Admin
مدير المنتدى
عدد المساهمات : 18938
التقييم : 35320
تاريخ التسجيل : 01/07/2009
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
 |  موضوع: كتاب Finite Element Analysis Theory and Application with ANSYS - Fourth Edition الأربعاء 14 أغسطس 2024, 12:34 am | |
| 
أخواني في الله
أحضرت لكم كتاب
Finite Element Analysis Theory and Application with ANSYS - Fourth Edition
Global Edition
Saeed Moaveni
Minnesota State University, Mankato
و المحتوى كما يلي :
Contents
Preface 13
Acknowledgments 17
1 introduction 21
1.1 Engineering Problems 22
1.2 Numerical Methods 25
1.3 A Brief History of the Finite Element Method and ANSYS 26
1.4 Basic Steps in the Finite Element Method 26
1.5 Direct Formulation 28
1.6 Minimum Total Potential Energy Formulation 57
1.7 Weighted Residual Formulations 63
1.8 Verification of Results 68
1.9 Understanding the Problem 69
Summary 74
References 74
Problems 74
2 matrix Algebra 86
2.1 Basic Definitions 86
2.2 Matrix Addition or Subtraction 89
2.3 Matrix Multiplication 89
2.4 Partitioning of a Matrix 93
2.5 Transpose of a Matrix 97
2.6 Determinant of a Matrix 101
2.7 Solutions of Simultaneous Linear Equations 106
2.8 Inverse of a Matrix 114
2.9 Eigenvalues and Eigenvectors 118
2.10 Using MATLAB to Manipulate Matrices 122
2.11 Using Excel to Manipulate Matrices 126
Summary 140
References 141
Problems 141
3 trusses 145
3.1 Definition of a Truss 145
3.2 Finite Element Formulation 146
3.3 Space Trusses 171
73.4 Overview of the ANSYS Program 173
3.5 Examples Using ANSYS 181
3.6 Verification of Results 213
Summary 215
References 215
Problems 215
4 Axial members, Beams, and Frames 225
4.1 Members Under Axial Loading 225
4.2 Beams 233
4.3 Finite Element Formulation of Beams 238
4.4 Finite Element Formulation of Frames 254
4.5 Three-Dimensional Beam Element 260
4.6 An Example Using ANSYS 262
4.7 Verification of Results 287
Summary 289
References 290
Problems 291
5 One-Dimensional elements 303
5.1 Linear Elements 303
5.2 Quadratic Elements 307
5.3 Cubic Elements 309
5.4 Global, Local, and Natural Coordinates 312
5.5 Isoparametric Elements 314
5.6 Numerical Integration: Gauss–Legendre Quadrature 316
5.7 Examples of One-Dimensional Elements in ANSYS 321
Summary 321
References 321
Problems 321
6 Analysis of One-Dimensional Problems 328
6.1 Heat Transfer Problems 328
6.2 A Fluid Mechanics Problem 347
6.3 An Example Using ANSYS 351
6.4 Verification of Results 366
Summary 367
References 367
Problems 368
7 two-Dimensional elements 371
7.1 Rectangular Elements 371
7.2 Quadratic Quadrilateral Elements 375
8 Contents7.3 Linear Triangular Elements 380
7.4 Quadratic Triangular Elements 385
7.5 Axisymmetric Elements 389
7.6 Isoparametric Elements 394
7.7 Two-Dimensional Integrals: Gauss–Legendre Quadrature 397
7.8 Examples of Two-Dimensional Elements in ANSYS 398
Summary 399
References 399
Problems 400
8 more ANSYS 407
8.1 ANSYS Program 407
8.2 ANSYS Database and Files 408
8.3 Creating a Finite Element Model with ANSYS: Preprocessing 410
8.4 h-Method Versus p-Method 424
8.5 Applying Boundary Conditions, Loads, and the Solution 424
8.6 Results of Your Finite Element Model: Postprocessing 427
8.7 Selection Options 432
8.8 Graphics Capabilities 433
8.9 Error-Estimation Procedures 435
8.10 An Example Problem 437
Summary 451
References 452
9 Analysis of two-Dimensional Heat transfer Problems 453
9.1 General Conduction Problems 453
9.2 Formulation with Rectangular Elements 460
9.3 Formulation with Triangular Elements 471
9.4 Axisymmetric Formulation of Three-Dimensional Problems 490
9.5 Unsteady Heat Transfer 497
9.6 Conduction Elements Used by ANSYS 507
9.7 Examples Using ANSYS 508
9.8 Verification of Results 548
Summary 548
References 550
Problems 550
10 Analysis of two-Dimensional solid mechanics Problems 562
10.1 Torsion of Members with Arbitrary Cross-Section Shape 562
10.2 Plane-Stress Formulation 578
10.3 Isoparametric Formulation: Using a Quadrilateral Element 586
10.4 Axisymmetric Formulation 593
10.5 Basic Failure Theories 595
Contents 910.6 Examples Using ANSYS 596
10.7 Verification of Results 618
Summary 618
References 620
Problems 620
11 Dynamic Problems 629
11.1 Review of Dynamics 629
11.2 Review of Vibration of Mechanical and Structural Systems 643
11.3 Lagrange’s Equations 660
11.4 Finite Element Formulation of Axial Members 662
11.5 Finite Element Formulation of Beams and Frames 671
11.6 Examples Using ANSYS 685
Summary 704
References 704
Problems 704
12 Analysis of Fluid mechanics Problems 711
12.1 Direct Formulation of Flow Through Pipes 711
12.2 Ideal Fluid Flow 723
12.3 Groundwater Flow 729
12.4 Examples Using ANSYS 732
12.5 Verification of Results 753
Summary 754
References 755
Problems 756
13 three-Dimensional elements 761
13.1 The Four-Node Tetrahedral Element 761
13.2 Analysis of Three-Dimensional Solid Problems Using Four-Node
Tetrahedral Elements 764
13.3 The Eight-Node Brick Element 769
13.4 The Ten-Node Tetrahedral Element 771
13.5 The Twenty-Node Brick Element 772
13.6 Examples of Three-Dimensional Elements in ANSYS 774
13.7 Basic Solid-Modeling Ideas 778
13.8 A Thermal Example Using ANSYS 789
13.9 A Structural Example Using ANSYS 806
Summary 819
References 819
Problems 819
10 Contents14 Design and material selection 828
14.1 Engineering Design Process 829
14.2 Material Selection 832
14.3 Electrical, Mechanical, and Thermophysical Properties of Materials 833
14.4 Common Solid Engineering Materials 835
14.5 Some Common Fluid Materials 842
Summary 844
References 844
Problems 844
15 Design Optimization 846
15.1 Introduction to Design Optimization 846
15.2 The Parametric Design Language of ANSYS 850
15.3 Examples of Batch Files 852
Summary 863
References 864
Problems 864
Appendix A mechanical Properties of some materials 865
Appendix B thermophysical Properties of some materials 869
Appendix C Properties of Common line and Area shapes 871
Appendix D Geometrical Properties of structural steel shapes 875
Appendix e Conversion Factors 879
Appendix F An introduction to mAtlAB 881
index 915
Index
A
Absolute humidity, 843
Adiabatic lines, 458, 548
Adiabatic surface, 457–458
Air, 842–843
Aluminum, 836
Aluminum bronze, 837
American National Standards
Institute (ANSI), 836
Angles having equal legs, 875
Anisotropic material, 838
ANSYS
applications for, 26, 27
backward Euler and, 507
basic concepts of, 175
batch files and, 852
Begin level, 407
boundary conditions, 424–426
creating finite element model
with, 410–424
databases and files, 408–410
degree of freedom and, 425
dialog box, 174–175, 411
dynamic problems using, 685–703
error-estimation procedures,
435–437
examples using, 181–212, 437–451
fluid mechanics problems using,
732–753
graphical picking and, 179–180
Graphical User Interface and,
176–177
graphics capabilities, 433–435
heat transfer problems using,
508–547
help system, 180
h-method, 424
input command, 409
loads, 424–426
main menu for, 176–177
meshing, 421–424, 780
method to enter, 173–175
in one-dimensional problems, 321,
351–366
overview of, 26
parametric design language of,
850–852
plotting model entities, 421–422
p-method, 424
postprocessing, 427–431
Processor level, 407
selection options, 432–433
solution, 427
stress component distribution, 595
structural example using, 806–819
three-dimensional beam element,
262–287
time integration and, 506–507
two-dimensional elements, 398–
399
two-dimensional solid mechanics
problems using, 596–618
utility menu for, 177–178
verification of results on, 213–214,
287–289, 548, 618, 753–754
ANSYS element types/options
BEAM188, 262–275
BEAM189, 262
KEOPTs, 410, 411
LINK180, 181
LINK31, 321916 Index
LINK33, 321
LINK34, 321
PLANE35, 398, 507, 596, 732
PLANE55, 507–508, 597, 732
PLANE77, 399, 508, 597, 732
PLANE182, 399, 410, 411, 596
PLANE183, 399, 410–411, 439, 596
SOLID45, 775
SOLID65, 775–776
SOLID70, 774
SOLID90, 774–775
SOLID185, 774, 777
SOLID186, 777
SOLID187, 777
SOLID285, 776
ANSYS files
Jobname.DB, 198, 409, 432
Jobname.EMAT, 410
Jobname.ERR, 409
Jobname.GRPH, 410
Jobname.LOG, 409
Jobname.OUT, 409
Jobname.RMG, 410
Jobname.RST, 410
Jobname.RTH, 410
ANSYS finite element model
creation of, 410–424
element real constants, 411–412
element types, 410–411
material properties, 412–413
meshing, 421–424
model geometry, 413–417
ANSYS processors
OPT, 408
POST1, 175, 407, 427, 451, 852
POST26, 175, 427, 430
PREP7, 175, 407–408, 451, 852
solution, 175, 407
ANSYS working plane
coordinate system, 418
display options, 418
explanation of, 417–418
grid control, 419–420
location status, 421
offset buttons, 420
offset dialog input, 420–421
offset slider, 420
snap options, 418
Area moments of inertia, 870
Axial members, finite element
formulation of, 662–671
Axisymmetric elements
explanation of, 389
rectangular, 391–394
triangular, 390–391
Axisymmetric formulation
formulation of stiffness matrix
using, 593–595
of three-dimensional problems,
490–497
B
Backward Euler, 507
Banded matrix, 88
Basic failure theories, for structural
solid analysis, 595–596
Batch files
examples of, 852–863
explanation of, 852
optimization, 852–863
Beams
deflection and, 233–237
finite element formulation of,
238–241, 671–673
function of, 233–234
load matrices and, 241–243
stiffness matrix and, 246–247, 255
strain energy and, 230–231
stresses in, 233, 237, 239, 261–262
three-dimensional, 260–262
Bilinear rectangular elements, 380
Biot number, 499–500, 506
Boolean operations, in solidmodeling approach, 414
Boundary conditions, 69
ANSYS, 424–427, 447
in conduction problems, 456–459
ANSYS element types/options (cont.)Index 917
convective, 467–468, 474, 478–479,
496
derivative, 467
differential heat equation, 500
in elemental resistance matrices,
717
in elemental stiffness matrices,
152, 159–160, 173, 191, 205
in engineering problems, 22, 25,
32–33, 35, 37, 39, 42, 46–47, 51,
54, 61
in finite element analysis, 424–427
global coordinate system, 312
global load matrix and, 232, 242,
244, 248, 251, 570
in heat transfer problems, 329–331,
336–339, 456–458, 471, 480, 504
in linear equations, 106
stiffness matrix for an axial
element, 665, 668, 684, 692, 698
weighted residual methods, 63–64
Boundary layer region, 723–724
Brass, 837
Brick elements
eight-node, 769–771
twenty-node, 772–773
Bronze, 837
Bulk modulus of compressibility, 835
C
Calcium chloride, 838
Carbon, 840
Centroids, 870
Chain rule, 334, 461, 473, 491, 493
Circular frequency, 646–647
Collocation method, 64–65
Column matrix, 87
Common shapes, 870–871
Composite materials, 841–842
Composite walls, 345–347
Compression strength, 834
Concatenation, 781
Concrete, 837–838
Conductance matrix
for axisymmetric triangular
element, 496–497
explanation of, 44, 47, 336–337
Conduction, 453–454
Conduction problems
boundary conditions in, 456–459
steady-state two-dimensional,
456
Conservation of energy
explanation of, 455–456
heat transfer problems and,
491–492
Convective heat transfer, 41, 42,
454–455
Conversion factors, 876–877
Cooling, 303
Copper, 837
Cramer’s rule, 102
Crank-Nicholson, 507
C shapes, 874
Cubic elements, 309–312
Cubic shape functions, natural
one-dimensional, 315
D
Darcy’s law, 730
Deflection, linear approximation of,
226–227
Deflection equations, 235–237
Degrees of freedom
ANSYS, 425
dynamic problems and, 643,
648–649
explanation of, 643
forced vibration of single,
648–649
multiple, 655–660
nodal, 246, 255
Density, 833
Design optimization
batch files and, 852–863
examples of, 847–850918 Index
overview of, 846–847
parametric design language of
ANSYS and, 850–852
Design process
common solid engineering
materials and, 835–842
fluid materials and, 842–844
material properties and, 833–835
material selection and, 832–833
overview of, 828–829
steps in, 829–832
Design variables, 848, 850
Determinants
examples using, 104–106
of matrices, 101–106
properties of, 103
of square matrix, 101
Diagonal, principal, 88
Diagonal matrix, 87–88
Differential equations, 22, 25
Direct expansion, 102–103
Direct formulation
of flow through pipes, 711–723
heat transfer problem using,
40–49
postprocessing phase in, 37–40
preprocessing phase in, 28–35
solution phase in, 36–37
stress distribution problem using,
52–55
torsional problem using, 49–52
Direct generation, 413
Discretization, 25
Displacement matrix, 32–35, 39
Displacement results, 62–63
Distortion-energy theory, 595
Dynamic problems
ANSYS used for, 685–703
degree of freedom, 643, 648–649
forced vibration and unbalanced
rotating mass and, 650–651
forces transmitted to foundation
and, 652–654
Lagrange’s equations and, 660–662
multiple degrees of freedom,
655–660
support excitation and, 654–655
Dynamics
finite element formulation of axial
members and, 662–671
finite element formulation of
beams and frames and, 671–685
kinematics of particles and,
630–632
kinematics of rigid body and,
636–638
kinetics of particles and, 633–635
kinetics of rigid body and, 638–643
Dynamic systems
examples of, 644
explanation of, 629–630
period and frequency for, 646
properties of, 643
E
Eigenvalues, 118
Eigenvectors
explanation of, 118
method to obtain, 119–121
Eight-node brick element, 769–771
Elastically coupled system, 119, 655
Elastic energy, 230
Elasticity
fundamental concepts of,
578–584
Hooke’s law and, 580–582, 593
modulus of, 565, 581, 834
Electrical networks, 24, 25
Electrical resistivity, 833
Elemental flow resistance, 718
Element real constants, 411–413
Elements
axisymmetric, 389–394
beam, 671–685
cubic, 309–312
eight-node brick, 769–771
four-node tetrahedral, 761–769
Design optimization (cont.)Index 919
frame, 254–260, 673–676
isoparametric, 314–316, 394–396
linear, 225–230
linear triangular, 380–385
one-dimensional, 227, 228,
303–321
quadratic, 307–309
quadratic quadrilateral, 375–380,
399
quadratic triangular, 385–389
quadrilateral, 375
rectangular, 371–375
structural-solid, 774–777
ten-node tetrahedral, 771–772
thermal-solid, 774
three-dimensional, 260–262
triangular, 383–391, 398, 471–482
twenty-node brick, 772–773
two-dimensional, 372–399
Energy conservation, 455–456
Engineering systems
parameters causing disturbances
in, 25
physical properties characterizing,
23–24
Engineers, 829
Error-estimation procedures,
ANSYS, 435–437
Euler parameter, 507
Excel (Microsoft), 126–132
dynamic problem, 666–671
finite element problem, solving,
132–140
finite element formulation
torsional problems, 572–578
fluid mechanics problem, 718–723
formulation with triangular
elements, 482–490
midpoint deflection, solving,
249–254
one-dimensional heat transfer
problem, 341–345
truss problems, solving, 163–171
Explicit finite difference method,
501, 504
F
Factor of safety (F.S.), 595
Failure theories, for structural solid
analysis, 595–596
Feasible solution region, 848–849
Fiberglass, 841
Fibers, 841
Finite difference method
explanation of, 25
explicit, 501, 504
for heat transfer problems,
501–503, 506–507
implicit, 502–503, 504–506
Finite element analysis (FEA).
See also ANSYS
examples using, 70–73
explanation of, 21
sources of error in, 68–69
verification of, 287–289, 753–754
Finite element formulation
of axial members, 662–666
of beams and frames, 238–241,
254–260, 671–685
of fluid mechanics problems,
716–717
of viscous fluid flow problems,
728
Finite element method
applications for, 26
basic steps in, 26, 28
direct formulation and, 28–56
explanation of, 25
for heat transfer problems,
506–507
historical background of, 26
minimum total potential energy
formulation and, 57–63
numerical methods and, 25
results verification and, 68–69
for torsional problems, 562,
564–572
for trusses, 146–171
weighted residual formulations
and, 63–68920 Index
Finite element modeling
of frames, 254–260
frames of reference for, 312
Finite element models (ANSYS)
element types and options,
410–411
geometry, 413–417
grid control, 419–421
material properties definition,
412–413
meshing, 422–424
plotting model entities, 421–422
working plane, 417–421
Finite element problems
direct formulation approach
to, 28–56
minimum total potential energy
formulation approach to,
57–63
steps in, 26, 28
weighted residual formulation
approach to, 63–68
Fins
determining temperature of, 307,
314–315
problems involving, 337–341
transient response of, 529–547
two-dimensional function and,
371, 372
use of, 303, 304
Fluid flow
ideal, 723–728, 732
parameters causing disturbances
in, 25
physical properties related to, 24
in porous media, 729–730
Fluid materials
air as, 842–843
water as, 843–844
Fluid mechanics problems
ANSYS used in, 732–753
direct formulation of flow through
pipes and, 711–723
groundwater flow and, 729–732
ideal fluid flow and, 723–728
one-dimensional, 347–351
verification of results in,
753–754
for commands, 891
Forced vibration
caused by unbalanced rotating
mass, 650–651
equations of motion for,
658–660
of single degree of freedom
system, 648–649
Foundation, forces transmitted to,
652–654
Fourier number, 499, 506
Fourier’s law, 43, 454, 482, 492
Four-node tetrahedral element
analysis of three-dimensional solid
problems using, 764–769
explanation of, 761–764
load matrix and, 769
Frame elements, 254–260, 673–676
Frames
finite element formulation of,
254–260, 673–676
Free-body diagrams, 633, 635, 639,
642
Free meshing, 781–783
free-stream velocities, 728
G
Galerkin method
for analysis of two-dimensional
laminar flow, 728
heat transfer problems and, 460,
473, 491
weighted residual formulations
and, 66, 332
Gauss elimination method
explanation of, 106–108
use of, 108, 114, 125
Galerkin residuals, 491
Gauss-Legendre formula, 316, 319,
320, 590Index 921
Gauss-Legendre quadrature
explanation of, 316, 318–320
two-dimensional integrals and,
397–398
General plane motion, 637–638, 640
Geometrical properties, of structural
steel shapes, 872–875
Glass, 840–841
Global conductance matrix, 45, 46,
475
Global load matrix, 475
Global matrix, 34, 35, 45, 47
Graphical picking, ANSYS and,
179–180
Graphical User Interface (GUI)
ANSYS and, 175–177, 180
graphical picking, 179
layout of, 176–177
Green’s theorem, 462, 465–471,
493, 496
Groundwater, 843
Groundwater flow, 729–732
H
Hardwood, 839
Heat capacity, 835
Heat conduction. See Conduction;
Conduction problems
Heat diffusion equation, 456–457
Heat flow matrix, 47
Heat transfer
conduction, 453–454, 456–459
convection, 41, 454–455
fin, 337–345
Fourier’s law and, 454, 482, 492
Galerkin method and, 460, 473,
491
Green’s theorem and, 462,
465–471, 493, 496
modes of, 453–455
one-dimensional elements and,
303
one-dimensional transient, 500
parameters causing disturbances
in, 25
physical properties related to,
23–24
unsteady, 497–500
Heat transfer problems
axisymmetric formulation of
three-dimensional, 490–497
conduction elements used by
ANSYS, 508–509
examples using ANSYS, 508–547
finite difference approach to,
501–503
formulation with rectangular
elements, 460–471
formulation with triangular
elements, 471–482
general conduction, 453–459
implicit method for, 502–503
unsteady, 497–500
verification of results to, 448
Heisler charts, 500
Hooke’s law
stresses and strains and, 580–582,
593
truss problems and, 146
Humidity, 843
I
Identity matrix, 88
if statement, 892
if and else statement, 893
Implicit finite difference method,
501–503
Impulse approach, 641
Incompressible flow, 715
Input data, 408
Integral formulations, 25
Integrals, two-dimensional,
396–398
Inviscid flow, 723–724, 727, 754
Iron, 837
Irrotational flow, 727–728922 Index
Isoparametric elements
explanation of, 314–315, 394–396
one-dimensional natural quadratic
and cubic shape functions and,
315–316
Isoparametric formulation
explanation of, 314, 394
quadrilateral element and, 586–592
Isotherms, 454, 548
J
Jobname.Ext, 198, 409–410, 432
K
Kinematics
of particle, 630–632
of rigid body, 636–638
Kinetics
of particles, 633–635
rectilinear translation, 638–639
of rigid body, 638–643
L
Lagrange interpolation functions
example using, 312
explanation of, 310–311
Lagrange polynomial formula, 312
Lagrange’s equations
examples using, 660–663, 671
explanation of, 660
Laminar flow, 713, 715–716
Laplace’s equation, 728
Least-squares method, 67
Legendre polynomials, 318
Lightweight metals, 836–837
Linear approximation
of deflection, 226–227
of temperature distribution for
element, 304
Linear elements
axial loading and, 225–230
one-dimensional, 303–307
Linear triangular elements
explanation of, 380–385
limitations of using, 571–572
Line segments, centroids of, 869
Lines of symmetry, 548
Load matrices
change of, 108
direct formulation and, 32, 33,
35, 39
formulation of nodal, 241–243
stiffness and, 230–233
three-dimensional problems
and, 769
two-dimensional plane stress
and, 584–586
Local coordinates, advantages
of, 312
Locational picking, 163
Lower triangular matrix, 88
LU method
application of, 112–114
explanation of, 108–112
Lumped capacitance method,
499
M
M-file, 894
Magnesium, 836–837
Magnetism problems, 24
Mapped meshing, 781–783
Mass moments of inertia of common
shapes, 871
Materials
electrical, mechanical, and
thermophysical properties of,
833–835
mechanical properties of
engineering, 866–867
selection of, 832–833
thermophysical properties of, 868Index 923
Mathematical models, 22, 455
MATLAB
basic ideas, 878–881
commands for, 122, 880–882,
890–891
conditional statements, 892–893
curve fitting with, 908–909
default mode, 878–879
desktop layout, 879–880
disp command, 880–881
element by element operation,
883–886
explanation of, 122
for and while commands, 890–891
format command, 880–881
formulas, 883
fprintf command, 880–881
functions, 888–889
generating range of values, 882
importing of Excel and other data
to, 903–905
line and symbol properties, 898
manipulating matrices using,
122–125
matrix computations with, 905–908
matrix operations, 122, 886
plotting with, 896–902
relational operators, 892
scalar operations, 122, 880
solutions to a set of linear
equations, 910–912
symbolic mathematics with,
909–910
workspace, 882
Matrices
banded, 88
column, 87
determinant of, 101–106
diagonal, 87–88, 118
elements of, 86
explanation of, 86–87
identity, 88, 118
inverse of, 114–118
lower triangular, 88
partitioning of, 93–97
row, 87
singular, 105–106
size of, 86
square, 87, 101
transpose of, 97–100
unit, 88
upper triangular, 88
using EXCEL to manipulate,
126–132
using MATLAB to manipulate,
122–125
Matrix addition, 89, 94
Matrix materials, 841
Matrix multiplication
example of, 91–93
multiplying by scalar quantity,
89–90
multiplying matrix by another
matrix, 90–91
using partitioned matrices,
94–95
Matrix subtraction, 89, 94
Maximum-normal-stress theory, 595
Maximum-sheer-stress theory, 595
Mechanical properties, of
engineering materials,
866–867
Members under axial loading
linear element and, 225–230
stiffness and load matrices and,
230–233
Meshing
ANSYS, 421–424, 780
free vs. mapped, 781–783
Microsoft Excel. See Excel
(Microsoft)
Minimum total potential energy
formulation, 57–63
Modal analysis, 659
Modulus of elasticity, 565, 581, 834
Modulus of resilience, 834
Modulus of rigidity, 563, 581, 834
Modulus of toughness, 834
Mohr failure criteria, 596
Momentum approach, 641924 Index
Motion
equations of, 658–660
general plane, 637–638, 640
Newton’s second law of, 633–635,
638–639, 645
plane curvilinear, 630–631
rectangular, 630
relative, 632
rotational, 643
translational, 642
N
Natural coordinates
advantages of, 312, 313
one-dimensional, 313–314
for triangular elements, 383–385
two-dimensional, 374–375
Natural shape functions,
quadratic, 315
Newton’s law of cooling, 41–42
Newton’s second law of motion,
633–635, 638–639, 645
Nodal degree of freedom, 246, 260
Nonhomogenous systems, 118
Normal coordinates, 631
Numerical integration, GaussLegendre quadrature and, 316,
318–320
Numerical methods, 25
O
Objective function, 848, 849
One-dimensional elements
in ANSYS, 321
cubic, 309–312
Gauss-Legendre quadrature and,
316–320
global, local, and natural
coordinates and, 312–314
isoparametric, 314–316
linear, 303–306
natural coordinates and,
312–314
quadratic, 307–309
shape functions and, 228,
306–307, 317
One-dimensional problems
ANSYS used for, 351–366
fluid mechanics, 351
heat transfer, 328–347
verifying results of, 366–367
One-dimensional transient heat
transfer, 500
Optimization, 846. See also Design
optimization
Optimization batch files, 852–863
P
Pappus-Guldinus theorem,
494–495, 497
Parametric design language,
850–852
Particles
explanation of, 630
kinematics of, 630–632
kinetics of, 633–635
Perfectly insulated surface, 458
Permeability matrix, 731
Pipe flow, 711–723
Pipes
in parallel, 716
in series, 715–716
Plane curvilinear motion, 630–631
Plane-strain situation, 579–580
Plane-stress formulation, 578–586
Plane-stress situation, 579
Plane truss, 145
Plastics, 839–840
Plotting, model entities with ANSYS,
421–422
Poisson’s ratio, 581, 590, 603, 808
Polar coordinates, 631–652
Polymers, 839
Polyvinyl chloride (PVC), 839Index 925
Postprocessing phase
ANSYS, 408, 427–431
direct formulation and, 37–40,
48–49
of finite element method, 28
for heat transfer problems, 329
Potential function, 727–728
Potential lines, 727–728
Prandtl formulation, 564–565
Precast concrete, 838
Preprocessing phase
ANSYS, 407–408, 410–424
direct formulation and, 28–35,
40–48
finite element method and, 26, 28
for heat transfer problems, 328
truss problems and, 152–160
Prestressed concrete, 838
Primitives, 414, 417
Principal coordinates, 659
Principal diagonal, 88
Q
Quadratic approximation, 308
Quadratic elements, 307–309
Quadratic natural shape functions,
315
Quadratic quadrilateral elements,
375–380, 396
Quadratic triangular elements,
385–389, 397
Quadrilateral elements
explanation of, 375
isoparametric formulation and,
586–592
R
Range, 132
Reaction forces, 39, 213
Reaction matrix, 32, 39
Real constants, element, 411–413
Rectangular elements
axisymmetric, 391–394
bilinear, 380, 460
explanation of, 371–374
heat transfer problems and,
460–471
natural coordinates and, 374–375
permeability matrix for, 731
Rectangular motion, 630
Rectilinear translation, 638–639
Reinforced concrete, 838
Relative humidity, 843
Relative motion, 632
Results data, 409
Retrieval picking, 163
Reynolds number, 711–713
Rigid body
explanation of, 636
kinematics of, 636–638
kinetics of, 638–643
Rigidity, modulus of, 563, 581, 834
Rotation
about fixed axis, 639
of rigid body, 636–637
Rotational kinetic energy, 641
Rotational motion, 643
Row matrix, 87
S
Seepage velocity, 730, 745, 754
distribution in the porous soil,
745–753
Semiconductors, 840
Shape functions
basic ideas of, 303–306
one-dimensional, 315–317
properties of, 306–307
quadratic, 312, 315
triangular, 382, 383
two-dimensional, 371–397
Shear modulus, 563, 565, 581, 834
Silicon, 840
Silicones, 840926 Index
Simple harmonic motion, 643
Singular matrix, 105–106
Soda-lime-silica glass, 840
Softwood, 839
Solid engineering materials
composites as, 841–842
concrete as, 837–838
cooper and its alloys as, 837
glass as, 840–841
iron and steel as, 837
lightweight metals as, 836–837
plastics as, 839–840
silicon as, 840
wood as, 838–839
Solid mechanics, 23, 25
Solid mechanics problems. See
Two-dimensional solid
mechanics problems
Solid-modeling approach
Boolean operations, 414
bottom-up, 778, 779
explanation of, 413–415
top-down, 778
Solution phase
ANSYS, 408
direct formulation and, 36–37, 48
of finite element method, 28
for heat transfer problems, 329
truss problems and, 160–163
Space trusses
explanation of, 171–173
solution to problem with,
198–212
Spring mass system, 654–655
Square matrix
determinant of, 101
explanation of, 87
inverse of two-dimensional, 588
St. Venant’s formulation, 564
State variables, 850
Static equilibrium, 31, 644, 645
Steel, 837
Stiffness
load matrices and, 230–233
in truss problems, 153
Stiffness matrices
beams and, 246–247, 255
direct formulation examples and,
32–35, 39, 52, 53
in dynamics problems, 677–678,
681–682
for a frame element, 256–260
truss, 150, 152–159, 173
using axisymmetric triangular
elements, 593–595
Strain energy, 230–231, 581
Stream functions, 724–729
Stream lines, 724–727, 729
Strength-to-weight ratio, 834–835
Stresses
in beams, 237, 261–262
computing principle and
maximum shear, 595–596
distribution of, 52–55, 378–380
von Mises–Hencky theory,
595–596
Structural steel shapes, 872–875
Subdomain method, 65–66
Support excitation, 654–655
Surface water, 843
System of linear equations,
nonhomogenous, 118
T
Tangential coordinates, 631
Temperature distribution
cubic approximation and, 309
heat transfer problems and, 453
linear approximation and, 304
quadratic approximation and,
308
Temperature matrix, 47
Ten-node tetrahedral element,
771–772
Tensile strength, 834
Tetrahedral elements
four-node, 761–769
ten-node, 771–772Index 927
Thermal conductance matrix, 44
Thermal conductivity, 835
Thermal diffusivity, 499, 504
Thermal expansion, 835
Thermal radiation, 455
Thermal transmission, 41
Thermal transmittance
coefficient, 41
Thermophysical properties of
engineering materials, 868
Thermoplastics, 839
Thermosetting, 839
Third-order polynomials, 309
Three-dimensional elements
in ANSYS, 260–287, 774–819
beam, 260–287
eight-node brick, 769–771
four-node tetrahedral, 761–769
solid-modeling ideas and,
778–789
structural-solid, 774–777
ten-node tetrahedral, 771–772
thermal example of, 789–805
thermal-solid, 774
twenty-node brick, 772–773
Three-dimensional solid problems,
using four-node tetrahedral
elements, 764–769
Three-dimensional trusses.
See Space trusses
Timber, 839
Titanium, 836
Torsional problems
direct formulation and, 49–52
finite element method and, 562,
564–578
finite element model to analyze,
72–73
Total potential energy, 230
Total potential energy formulation,
minimum, 57–63
Translation
rectilinear, 638–639
of rigid body, 636
Translational motion, 642
Triangular elements
axisymmetric, 390–391
heat transfer problems and,
471–491, 493, 496–497
hydraulic head for, 731
linear, 380–385, 397
natural coordinates for, 383–385
permeability matrix for, 731
quadratic, 385–389, 397
Trusses
explanation of, 145–146
global and local frames of
reference for, 148–152
space, 171–173, 198–212
Truss problems
finite element formulation and,
146–171
space, 198–212
statistically determinate, 146, 147
statistically indeterminate, 146, 147
stiffness matrix and, 150, 152–159
using ANSYS to solve, 173–214
(See also ANSYS)
Turbulent flow, 715
Twenty-node brick element, 772–773
Two-dimensional elements
in ANSYS, 398–399
axisymmetric, 389–394
Gauss-Legendre quadrature and,
396, 398
isoparametric, 394–396
linear triangular, 380–385, 397
quadratic quadrilateral, 375–380
quadratic triangular, 385–389, 397
rectangular, 371–375
shape functions, 371–397
Two-dimensional flows, 724, 727, 730
Two-dimensional solid mechanics
problems
ANSYS used for, 596–618
axisymmetric formulation and,
593–595
basic failure theories and, 595–596
isoparametric formulation and,
586–592928 Index
plane-stress formulation and,
578–586
torsion of members with arbitrary
cross-section shape and, 562–578
Two-point sampling formula, 398
U
U-factor
conductance matrix and, 44
explanation of, 41–43
Unit matrix, 88
Upper triangular matrix, 88
V
Vapor pressure, 835
Vibration, forced, 648–651
Viscosity, 723, 727–728, 730, 835
Viscous flows, 723, 728
von Mises–Hencky theory, 595–596
von Mises stresses, 596, 806, 818
W
Water, 843–844
Weighted residual formulations
collocation method and, 64–65
comparison of, 68
explanation of, 63–64
Galerkin method and, 66, 301
least-squares method and, 67–68
subdomain method and, 65–66
while command, 891
Wood, 838–839
Work-energy principle, 634, 635,
640–641
W shapes, 872–873
Y
Young’s modulus, 565, 581, 834
كلمة سر فك الضغط : books-world.net
The Unzip Password : books-world.net
أتمنى أن تستفيدوا من محتوى الموضوع وأن ينال إعجابكم
رابط من موقع عالم الكتب لتنزيل كتاب Finite Element Analysis Theory and Application with ANSYS - Fourth Edition
رابط مباشر لتنزيل كتاب Finite Element Analysis Theory and Application with ANSYS - Fourth Edition 
|
|
