7)
7.8 Numerical implementation
209(2)
7.9 Treatment of boundary conditions
211(4)
7.10 Other methods for meshless analysis
215(2)
7.11 Generalizations
217(3)
7.11.1 Dynamic problems
218(1)
7.11.2 Heun's method
219(1)
7.12 Closing remarks
220(5)
References
221(3)
Bibliography
224(1)
8 Multiphysics in molecular dynamics simulation
225(40)
James D. Lee
Jiaoyan Li
Zhen Zhang
Kerlin P. Robert
8.1 Introduction
225(1)
8.2 Governing equations
226(2)
8.3 Interatomic potentials for ionic crystals
228(3)
8.3.1 Lennard--Jones potential
229(1)
8.3.2 Coulomb--Buckingham potential
229(2)
8.4 Interatomic potentials for 2D materials
231(7)
8.4.1 Graphene
231(1)
8.4.2 Tersoff potential
232(3)
8.4.3 Molybdenum disulfide
235(1)
8.4.3.1 Interatomic potentials for Mo--S systems
235(3)
8.5 Objectivity in MD
238(3)
8.6 Reformulation of Nose--Hoover thermostat
241(6)
8.6.1 Hamiltonian of the material system
245(2)
8.7 Microscopic Maxwell's equations and Lorentz force
247(4)
8.7.1 Microscopic Maxwell's equations
247(1)
8.7.2 Scalar and vector potentials
248(1)
8.7.3 Nonrelativistic EM fields
249(1)
8.7.4 Equation of motion of a point particle
250(1)
8.8 Heun's method
251(3)
8.9 Numerical results of a sample problem
254(2)
8.10 Closing remarks
256(9)
Appendix: Lorentz transformation
256(4)
References
260(3)
Bibliography
263(2)
9 Multiscale modeling from atoms to genuine continuum
265(38)
James D. Lee
Jiaoyan Li
Zhen Zhang
Kerlin P. Robert
9.1 Introduction
265(1)
9.2 Force-based CGMD
266(3)
9.3 Stiffness-based CGMD
269(5)
9.3.1 General dynamical matrix
271(3)
9.4 From AAMD to CGMD
274(5)
9.4.1 Nose--Hoover thermostat in the ABC region
274(3)
9.4.2 Hamiltonian of AAMD CGMD
277(2)
9.5 Sequential multiscale modeling from MD to thermoelasticity
279(7)
9.5.1 Thermoelasticity and sequential multiscale modeling
279(2)
9.5.2 Material constants from MD simulation
281(1)
9.5.2.1 Elastic constants
282(2)
9.5.2.2 Thermal conductivity
284(1)
9.5.2.3 Specific heat and thermal expansion coefficients
285(1)
9.6 Concurrent multiscale modeling from MD to CM
286(12)
9.6.1 One specimen, two regions
286(2)
9.6.2 Inter facial conditions
288(1)
9.6.3 Multiple time scale algorithm
289(3)
9.6.4 Sample problems and numerical results
292(1)
9.6.4.1 Material constants obtained from MD simulations
292(1)
9.6.4.2 Case studies
293(5)
9.7 Closing remarks
298(5)
References
300(1)
Bibliography
301(2)
Author Index 303(8)
Subject Index 311
Ken P. Chong was the former Interim Division Director, Engineering Advisor, and Program Director of Structural Systems, Mechanics and Materials at the National Science Foundation (NSF), 1989 - 2009. Currently he is a Research Professor at George Washington University. He earned a Ph.D. in Engineering Mechanics from Princeton University in 1969. He specializes in solid mechanics and materials, computational mechanics, nano-mechanics, smart structures and structural mechanics. He has been the principal investigator of over 20 federally funded research projects (from NSF, DOD, DOE, DOI, etc). He was a senior research engineer with the National Steel Corp. for 5 years after graduation from Princeton. After that he was a professor for 15 years at a state university. He has published 200 technical papers, authored 4 textbooks on engineering mechanics including Elasticity in Engineering Mechanics; Approximate Solution Methods in Engineering Mechanics, and edited 10 books including University Programs in Computer-Aided Engineering, Design, and Manufacturing; Materials for the New Millennium; Modeling and Simulation-based Life-cycle Engineering. He was the editor of the Elsevier Journal of Thin-Walled Structures, 1987-2013. He is co-editor of the UK Journal of Smart and Nano Materials, a CRC/Spon book series on structures as well as serving on several editorial boards. He has given over 50 keynote lectures at major conferences, the Mindlin, Sadowsky and Raouf Lectures, received awards including the fellow of ASME, American Academy of Mechanics, SEM, and United States Association for Computational Mechanics; Edmund Friedman Professional Recognition Award; Honorary Doctorate, Shanghai University; Honorary Professor, Harbin Institute of Technology; NCKU Distinguished Alumnus, Distinguished Member, ASCE; NSF highest Distinguished Service Award, AWU-DOE Outstanding Academic and Professional Achievement Award, and the ASME Belytschko Mechanics Award. He was the ASME Thurston Lecturer for 2014.









Arthur P. Boresi: Professor Emeritus in the Mechanical Science and Engineering Department at the University of Illinois at Urbana-Champaign, where he taught for more than 20 years, and later as the Head of the Department of Civil and Architectural Engineering at the University of Wyoming in Laramie. He is currently Professor Emeritus in the Civil and Architectural Engineering Department of the University of Wyoming. He has published over 200 refereed papers and several books including Elasticity in Engineering Mechanics, Advanced Mechanics of Materials, Engineering Statics and Engineering Dynamics. He had chaired and organized national conferences for ASCE and other societies. He is a fellow of AAM, ASME and ASCE.









Sunil Saigal: Ph.D.(Purdue), PE is a Distinguished Professor in the Department of Civil and Environmental Engineering and former Dean of Engineering at New Jersey Institute of Technology as well as a former NSF Program Director. His research in the area of computational mechanics has spanned numerous sub-disciplines and industrial applications. Much of his research has been focused on interactions with the industry and these contributions have included: development of boundary element shape optimization in collaboration with United Technologies; formulations for powder packing in collaboration with Alcoa and DuPont; development of computational models for nonlinear soil behavior in collaboration with ANSYS; cohesive element formulations for post crack behavior of glass-polymer composites in collaboration with DuPont; explicit algorithms for high velocity impact in collaboration with Naval Surface Warfare Center; computational simulations of acetabular hip component in collaboration with University of Pittsburgh Medical Center. These interdisciplinary efforts involved diverse elds ranging from anatomy to computer science to materials and solid mechanics. Recognition of his work has occurred through awards/honors including: Leighton and Margaret Orr Award for Best Paper, ASME, 2004; George Tallman Ladd Research Award, Carnegie Mellon University, 1990; Presidential Young Investigator Award, NSF, 1990; Ralph R. Teetor Award, Society of Automotive Engineers, 1988. He is the co-author of ve books on engineering mechanics and holds a patent for a method of manufacturing hot rolled I-beams. He is the author of over 100 peer-reviewed articles in archival journals. He has served on the editorial boards of several journals including International Journal for Numerical Methods in Engineering, Engineering with Computers, and International Journal for Computational Civil and Structural Engineering. He is a fellow of numerous societies including, ASCE, ASME and AAAS.









James D. Lee: Professor of Engineering and Applied Science in the Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC. He was an Associate Professor at West Virginia University and University of Minnesota. He worked at General Tire and Rubber Company for one year, National Institute of Standard and Technology for four years, NASA/Goddard Space Flight Center for one year. He earned a Ph.D. degree from Department of Mechanical and Aerospace Engineering, Princeton University in 1971. He has been doing research in many fields, including Nano Science, Multiscale Modeling, Mechanobiology, Microcontinuum Physics, Continuum Mechanics, Fracture Mechanics, Finite Element Method, Meshless Method, Optimal Control Theory, and Robotics, etc. He has been the principal investigator of federally funded research projects from NASA, NSF and DOT. He has published 120 journal papers, 20 book chapters, 2 textbooks "Meshless Methods in Solid Mechanics" and "Elasticity in Engineering Mechanics", and numerous conference papers and presentations. He has received the Distinguished Researcher Award from the School of Engineering and Applied Science, The George Washington University. He is the Fellow of ASME and Honorary Fellow of Australian Institute of High Energetic Materials.