كتاب Application of Numerical Methods in Engineering Problems Using MATLAB
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 كتاب Application of Numerical Methods in Engineering Problems Using MATLAB

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أحضرت لكم كتاب
Application of Numerical Methods in Engineering Problems Using MATLAB
M.S.H. Al-Furjan, M. Rabani Bidgoli, R. Kolahchi, A. Farrokhian, and M.R. Bayati  

كتاب Application of Numerical Methods in Engineering Problems Using MATLAB  M_a_o_13
و المحتوى كما يلي :


Contents
Preface to the First Edition .xi
Foreword xiii
About the Authors xv
Acknowledgments xvii
Chapter 1 Basic Theories 1
1.1 Introduction 1
1.2 Strain–Displacement Equations .1
1.3 Beam Theories .4
1.3.1 Introduction 4
1.3.2 Preliminaries 4
1.3.3 Euler–Bernoulli Theory .6
1.3.4 Timoshenko Beam Theory 6
1.3.5 Sinusoidal Shear Deformation Theory 7
1.3.6 Hyperbolic Shear Deformation Beam Theory .7
1.3.7 Exponential Shear Deformation Beam Theory .8
1.4 Plate Theories 8
1.4.1 Classical Theory 8
1.4.2 First-Order Shear Deformation Theory .9
1.4.3 Reddy Theory 10
1.4.4 Sinusoidal Shear Deformation Theory 11
1.5 Shell Theories 12
1.5.1 Classical Shell Theory . 12
1.5.2 FSDT or the Mindlin Theory . 13
1.5.3 Reddy Theory 13
References . 15
Chapter 2 Solution Methods 17
2.1 Analytical Methods 17
2.1.1 Navier Method . 17
2.1.2 Galerkin Method 17
2.2 Numerical Methods for Space Domain . 18
2.2.1 Differential Quadrature Method 18
2.2.2 Harmonic Differential Quadrature Method .20
2.2.3 Discrete Singular Convolution Method .22
2.2.4 Differential Cubature Method .23
2.3 Numerical Methods for Time Domain 24
2.3.1 Newmark Method 24
2.3.2 Poincaré–Lindstedt Method .25
2.3.3 Multiple Scale Method .26
vvi Contents
2.3.4 First-Order Two-Scale Expansion Method 26
2.3.5 Second-Order Three-Time Scale Expansion
Method .27
References .28
Chapter 3 Buckling of Nanoparticle-Reinforced Beams Exposed
to Fire .29
3.1 Introduction 29
3.2 Mathematical Modeling .30
3.2.1 Energy Method 30
3.2.2 Hamilton’s Principle 33
3.3 Mori–Tanaka Rule . 35
3.4 Numerical Results 36
3.4.1 Accuracy of DQM 36
3.4.2 Validation .36
3.4.3 Effect of Different Parameters .37
References . 41
Chapter 4 Dynamic Response of Nanofber-Reinforced Beams
Subjected to Seismic Ground Excitation 43
4.1 Introduction 43
4.2 Mathematical Model 45
4.3 Mori–Tanaka Model .46
4.4 Energy Method 49
4.5 Numerical Results 54
4.5.1 Convergence of HDQM . 55
4.5.2 Validation of Results 55
4.5.3 Effect of an NFRP Layer on the Dynamic
Response 55
4.5.4 Effect of Carbon Nanofbers on the Dynamic
Response 59
4.5.5 Effect of Geometric Parameters of a Beam on
the Dynamic Response 62
4.5.6 Effect of Boundary Conditions on Dynamic
Response 65
References . 67
Chapter 5 Buckling Analysis of Plates Reinforced with Graphene
Platelets 69
5.1 Introduction 69
5.2 Kinematics of Different Theories 70
5.3 Motion Equation 72
5.4 Numerical Result and Discussion 77
References .82Contents vii
Chapter 6 Vibration Analysis of Agglomerated Nanoparticle-Reinforced
Plates
6.1 Introduction
6.2 Mathematical Modeling
6.2.1 Stress–Strain Relations
6.2.2 Energy Method
6.3 Numerical Results and Discussion
6.3.1 Validation
6.3.2 Effects of Different Parameters
References
Chapter 7 Vibration Analysis of Plates with an NFRP Layer 103
7.1 Introduction 103
7.2 Stress–Strain Relations 105
7.3 Energy Method 106
7.4 Numerical Results and Discussion 111
References 115
Chapter 8 Vibration Analysis of Plates Reinforced with Nanoparticles
and a Piezoelectric Layer 119
8.1 Introduction 119
8.2 Constitutive Equations of Piezoelectric Material 121
8.3 Energy Method 123
8.4 Numerical Results and Discussion 127
References 132
Chapter 9 Forced Vibration Analysis of Plates Reinforced with
Nanoparticles 135
9.1 Introduction 135
9.2 Mathematical Modeling 137
9.3 Numerical Results and Discussion 146
9.3.1 Convergence of Numerical Method 146
9.3.2 Validation 146
9.3.3 Effects of Different Parameters 147
References 153
Chapter 10 Seismic Analysis of Plates Reinforced by Nanoparticles 157
10.1 Introduction 157
10.2 Stress–Strain Relations 159
10.3 Numerical Results and Discussion
10.3.1 Convergence of DQM 164
10.3.2 Validation of Results 165viii Contents
10.3.3 Effect of the Magnetic Field 166
10.3.4 Effect of AL2O3 Nanoparticles 166
10.3.5 Effect of Concrete Plate Length 168
10.3.6 Effect of Boundary Conditions on the Dynamic
Response 168
References . 169
Chapter 11 Stress Analysis of Shells Reinforced with Nanoparticles 171
11.1 Introduction 171
11.2 Governing Equations . 172
11.3 Numerical Results and Discussion . 175
References . 180
Chapter 12 Earthquake Response of Submerged Nanocomposite Shells
Conveying Fluid . 181
12.1 Introduction 181
12.2 Mathematical Modeling . 183
12.3 Numerical Results and Discussion . 187
12.3.1 Validation 188
12.3.2 Convergence of the Present Method 188
12.3.3 Effects of Various Parameters . 188
References . 193
Chapter 13 Vibration and Instability Analysis of Shells Reinforced
by Nanoparticles . 197
13.1 Introduction 197
13.2 Formulation 198
13.3 Numerical Results and Discussion .203
13.3.1 DQM Convergence 203
13.3.2 Effects of Different Parameters .204
References .209
Chapter 14 Dynamic Response of Nanocomposite Shells Covered with
a Piezoelectric Layer 213
14.1 Introduction 213
14.2 Geometry of the Problem . 214
14.3 Constitutive Equations . 215
14.3.1 Piezoelectric Layer 215
14.3.2 Nanocomposite Pipe 216
14.4 Energy Method 217
14.5 Hamilton’s Principle 220
14.6 Numerical Results 224Contents ix
14.6.1 Verifcation 224
14.6.2 Convergence of the Numerical Method .226
14.6.3 Effects of Various Parameters .226
References .230
Appendix A: The MATLAB Code for Chapter 4 . 233
Appendix B: The MATLAB Code for Chapter 6 237
Appendix C: The MATLAB Code for Chapter 7 .247
Appendix D: The MATLAB Code for Chapter 8 . 253
Appendix E: The MATLAB Code for Chapter 11 259
Appendix F: The MATLAB Code for Chapter 12 263
Index 277
Index
A
AL
2O3 nanoparticles, 141, 145, 147, 148, 152, 153,
154, 156, 157, 158
analytical methods, 15, 52, 146
B
beam theory, 4, 6, 7, 29, 32, 43
boundary conditions, 16, 17, 22, 23, 24, 31, 32,
41, 51, 57, 62, 76, 92, 109, 120, 135, 136, 139,
141, 144, 149, 153, 154, 155, 156, 157, 158,
162, 163, 164, 168, 171, 177, 179, 186, 193,
194, 201, 205, 244
buckling, 27, 28, 34, 35, 36, 37, 38, 42, 43, 61, 62,
63, 67, 68, 69, 70, 71, 72, 76, 77, 91, 92, 93,
106, 107, 121, 122, 140, 141, 164, 178, 185, 193
classical shell theory, 11
classical theory, 164, 195
constitutive equations, 44, 107, 142, 195
convergence of, 51, 130, 145, 170, 183, 203
D
DCM, 15, 21, 193
DQM, 17, 19, 27, 28, 34, 42, 92, 139, 140, 145,
153, 162, 164, 168, 169, 170, 177, 178, 183
DQM convergence, 183
DSCM, 15, 20, 192, 194
dynamic response, 41, 42, 43, 51, 52, 53, 54, 56,
57, 62, 121, 139, 140, 141, 145, 147, 149, 162,
163, 169, 178, 192, 202, 203
E
earthquake, 42, 43, 49, 51, 121, 140, 141, 144, 145,
162, 163, 164, 167, 168, 170, 178, 192, 193,
194, 198, 201, 202, 211
energy method, 28, 29, 47, 90, 164, 177, 194
Euler-Bernoulli beam theory or model, 1, 6, 43,
77, 93, 107, 122, 141, 163, 164
Eulerian description, 2
exponential shear deformation beam theory, 7
F
fre, 27, 28, 29, 31, 34, 164
frst order shear deformation theory (FSDT), 6,
43, 105, 107, 121, 141, 153, 178
frst-order two-scale expansion method, 23
formulation, 17, 28, 42, 92, 141, 179
G
Galerkin method, 16, 92
geometric parameters, 51, 56
governing equations, 16, 18, 27, 28, 31, 41, 42, 43,
47, 49, 52, 61, 63, 64, 65, 80, 81, 92, 96, 106,
109, 110, 111, 112, 126, 127, 139, 140, 144,
154, 162, 163, 164, 167, 168, 169, 180, 192,
194, 196, 199, 201, 203
H
Hamilton’s principle, 31, 41, 49, 105, 144,
167, 199
HDQM, 15, 18, 19, 41, 43, 51, 120, 123, 141
hyperbolic shear deformation beam theory
(HSDBT), 7, 41
I
instability, 42, 121, 140, 153, 163, 177,
178, 183
L
Lagrangian description, 2
Love’s frst approximation theory, 43
M
magnetic feld, 42, 62, 107, 139, 140, 141, 142,
144, 145, 146, 147, 153, 155, 156
mathematical modelling, 1, 29, 77, 93
Mindlin theory, 11, 107, 192, 194
Mori-Tanaka rule, 27, 33, 41, 42, 43, 44, 75,
77, 78, 90, 93, 94, 105, 107, 108, 120,
122, 123, 140, 141, 152, 154, 162, 163,
164, 177, 178, 192, 194, 196, 209, 213,
223, 228, 233
motion equation, 16, 18, 49, 64, 75, 77, 90, 93,
107, 120, 122, 144, 168, 177, 178
multiple scale method, 23, 24, 201
N
nanocomposite, 42, 43, 62, 63, 91, 106, 107, 140,
141, 162, 164, 168, 177, 178, 183, 192, 193,
194, 196, 197, 204278 Index
nanoparticle, 27, 29, 62, 75, 76, 77, 83, 84, 85, 86,
87, 93, 105, 107, 113, 114, 120, 121, 122, 129,
132, 133, 139, 141, 145, 147, 148, 152, 153,
154, 156, 157, 158, 162, 164, 165, 168, 173,
177, 178, 179, 183, 184, 185
Navier method, 16, 61, 63, 67, 77, 83, 90, 93, 97,
107, 113
Newmark method, 22, 41, 43, 120, 122, 129, 141,
162, 164
NFRP, 41, 43, 44, 47, 51, 53, 54, 90, 93, 94, 97,
98, 99, 100, 101
numerical methods for space domain, 15, 17
numerical methods for time domain, 15, 22
P
piezoelectric, 62, 105, 106, 107, 108, 109, 113,
116, 122, 153, 164, 192, 193, 194, 195, 196,
197, 202, 206
pipe, 12, 152, 153, 154, 156, 158, 162, 163, 164,
166, 168, 169, 170, 171, 172, 177, 178, 179,
183, 184, 185, 186, 187, 192, 193, 194, 196,
197, 198, 202, 205, 206
plate theory, 8, 42, 76, 106, 107, 140
Poincaré-Lindstedt Method, 22
postbuckling, 42, 140
R
Reddy theory, 9, 12, 75, 77, 120, 122
S
seismic ground excitation, 41
shell theory, 2, 11, 162, 164
sinusoidal shear deformation theory, 7, 10, 62,
90, 92
strain-displacement equations, 2, 9, 10
stress analysis, 42, 140, 152, 153
stress-strain relations, 44, 77, 93, 94, 95, 141, 167,
179, 199
T
Timoshenko beam theory, 6, 29, 141
V
validation, 35, 52, 83, 131, 146, 169
vibration  

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