Matlab for Engineering

Matlab for Engineering
اسم المؤلف
Berardino D'Acunto
التاريخ
16 فبراير 2023
المشاهدات
643
التقييم
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Matlab for Engineering
Berardino D’Acunto
University of Naples Federico II, Italy
Contents
Preface v
Chapter 1. Function Files 1
1.1 Matrices 1
1.1.1 Creating Matrices 1
1.1.2 Matrix Indexing . 2
1.1.3 Matrix Manipulation 4
1.1.4 Tridiagonal Matrices . 6
1.1.5 Matrix Operations 8
1.1.6 Right and Left Divisions 9
1.2 Script Files 10
1.2.1 For Loop . 10
1.2.2 Examples of Script Files 11
1.3 Introduction to Function Files 15
1.3.1 Structure of Function Files . 15
1.3.2 Function with a Multiple Output Variable 17
1.3.3 Flow Control Structures . 19
1.3.4 Local Functions, Anonymous Functions 25
1.3.5 Logical Operators and Logical Functions . 27
1.4 Exercises 33
Chapter 2. The Finite Difference Method 39
2.1 Finite Difference Approximations of Derivatives 39
2.1.1 Forward, Backward and Central Approximations . 39
viiviii Matlab for Engineering
2.1.2 Approximation of Functions Depending on Two
Variables . 46
2.1.3 Approximation of Higher Order Derivatives 47
2.2 Diffusion 49
2.2.1 Fourier’s Law and Heat Equation . 49
2.2.2 Fick’s Law and Diffusion 55
2.2.3 Free Boundary Value Problems . 56
2.3 Finite Difference Method . 58
2.3.1 Explicit Euler Method 58
2.3.2 Stability, Convergence, Consistence 64
2.3.3 Boundary Value Problems . 68
2.3.4 Diffusion in a Multi-layer Medium . 76
2.3.5 Implicit Euler Method 80
2.3.6 Crank–Nicolson Method . 84
2.3.7 Von Neumann Stability Criterium . 89
2.4 Exercises 93
Chapter 3. Diffusion and Convection 99
3.1 Convection-diffusion Equation 99
3.1.1 Upwind Method . 99
3.1.2 Other Finite Difference Methods for the
Convection-Diffusion Equation . 107
3.1.3 Advection Equation . 111
3.2 Method of Lines . 118
3.2.1 Heat Equation 118
3.2.2 Nonlinear Equations . 127
3.2.3 Variable Diffusivity Coefficient . 133
3.2.4 Convection-Diffusion Equation . 136
3.3 Saving Data and Figures . 140
3.3.1 Save Function 140
3.3.2 Load Function 142
3.3.3 Saving Figures 143
3.4 Exercises 143
Chapter 4. Introduction to the Finite Element Method 153
4.1 Numerical Integration 153
4.2 Finite Element Method . 164
4.2.1 Axial Motion of a Bar 164
4.2.2 Weak Solution 167Contents ix
4.2.3 Shape Functions . 169
4.2.4 Boundary Value Problems . 171
4.2.5 Axial Displacement and Stress in a Bar 180
4.2.6 Concentrated Force and Dirac Function 184
4.3 Partial Differential Equations 189
4.3.1 Diffusion Equation 189
4.3.2 Wave Equation 197
4.4 Exercises 205
Chapter 5. Introduction to the Finite Element Method
in Two Spatial Dimensions 213
5.1 Elliptic Partial Differential Equations 213
5.1.1 Green’s Identities 213
5.1.2 Boundary Value Problems . 214
5.2 Finite Element Method in Two Spatial Dimensions 217
5.2.1 Shape Functions . 217
5.2.2 Weak Form of the Poisson Equation 225
5.2.3 Dirichlet–Neumann Problem 230
5.2.4 Applications to the Dam and Sheet Pile Wall . 234
5.3 Finite Difference Method . 240
5.3.1 Five-Point Method 240
5.3.2 Model of a Dam . 247
5.4 Exercises 257
Chapter 6. The Euler–Bernoulli Beam 267
6.1 Finite Element Method . 267
6.1.1 Euler–Bernoulli Beam Equation 267
6.1.2 Shape Functions . 270
6.1.3 Weak Form 274
6.2 Statics . 277
6.3 Beam Subjected to Concentrated Forces 296
6.4 Exercises 305
Bibliography 311
Index 313
Index
< (less), Matalab operator, 20
<= (less or equal), Matalab operator,
20

= (greater or equal), Matalab
operator, 20
= (greater), Matalab operator, 20
== (equal), Matalab operator, 20
˜= (not equal), Matalab operator, 20
abs, Matlab command, 42
all, logical function, Matlab, 30
anonymous function, Matlab, 26
any, logical function, Matlab, 31
axis, Matlab command, 13
backward, function file, 93
beam c pn pn, function file, 297
beam fx fr, function file, 282
beam fx fx uA, function file, 293
beam fx pn, function file, 288
beam ov, function file, 303
beam pn pn, function file, 285
Bessel, historical note, 158
besselj, Matlab command, 158
break, Matlab command, 24
burgers, function file, 128
Burgers, historical note, 127
central, function file, 43
central implicit, function file, 108
clc, Matlab command, 12
consolidation1, function file, 121
consolidation2, function file, 125
crank, function file, 86
Crank, historical note, 85
dam, function file, 235
dam 5p, function file, 254
Darcy, historical note, 49
diag, Matlab command, 5
diffusion d, function file, 192
diffusion n, function file, 195
Dirac δ function, 184
Dirac, historical note, 184
Dirichlet boundary condition, 52
Dirichlet, historical note, 52
disp, Matlab command, 13
error, Matlab command, 20
errordlg, Matlab command, 20
Euler, historical note, 39
Euler–Bernoulli equation, 268
Euler–Lagrange equation, 268
euler e, function file, 60
euler edn, function file, 72
euler el, function file, 92
euler em, function file, 62
euler en, function file, 70
euler enm, function file, 71
euler i, function file, 81
eye, Matlab command, 4
fem dd, function file, 174
fem dn, function file, 177
313314 Matlab for Engineering
feval, Matlab command, 26
Fick’s law, 55
Fick, historical note, 49
find, logical function, Matlab, 31
five point, function file, 243
five point f1, function file, 246
for, Matlab structure, 10
forward, function file, 41
Fourier’s law, 49
Fourier, historical note, 49
fplot, Matlab command, 27
fprintf, Matlab command, 42
ftbs, function file, 113
ftfs, function file, 115
full, Matlab command, 7
function file, Matlab, 15
Gauss, historical note, 51
gradient, Matlab command, 17
Green’s identities, 214
Green, historical note, 214
hermitian functions, 271
hold off, Matlab command, 122
hold on, Matlab command, 121
homogeneous boundary condition, 53
Hooke, historical note, 165
if-elseif-else, Matlab structure, 19
int, Matlab command, 155, 160
integral, Matlab command, 155
integral2, Matlab command, 160
integral 1, function file, 155
integral 2, function file, 156
integral 2D 1, function file, 160
integral 2D 2, function file, 205
integral 2D 3, function file, 163
integral 2D 4, function file, 163
integral 3, function file, 157
integral 4, function file, 158
ismember, logical function, Matlab,
32
isspace, Matlab command, 25
Kronecker δ function, 169
Kronecker, historical note, 169
Lagrange, historical note, 169
laplace, function file, 229
Laplace, historical note, 52
layers, function file, 77
left division, Matlab, 10
legend, Matlab command, 13, 21
lines c d 1, function file, 137
lines c d 2, function file, 138
lines heat1, function file, 123
linspace, Matlab command, 3
load, Matlab command, 142
local function, Matlab, 25
logical operators, Matlab, 27
mass, function file, 276
max, Matlab command, 42
Neumann boundary condition, 52
Neumann, historical note, 52
Newton, historical note, 53
Nicolson, historical note, 85
nonlinear, function file, 131
norm, Matlab command, 96
num2str, Matlab command, 13
ode15s, Matlab command, 132
ode45, Matlab command, 121
ones, Matlab command, 4
P´eclet, historical note, 100
pause(s), Matlab command, 13
pause, Matlab command, 15
plot, Matlab command, 13
Poisson, historical note, 214
pure Neumann problem, 179
pyramid, function file, 223
pyramid phi, function file, 225
quiver, Matlab command, 18
Rectangle Rule, 153
rectangle, Matlab command, 18
relational operators, Matlab, 20
repmat, Matlab command, 7
reshape, Matlab command, 5
right division, Matlab, 9Index 315
Robin boundary condition, 53
Robin, historical note, 53
save, Matlab command, 141
sheet pile wall, function file, 262
Simpson Rule, 154
Simpson, historical note, 154
simpson, function file, 156
simpson2d, function file, 161
size, Matlab command, 29
spdiags, Matlab command, 6
spy, Matlab command, 7
sqr, function file, 15
Stefan condition, 57
Stefan problem, 58
Stefan, historical note, 57
stiffness, function file, 276
stiffness s, function file, 306
strcat, Matlab command, 23
stress 1, function file, 181
stress 2, function file, 210
surf, Matlab command, 15
switch, Matlab structure, 22
sym, Matlab command, 156
symbol O, 40
Taylor, nota storica, 40
test function, 167
tic, Matlab command, 123
title, Matlab command, 13
toc, Matlab command, 124
transpose matrix, Matlab, 1
Trapezium Rule, 154
triangulation plot1, function file, 217
triangulation plot2, function file, 218
type, Matlab command, 142
upper, Matlab command, 23
upwind, function file, 101
variable1, function file, 134
Von Neumann criterium, 89
Von Neumann, historical note, 89
wave d, function file, 200
wave n, function file, 203
while, Matlab structure, 24
whos, Matlab command, 7
xlabel, Matlab command, 13
ylabel, Matlab command, 13
Young, historical note, 165
zeros, Matlab command, 4
zlabel, Matlab command, 15

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