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 |  موضوع: كتاب Using Finite Elements in Mechanical Design السبت 14 أغسطس 2021, 1:57 am | |
| 
أخواني في الله
أحضرت لكم كتاب
Using Finite Elements in Mechanical Design
Dr. J. Toby Mottram and
Dr. Christopher T. Shaw
و المحتوى كما يلي :
CONTENTS
Preface xi
Notation xiv
1 Relationship Between Design and Finite Elements 1
I . I The Design Process
1.2 Evaluating Designs
1.3 Using Computers for Design Evaluation
1.4 Typical Design Situations
1.5 Historical Review of Obtaining Structural Design Solutions
by Computer
1.6 Overview of the Modern Finite Element Method
1.7 Industrial Implementation and Research in Finite Elements
1.8 References and Further Reading
2 Structural Mechanics
2.1 The Use of Load-Bearing Structures
2.2 Engineering Stress and Strain
2.3 Some Simple Situations
2.4 Describing Problems in Structural Mechanics
2.5 References and Further Reading
3 Finite Element Solutions of the Equations
Developing the Finite Element Methodology
3.2 Satisfying Equilibrium and Compatibility
3.3 Use of Elements with Different Spatial Dimensions
3.4 Overview of Methods for Calculating Element Equations
3.5 The Role of Displacement Distributions
3.6 The Direct Approach to Element Formulation
3.7 Isoparametric Elements
3.8 Other Types of Elements
3.9 Producing a Solution from the Element Equations
3.10 References and Further Reading
4 Implementing a Computer-based Analysis Procedure
4.1 A Process for Analysing a Structure
CONTENTS
4.2 Generic Software Packages for Stress Analysis
4.3 Available Computer Hardware Systems
4.4 Matching Hardware Types to Analyses
4.5 Acquiring the Technologies
5 Building the Geometry Description and the Mesh 111
5.1 Think First—Compute Later
5.2 Overview of Computer Models of Geometry
5.3 Wireframe Models
5.4 Surface Models
5.5 Solid Models
5.6 Choice of Geometry Description
5.7 Overview of Mesh Generation
5.8 Advice on Choosing Element Types
5.9 Determining a Strategy for Distributing the Elements
5.10 Types of Mesh Structure
5.11 Building Meshes
5.12 Adapting a Mesh to Improve a Solution
5.13 Checking a Mesh
6 Obtaining and Analysing the Results 140
6.1 Specifying Material Properties
6.2 Finding the Boundaries of the Mesh
6.3 Imposing the Boundary Conditions on the Mesh
6.4 Controlling the Solution
6.5 Running the Solver
6.6 Troubleshooting
6.7 The Results Generated by the Solver
6.8 Using Computer Graphics to Evaluate Solutions
6.9 Checking a Solution for Accuracy
6.10 Making Refinements
6.11 Failure Criteria
7 Some Example Problems 161
7.1 The Brazilian or Split Tensile Test
7.2 A Pressure Vessel
161
174
8 More Advanced Problems 192
8.1 Composite Material Open-sectioned Beam
8.2 Design Example with Submodels
192
209
9 Industrial Case Studies 231
9.1 Analysing a Bicycle Frame
9.2 Design of a Connecting Rod
231
239CONTFNTS lx
9.3 A Composite Suspension Arm
9.4 Displacement Analysis of a Vehicle Body Shell
246
249
10 Solving More Complex Problems 252
10.1 Transient Problems
10.2 Vibration Problems
10.3 Optimization
10.4 Nonlinear Problems
10.5 Calculating Thermal Effects within Structures
10.6 References and Further Reading
References and Further Reading 262
Index 266INDEX
Accuracy. 12. 16, 36. 49, 54. 57. 71. 81. 108,
119-125, 142, 150
checking. 159
Backup of data. 98, 100 , 107
Bandwidth, 56, 86
algorithm, Culhill-McKee, 137
reduction, 136-137
Bar, 9-10, 15. 19, 30-32, 36 39
element, ( sec Element, bar)
Beam. 9-10, 15, 19. 37, 40, 182, 192-204.
20R-200, 254
element, ( see Element, beam)
Benchmarks, 16, 42, 71, 120
Bending, 15. 19. 40, 64, 66, 120, 124, 177,
184-185, 188, 192-210. 209-230, 238,
243, 249
element, Element, beam, plate, shell
moment. 40, 79. 194. 198. 214 217. 223. 225
Bezier surface, 114— 11 $, 129
Bicycle frame example, 231-239
Biharmonic equation, 41^32
Binary files, 107. 151 152
Body forces, 19, 24-25. 38^10, 48 49. 51 52, 77.
estimation of
, 16
of consistent element force vector. 76-77
of different elements, 56
of element stresses, 77-78
of examples. 16^169. 172-173. 180. 183. 185.
202. 205.210, 213. 220
of integration. 64. 69-75
ol solution. 134-136. 152. 259
Acquisition of technology. 4, 91, 101
hardware, 106
software, 42^13, 102
Admissible functions, 12. 49. 50-51. 214, 223
Advancing front method, 133
Aircraft design, 5. 6, 10, 12, 192, 256
Airy stress functions. 6. 14, 17, 41-42, 162
Aluminium, 29 30. 35, 107, 240, 242. 244
black. 201
ASCII files. 107. 149, 151-153
Analysis process:
for structural problems. 43. 91-92. 94, 105,
108. 112. 130, 140, 149. 164- 165, 175
goals, 108. 240
initial thinking, 92, 140. 164, 175
mesh generation, (sec Mesh, generation)
numerical problem specification, 92, 142, 160
numerical solution. 8, 47, 90, 9,7-94, 98, 140,
92
Bound:
lower, 58
upper, 57. 175
Boundary conditions, (sec also Restraints)
application to faces. 93, 143-146, 148, 180
application to global equations, 84-85, 125
essential, 14
natural. 14
symmetry. 118. 165, 182, 201-202. 243
Boundary element (integral) method. 7
B-Rcp solid model, 115-117
Brazilian tensile test example, 42, 161-174
Brick elements, (see Element, brick )
Brittle material, (see Material, brittle)
Duckling213 , 38 -214 , 44,—259 *5. 75, 81, 102, 109. 192.
Bytes, 106-107, 151-152
147
results analysis. 43. 53. 78. 81. 93-94. 96.
108-110, 122-124. 135, 141. 152-154,
157-158. 160-251
troubleshooting. 140. 150
Analyst:
team, 108. 191
skills. 4. 17. 91. 108 110, 112
Anisotropy. 30. 34, 44. 46. 81. 192-195. 197.
206. 200
Architecture:
computer. 91. 97. 100
novel. 98
Assembly of equations. 7, 52, 58. 61. 82-84. 86
Axial load. 31-32. 38- 39. 45, 61. 212. 214.
216 217
. 22.7. 243
Axisymmetric elements, ( see Element,
axisymmeiric)
Computer-aided Design (CAD). 44. 74, 103,
113. 115. 129. 247, 250
model types:
solid:
B-Rep. 115-117
Constructive Solid Geometry (CSG).
115-116, 23.7
surface:
Bezier, 114-115. 129
266I N D E X 267
Coons patch. 114. 129
Non-uniform rational B-spline ( NURBS ).
115. 129
wireframe, 112-115. 234, 247
Computer-aided Engineering (CAE) svstems.
96-97
Conjugate gradient method. 89
Calculus of variations. 9-10. 12
post- processors. 16. 94. 96- 98, 103. 106,
109. 137. 150. 153-154. 156. 158. 182.
185-180. 204- 205. 207. 226. 238
solvers. 85. 94-97, 103. 107-109. 111. 122.
136. 140. 149- 153. 159. 167. 182.
195-196. 204. 252- 253. 258 259
Ulililies. 94. 96-97
specifying. 102-106
speed:
millions of instructions per second (mips).
100. 106
millions of floating point operations per
second ( M FLOPS), 100. 106
Carbon fibre composite material , (.see Material.
Carbon fibre composite)
Checking:
data. 96, 144
mesh. 134. 137
coincident nodes. 138. 150-151
exploded mesh. 139
free-edge. 139
free-faee, 138
model , 94. 109. 117. 151, 255
solution, 93-94, 150. 149
Command files. 96. 109. 150-151. 153
Commercial software, 7. 14- 16. 36. 54-57,
70-7 ] , 74, 79. 92. 98. 101. 116. 129. 133,
136-137. 167. 179. 184, 192. 209 210.
212, 214, 231
Communication of design solutions. 3, 100
Comparison of Knite element and classical
solutions, 169-173
Compass point notation. 142
Compatibility'. 6 8, 20. 28- 29, 37, 39 42. 49.
53-54, 59.66. 79. 122. 125. 172. 206
satisfying, 53- 54
Completeness, 59, 71
Complementary energy, Principle of minimum
Concept design, 3
Condensation technique. 77
Conforming element, 59. 63
non-, 79
Connecting rod example. 239-245
Connections. 9, 53. 113, 209 -210. 212
semi-rigid. 9
Connectivity list. 84. 97, 118, 138. 149. 152
Consistent clement force vector, (.we Element,
force vector)
Consistent transformation, 51-52. 61 62.75 77.
146, 180
Contour plots. 78. 96, 154. 158-159. 167 173.
182 191, 203- 204. 222. 226-230.
239-240, 244-245.248
Control ,
of solution. 149-152, 253
parameters, 92, 95, 235
Convergence. 7, 59, 63, 66, 109, 119 -120. 122.
136. 161. 179. 220, 253, 258- 259
Constraints. 77. 81. 85, 108-109. 119, 124-125.
149, 243
on design variables, 3. 256-257
multi-point, 108
Coons patch. 114, 129
Coordinates. 13-14, 21 -23, 33. 40. 48. 60.
78- 79, 96. 107. H 3- II4. 118. 129.
148-149. 152. 165, 177, 180, 182. 185.
199. 221
generalized. 49-50
global. 57. 59. 61-62. 65. 76-77. 125. 128.
156-158. 160
local. 57. 63. 125. 128. 142. 154. 197, 200,
57
Compliances, 34
Composite material, (see Material, composite)
Composite material I-beam example. 192-209
Computer, 97-101
-aided design. 44. 74. 103, 113. 115, 129, 247.
250
hardware. 16, 43, 56, 91, 96-101. 103,
106-108, 145, 152-154. 156. 191. 202
graphics. 152-154
minicomputers, 98. 101
minisupercomputers. 98. 101. 152
personal computers, 97. 100. 107
parallel , 16. 97-8
massively, 98
supercomputers, 88, 98. 101, 107
workstations, 97-8, 101, 107, 145. 152-153
networks
, 97-98, 109, 153
peripherals, 97-100
software:
commercial, 7. 14-16, 36. 54, 56-57, 68.
70 -71. 74. 79, 92. 98. 101, 116, 129, 133,
1.36-137. 167. 179. 184. 192, 209 -210,
212, 214, 231
for finite element analysis:
pre-processors, 16, 94-96, 106. 129-150.
152-153, 160. 195, 20Q. 214, 241
204
natural. 64 78
polar. 162
Cost function. 256-257
Coupon test, 31, 38, 175. 194. 197
Crank-Nicholson method. 253
Constructive Solid Geometry (CSG ) solid
model. 115 116. 233
Cuthill-McKee algorithm. 1.37
Cutting plane, 154, 158
Damping matrix, 254268 INDEX
Data:
checking, 96, 144
files, 96-97, 107, 150-152, 155
management, 93-94. 149'150
storage:
disk, 2, 97-100, 106-107, 149-150, 152,
254, 259
primary, 103, 106
secondary, 98, 103, 106-107, 254
Dead load, 19, 161, 189, 210, 227, 237-238
deformed geometry. 96. 158, 167-168,
182-184, 203-204, 216. 226, 238.
243-244, 250-251
vector plots, 96, 158
Direct:
method:
solving simultaneous equations. 9, 16.
85-89, 149, 152
search method, 256-257
stiffness, 9, 13-15, 85-86
Divergence, 253, 258
Domain creation, 129
Drawings, engineering, 3, 5, 44, 177, 240
Dynamic magnification, 210
Dynamics of structure, 4, 43, 81, 101, 109, 127,
210, 213, 227, 249, 254-255
Decomposition:
cell, 117
LU, 86
Deformation, 12-13, 18, 20, 26-35, 47-52. 75,
82, 118, 120, 124
of bar, 38
of beam, 40, 56, 64, 78, 120
of examples, 163, 167, 177, ISO, 182, 189-
191, 195-206, 210, 214, 216, 225, 238,
Eigenvalue, 149, 255, 259
Eigenvector, 255
259 Elastic:
constants, 20, 29, 30, 33-34, 44, 81, 142, 165,
175, 194-195, 200, 213, 215, 260
range, 32, 34
Elasticity, 8, 18-46, 53-54, 56, 202
classical, 9, 12, 14-15, 21, 108, 161-163, 173
Element, 54-56
aspect ratio, 74, 121-122, 124, 156, 220, 222
axisymmetric:
formulation, 80
use of, 80, 101, 119, 121, 176
of shell, 80, 120
large, 7, 19, 44, 191, 259
Delaunay triangulation, 130, 133, 135
Design:
analysis, 4, 37
communication, 3
detailing, 3
evaluation, 3-4
generation of solutions, 3
of frame, 209-230
process, 1-6, 9-10, 12, 17, 25, 29, 32, 34-36,
42, 44, 56, 58, 78, 91-93, 109. 175, 204,
232, 240, 255-256
situations, 5-6
specification, 3, 92, 123, 141
of examples, 160, 176, 179, 185, 189, 194,
198, 204, 210, 244, 248-249
synthesis, 3 ,
variable, 175, 256-257
Differential operator matrix, 28, 51, 67
Dimensions, effect on model size, 37, 55-56,
102. 121
Discontinuities, 108-109, 120, 124-125, 159,
174-175, 183, 185-186, 189, 191
Discretization of space, (see Mesh, generation)
effect on solution speed , 103
Disk storage, 2, 97-100, 106-107, 149-150, 152.
254, 259
Displacement:
distributions. 9-13. 15. 49-51, 53-54. 57-58.
62, 66, 74-75, 80
requirements. 58-59
Display:
of geometry, 154, 167, 179
of results:
contour plots, 78, 96, 154, 158-159,
167-173, 182-191 , 203-204, 222,
226-230, 239-240, 244-245.248
bar:
formulation, 54-55, 59-62, 66-68, 70, 72
use of, 112-113, 118-119, 209, 225, 238
beam:
formulation, 78-79
use of, 15, 112-113, 118, 120, 122,
124-125, 209, 214-220, 228, 248
brick, (sec Element, solid )
characteristics, 11-15, 51-52, 57, 61-65, 75,
77-78, 80
compatibility, 53, 63, 79, 122
contact, 122-123
crack, 81
distribution of, 158
distortion of, 74
equations, assembly, 7, 52, 61, 62, 82-85
force vector, 11-14, 52, 56-57, 61. 82, 83
consistent. 51-52, 57-58, 60, 61-63, 72,
75-77, 146, 180
gap, 81, 85, 119, 123
hierarchical, 66
interior angles of, 74
lumped mass, 54, 253
master, 64-68, 70, 74, 77, 166
membrane, (See Element, plane stress/slrain
or membrane)
nodal degree of freedom vector, 11-15,
50-54, 56-58, 60-63, 72, 75-79, 82-83,
257INDEX 269
plane stress/strain or membrane:
formulation, 13-14, 54-56, 61-65, 68.
70-75. 77-78. 80
use of, 82-85, 119-120, 124, 126-127, 130,
132-133, 136, 161-174
Examples:
bicycle frame, 231-239
Brazilian tensile test. 161-174
composite laminate beam, 192-209
connecting rod, 239-245
machine support frame, 209-230
pressure vessel, 174—191
suspension arm, 246-249
vehicle body shell, 249-251
Explicit methods. 253
Eye position, 155-156
plate bending:
formulation, 55, 59, 77, 80
use of, 115, 121-122
requirements of, 53-54
shape functions, li , 13, 51-52, 57-80, 177,
253. 260
shell:
formulation, 55, 59, 64, 77-81, 177,
195-197, 206
Mindlin, 80, 177, 195, 206
use of, 119-122, 124-125, 148. 174.
177-184. 191, 195, 199-207, 210, 212,
220-231, 233, 235, 238-239, 250-251
Faces, of an element:
applying boundary conditions, 93, 143-146,
148, 180
finding free faces. 138
Failure criteria, 5, 23, 35-36, 108, 12.3, 141. 162
Tresca or maximum shear stress, 36
von Miscs’ or distortions!, 36, 78, 154. 160,
168, 206, 222, 229-230, 239, 244
Fatigue, 4. 6. 30. 35, 43, 209-210, 212, 218, 220,
222, 227, 240, 243-234
solid:
formulation, 63, 74-75
use of, 80, 119-121, 123, 133, 196, 220,
241-245, 247-249
special, 47, 79, 81
stiffness matrix, (see Matrix, element
stiffness)
stress-hybrid, 57
sub-parametric, 65
super-parametric, 65
transition, 81, 122
types, choice of, 63, 112, 120, 123, 125, 177
Embodiment design: 3
Energy:
method, 9-12, 15, 38. 47-52, 182, 253
Principle of complementary, 57
Principle of minimum potential, 10-12, 47-50
Engineering drawings, 3, 3, 44, 177, 240
Equations:
algebraic, 9, 14-15, 50, 52. 61
assembly, (see Assembly of equations)
compatibility, 28-29, 39-41, 172
equilibrium, 37, 40, 53, 172, 205
stiffness, (see Stiffness, equations)
stress-strain, (see Stress, -strain relationships)
Equilibrium, satisfying, 7, 20-25, 37, 53-54,
206, 212-213, 226
Errors, 93, 107, 137, 150
of discretization, 53-54, 70, 74. 79, 120
of distorting element, 124, 130, 148
estimation of, 15, 36
handling of, 5
of geometry modelling. 129-130
of integration, 64
of off-set element, 122
residual, 88, 152
round-off, 56, 74. 81, 108, 117, 120
of solution, 88-89, 135
in solving examples, 166, 171. 178-180, 182,
184, 206-207, 209, 243, 249
Essential boundary conditions, 14
Evaluation of designs, 3 4
Files:
ASCII, 107, 149. 151-153
binary, 107, 151-152
command, 96, 109, 150-151, 153
data, 96-97, 107, 150-152, 155
EBCDIC, 151
neutral
, 97, 149
results, 151-152
Finite difference method, 7, 10, 42
Finite element method,
assembly of equations, 7. 52, 58, 61, 82. 84,
86
connectivity list, 84, 97, 118, 138, 149, 152
Galerkin method, 10, 17
research, 7, 14-15, 120, 122, 130
shape functions, (.tee Element, shape
function)
stiffness matrix, ( see Stiffness, matrix)
test (or trial) function, 11, 260
variational form, 12, 47-50
Flexural modulus, 197-198, 206, 209
Force:
body. 19, 24. 25, 38-tt), 48-49, 52. 76-77, 92
matrix method. 10
vector:
element, ( see Element, force vector )
global, (.tee Global, force vector)
Fracture. 30. 35-36. 68. 81
Free mesh, ( see Mesh, free)
Free-face, 138-139, 144-145, 151, 154
Functional, 12, 48-51, 91. 256
Functions:
admissible, 12. 49, 50-51, 214, 223
cost. 256-257
objective, 256-257
shape, ( jee Shape, function)270 INDEX
Galerkin method, 10. 17
Gauss:
Hooke's Law, 29. 32, 194
Homogeneity, 25. 29-30, 33-34. 195. 213, 141,
Legendre quadrature rule, 69, 72 161. 163. 174. 192-193
points, 69, 72. 75. 77-78, 124. 168. 184
rule. 69
-Seidel method, 87-88
Generalized :
coefficients, 59 60, 62 -63
coordinates, 49- 50
Generation of design solutions, 3
Geometry:
creation, 129
description, choice of. 117
models:
wireframe, 112-115, 234, 247
surface, 114-115, 129
solid. 115-117, 233
sources:
analytical equations, 44
Computer-aided Design (CAD), 44. 74,
103, 113, 115, 129, 247, 250
engineering drawings. 3, 5. 44, 177, 240
measurement of models. 44
specification, 44
surface. 114-115, 129
Global:
stiffness matrix, (see Matrix, global stiffness)
nodal degree of freedom vector, 14, 50.
52-53, 61, 77. 84
force vector, 12, 14, 52, 77, 84
Graphics:
concepts:
cutting plane, 154, 158
eye position, 155-156
hidden-line display, 145, 157—158
magnification, 156, 182
target position, 155-156
up direction, 155-156
view area, 156
volume clipping, 157
zooming in, 153, 156, 227
hardware, 98, 100-101. 103. 107, 145,
152 154, 202
button box, 153, 156
mouse, 153
Visual Display Unit (VDU), 153
software, 97 100 107, 141
using, 152-155
111-conditioning, 74, 121. 124, 213
Implicit methods, 253
Inconsistent:
loading, 77
Initial conditions. 13, 32. 44. 48-49. 52, 61,
76-77. 79. 81, 91-93. 95. 109, 149. 254,
2S7-258. 260
Instability of mesh. 75, 119
Integration, 47, 49- 50, 61 , 64, 79
closed-form, 64
full, 75, 78. 253
numerical, 47. 64, 67, 73, 72-76, 253
in one dimension, 68-70
in two dimensions, 72
points, (see Gauss, points)
reduced, 75
rule:
Gauss quadrature, 69
Gauss-Legendre quadrature, 69, 72
Newton-Cotes, 69
Simpson’s, 69
Trapezoidal, 69
Interfacing software, 95-96, 103-104, 109, 129
Irregular mesh structure, (see Mesh, irregular)
Isoparametric elements, 57, 62. 64-67, 70- 72,
74-78, 80, 120. 128
Isotropy, 63
Iteration:
controlling, 149, 258
processes:
in design, 3, 93-94
in mesh generation. 130
to resolve nonlinearity, 85, 254, 258 -259
to solve simultaneous equations, 86-89,
149
, 152
w'ith time variation, 254, 258-259
solution methods:
Crank-Nicholson, 253
conjugate gradient, 89
Gauss-Seidel, 87-88
Jacobi, 87
line relaxation, 88
multigrid. 89
point relaxation, 88
preconditioning, 89
Stone's method, 88
successive overelaxation. 88
Half-bandwidth, 56. 86, 136 137
Hardware specification, 43, 56, 96 101. 103,
106, 108
Heat transfer. 4. 6. 43. 82, 102
links to structure, 252. 260
Hidden-line display. 134 , 145, 157-158
Hierarchical elements, 66
Hierarchy of entities, 113, 120. 128-129. 154,
Jacobi method, 87
Jacobian. 67-68, 72, 124
boundary. 76-77
matrix, 72
Joints. 109, 209-210, 246, 248
analysis of, 123, 204, 210-222, 243
fabrication of. 210, 233
177
Historical development, 1. 6-16, 47. 50INDEX 271
pin-, 62. 148, 210. 212. 214-215
rigid-. 210, 212-220, 232
properties, 20, 29-32, 34-36, 38, 44-45, 81,
92-93, 122-124, 141-142, 151, 193-195,
197, 206, 209, 257, 260
specification, 42-43, 141-142, 165, 175-176,
200, 213, 229, 237, 242. 247-248, 250
steel, 29-35, 45. 81, 167, 176, 213, 215, 229,
237, 239, 250
Keyboard, 153
Kirchoffs assumption, 195, 197, 199
Lagrajigian.
elements, 67, 70-72. 76
strain, 25
Lamina, 193-195, 200
Laminate:
element , 195, 197, 201, 204-205
material, 36. 81. 192-198, 200, 202-205
Line relaxation method, 88
Load , 18-20, 44-45, 47^19. 80-81, 108-109.
119, 124
applied to examples, 85, 161-163, 165-166,
173-174. 176, 183, 189, 196, 201-202,
209 212,
214-217, 223-225, 231, 237-238, 241, 243.
246. 248, 252, 254
axial. 30- 32, 35 -36. 38- 39
axisymmetric. 80
boundary conditions. 36-37. 143, 146-148
dead, (.tee Dead , load)
distributed, 13, 52, 61, 75-77
element nodal force vector, i^ec Element.
nodal force vector)
global nodal force vector. (see Global, nodal
force vector)
Matrix:
damping, 254
differential operator. 28. 51. 67
element stiffness, 11-15, 28, 51-52. 56-58,
60-68, 70, 72, 74-75. 78-79, 81-83, 124,
195, 257. 259
global stiffness, 14, 50-53, 56, 59, 61, 77-78.
82-85, 149, 254-255, 257-258
Jacobian, 72
mass, 253-255
material property, 33, 41, 48, 53, 57, 61-63,
72, 77. 79, 81. 194-195, 258
shape function. 51-52. 57-68, 75-76, 79, 253,
260
spatial derivative!s) of field variable(s), 51,
33, 57, 60, 62-63, 67, 69-70. 72,
77
. 79
system matrix, 255
Vandermode, 60, 62, 64, 67, 79
Membrane deformation, 13, 40-41, 62-63, 80.
82, 119-120, 124, 127, 161-174, 177,
184-185, 188, 194-195, 197, 199, 201,
206, 208
element, free plane stress/strain or membrane)
Mesh, 7. 44, 64. 93, 96, 111-139
adaption, 136
enrichment, 134-136
refinement. 53, 56, 109, 120-121, 123,
134-136
boundary, 92, 95, 130, 132
finding, 137-138
checking, 134, 137
generation, 44, 71. 73, 81, 92, 95, 112-114,
117-120. 123-125. 128-129, 159. 177.
live, 19
Locking of mesh, 79, 108, 119, 122
LU decomposition, 86
Lumping:
load. 77
mass, 54, 81. 253
properties. 39. 80. 197. 204. 214
Machine support frame example. 209-230
Mapped mesh, ( see Mesh, mapped)
Mapping. 65, 128
from/to master element, 65-68, 72
distortion, 70-71, 73-74. 77. 117. 122-124.
178, 200. 221. 244
Massively parallel computer. 98
Master:
degrees of freedom. 255
element, (see Element , master )
shape function, (see Shape function, master)
Material, 29-36
anisotropic. 30. 34. 44. 46. 81. 192-195. 197.
206, 209
brittle. 35-36.42, 161-163
carbon fibre composite, 193-194, 196.
200-201
composite. 29 30. 32. 34, 36. 81, 141,
192 -209, 231, 246-249
orlhotropic. 193-194, 201
plastic. 29-30, 32. 36. 174 -175, 189, 191
250
algorithms
Delaunay triangulation, 130, 133, 135
advancing front method, 133
Octree methods, 131, 133
Quadtree methods, 131, 133
examples. 11, 56, 82-85, 131 -136, 166-167,
177-180. 199-200. 215, 221-222, 234 ,
237-237, 241-242, 247, 250-251
need for. 118
simple, 82-86, 114, 136, 145
using:
commercial software. 92
local software, 92
instability. 75, 119
locking, 108. 119. 122
parts:272 I N D E X
mesh {continued)
elements. 53, 56. 63, 77. 92. 94, 103, 112.
114. 117-140, 142-144. 147-148.
151-152, 154. 157. 160-161. 165-166.
169. 174. 177-179. 199-200. 214-215.
221-223, 231, 235. 241. 247. 250. 259.
National Agency for Finite Element Methods
and Standards (NAFEMS). 15. 80
benchmarks. 16. 71. 120
Natural:
boundary conditions, 14
coordinates 64-78
frequency. 255
Need:
recognition of. 2
Network
. 97-98. 109. 153
Neutral files. 97, 149
Nodal:
260
nodes. 92. 94. 103. 107, 114, 118, 122-123.
125-127. 130-140. 142-144. 147-148.
152. 157. 159. 166, 174, 178-179. 200,
215 222 235 "’50 259
refinement, 59. 108, 124. 134-136. 161-191
h-, 109, 136, 169, 174. 179. 183. 189
hp-. 136
P-. 109, 136, 161, 166. 169
structure, 125-129, 136
comparison of, 56
determining, 114, 118, 125-128
regular, 10, 125-127, 135
irregular, 13. 125-127
topology, (see Mesh, structure)
types:
free (and unstructured), 74, 102. 125. 127.
129, 133. 138-139. 154. 160-161. 166,
degree of freedom vector, element, (see
Eleinent. nodal degree of freedom
vector)
Node:
interior. 68-71. 74. 77
numbering, 136- 137
Non-dimensional quantities, 162- 172
Nonlinearity. 86, 109, 140. 149, 254
of geometry, 7. 19. 44. 191. 259
of material properties. 7. 15. 34-35, 44. 102.
168. 162. 251. 253. 259
Number crunching, 96-98
234 Numerical:
control parameters, 92, 95. 149. 235, 252
error. 56, 64. 70. 74. 81.90, 108, 117. 122.
124. 130. 135. 166. 178, 180. 185, 209
integration , 47, 64. 68-70. 72 -76. 253
solution process. 82-89. 119, 122. 135. 137.
mapped (and structured ), 10, 125-127, 129,
135, 142-146, 154. 157-160. 174.
177-179, 221-222, 241, 247
Millions of floating point operations per second
(MFLOPS), 100, 106
Mindlin theory. 79-80, 120, 177, 195, 197. 206
Minicomputer, 98, 101
Minimization, 9, 50-53, 256
Millions of instructions per second (mips), 100,
147
Non-uniform rational B-spline ( NURBS), 115,
129
106 Objective function. 256-257
Objectives, 246
Octree methods, 131, 133
Optimization. 13, 101-102, 140, 149, 171, 252.
255-257
Orthotropic material, (see Material, orthotropic)
Mode:
failure of, 36, 45. 194
of instability, 36
of vibration, 255
rigid-body, 59
shape, 252
Model checking, (see Checking, model)
Modulus:
elastic constants, 20, 29, 30, 33-34, 44, 81,
142, 165, 175, 194-195, 200, 213, 215,
Parallel computer, massively, 16, 97-98
Parent , (see Master)
Partial differential equations, 6-14, 24-25,
36-37, 54. 82. 91. 103. 109. 129. 136.
260 142
flexural, 197-198. 206. 209
section, (see Section, modulus)
shear, 34, 40, 194, 197-199, 208-209, 214
Young's, 29, 32-35, 40. 44. 92, 141, 175-176,
194. 198. 209, 213, 237, 248
Mohr’s circle, 23, 28
Moment, 47-52
causing bending, 19-20, 40, 45, 79, 194, 198,
212, 214-217, 223, 225
-curvature expression, 79, 197-198, 204
Mouse, 153
Multigrid method, 89
Multi-point constraint. 108
Pascal's triangle. 63. 71
Patch test. 59. 80. 119-120. 177
Pattern search method, 256
Peripheral devices, 97- 100
backup devices. 98. 100
graphics displays, 97. 100. 134, 152 154
hardcopy devices, 100
data storage, 98. 106
Personal computers. 97. 100. 107
Pixel, 100, 153
Plane:
dement, (see plane stress/strain or membrane)
strain. 10. 13.41^12INDEX 273
stress, 13, 4fMl2,
example of, 161-174
Plastic material, (see Material, plastic)
Plasticity, 7, 15, 34-35, 44, 102, 168, 251
Plates, 13, 36-37
element for bending, (see Element, plate
bending)
element for membrane action, (we Element,
plane stress/strain or membrane)
Plotting, ( see Display, contour plots)
Point relaxation method , 88
Poisson's:
equation, 260
ratio, 29. 32, 44. 92, 175-176, 194, 213, 237,
mesh, 110. 125-127. 129, 135, 142-146, 154,
157-160, 177-179, 199-200, 222. 241,
247
Relaxation:
method, 9
successive over-, 88
parameter, 148, 253, 258-259
point, 88
technique, 258
Residual:
error, 88, 152
methods,
weighted, 10, 15, 261
stress, 48, 81
248 Restraints, 6, 39, 43, 44, 84-85, 92, 146-148,
Polymer, 174-175 150
matrix, 193-194
Polynomial, 11, 49-50, 54, 57-63, 69-75,
113 115, 136
incomplete, 63
Legendre, 69
Post-processing, 16, 94-98, 103, 106, 108, 109,
X 37, ISO, 153 154, 156, 158, 182,
185-186,
204-207, 226, 238, 241
results analysis, 151-159
software tools, 94. 96, 103, 153—158
Potential energy, 9-12, 47-51
Principle of minimum, 10-12, 47-50
Pre-processing, 6, 16, 94-96, 106, 152-153, 160,
195, 200, 214, 241
stages in process, 94-95, 129-150
geometry generation, 94, 129-130
mesh generation, (see Mesh, generation)
setting boundary conditions, 93, 141-148
setting initial conditions, 95
setting numerical solution parameters, 95,
of examples, 164-165, 175-177, 180-183,
201-202, 215. 222-223, 238, 248, 250
Results analysis, 43, 53, 78, 81, 93-94, 108-110,
124-124, 135, 141, 152-154, 157-158,
from ASCII files, 151-2
of examples, 161-250
using graphics, 16, 96-98, 103, 108, 109. 137,
150, 153-154, 156, 158, 185-186,
204-207, 226, 238
Requirements:
of the analysis, 42-43, 112, 161, 164.
174-175, 185, 192, 196-197, 209-212,
220, 231, 240, 246, 249
of displacement distributions, 58-S9
Rigid-body modes, 59
Saint-Venant’s principle, 38-39, 186, 223
Search method:
direct. 256
pattern, 256-257
Section:
modulus. 197-199, 208-209
properties, 215
Semi-discrete form, 253
Sensitivity analysis, 257
Shape function, 11, 13, 51-52, 57-80, 253, 260
Hermitian, 66
Lagrangian, 67-68, 70-72, 77
master, 64-67, 70-71, 74-75, 77, 80, 177
matrix, (see Matrix, shape function)
serendipity. 70-71. 74
Shear:
deformation, 78-80, 195-200, 208-209
force, 198, 206, 212, 216, 223
modulus, 34. 39^10. 194. 197-198. 208-209.
149
software tools, y4~9b
Preconditioning methods, 89
Pressure vessel example, 174-191
Properties of a material, (see Material,
Modulus, Poisson’s ratio, strength)
Quadrature, (see Integration, numerical)
Quadtree methods, 131, 133
Quality assurance (QA), 103-104
Quasi:
-isotropic, 201, 204
-static load. 210-211
214
Random Access Memory ( RAM ), 97-100, 106
Rayleigh-Ritz method, 9, 49-50
Refinement:
mesh, 59. 108-109, 124, 134-136, 161-191
model, 94, 159-160, 161-191. 209-231
Regular structure:
geometry, Ml
strain, 25-29, 32-37, 3?M2, 206
stress, 21-25, 32-37, 39-42, 77, 164, 168-171,
177. 205-206. 216.225
Shell:
element, (see Element, shell)
theory, 79-80, 197
Mindlin. 80. 120. 177. 195. 206274 INDEX
Simultaneous equations. 9-10, 52-53. 58, 77
solution:
direct method, 85-86
iterative methods:
Crank- Nicholson. 253
conjugate gradient, 89
Gauss Seidel. 87-88
Jacobi. 87
line relaxation, 88-89
multigrid relaxation, 89
point relaxation, 88
preconditioning, 89
Stone’s, 88-89
successive overrelaxation. 88
Singularity, 68. 161-163
Slender:
members, 9. 17, 45, 56
Software:
commercial, (see Commercial, software)
perpetual licences, 104-105
specification, 94-97, 102-106
suppliers, 103-110
Solid element, (eee Element, solid)
Solid model, 112, 115-117
B-rep, 115-117
Constructive Solid Geometry (CSG),
1 IS—117, 233
of bicycle frame, 231-234
of connecting rod, 240-241
Solution:
accuracy, 36, 77-78. 81, 119-125, 134-130,
142, 152
of examples, (we Accuracy, of examples)
checking, 93-94, 150. 159
control, 92, 95, 149-152, 253
of linear simultaneous equations, 85-89
direct methods, 85-86
iterative methods, 85
Crank-Nicholson, 253
conjugate gradient, 89
Gauss-Scidel, 87-88
Jacobi, 87
line relaxation, 88-89
multigrid. 89
point relaxation, 88
preconditioning, 89
Stone’s, 88-89
successive overrelaxation, 88
singular, 82, 151, 260
stability. 254
Solver. 85, 94-97. 103, 107-109, 111. 122. 136,
140, 149-153, 159, 167. 182. 195-196,
204. 252-253, 258-259
running, 107-108. 150-151. 167, 182
re-running, 159
Specification:
design, ( tee Design, specification)
hardware. 43. 56, 96 -101. 103. 106. 108
geometry of examples, 162, 164-165,
174-175, 177, 199, 211, 214-215,
220-222, 225. 231, 233. 240-241. 247
geometry of structure. 44
material properties. 42-43. 141-142
for examples, (.we Material, specification)
of problem. 2-3, 42-45, 92. 111-112, 162,
171-177, 196-197, 210-212, 232.
240 -241. 246, 249
software, 102-106
Speed:
of solution. 55-56, 96-103
Split tensile test example, ( see Brazilian test
example)
Steel:
frame. 9, 209-230
material, (see Material, steel )
members, 45, 198, 209-230
Stiffness:
equations, 13-15, 50-53. 61, 82-85, 98
matrix, 11-15, 28. 50-53, 56-58. 60-68, 70,
72, 74-75, 77-79, 81-85, 124, 149. 195,
254- 255, 257-259
method:
direct, 9, 13-15, 85-86
Stone's method, 88-89
Strain:
axial, 25-29, 32-36. 39^41, 56, 67, 78
-displacement relationship, 27-28, 51, 64
direct, (we Strain, axial)
energy, 12, 48-51, 57-78, 75
engineering, 25-27
initial, 13, 48-51, 61, 76-77, 81, 92, 260
Lagrangian, 25
normal, (see Strain , axial)
plane, 10, 13, 41, 56, 62, 64
principal values, 28
shear, (we Shear, strain )
true, 27
Strength:
yield, 32, 35 -36, 45. 160, 213, 222. 228-230
ultimate, 35-36, 45, 123
Stress:
at a point, 20-21. 25
axial, 21- 25. 30^12. 56. 79-80. 216 248
concentration, 108, 135 136, 160, 161-174,
223
distribution, 10, 57, 123. 260
direct, (s-ee Stress, axial)
engineering, 20
experimental, 30-36, 246. 248
from elements. 14, 53, 61-63, 75. 77 78, 119.
123, 152, 166, 168, 183-185. 220. 258
from isoparametric elements. 77-78
functions (Airy), 6. 14, 17, 41-42, 162
gradient, 127. 161. 165-166, 168-174
-hybrid element. 57
infinite. 163
initial, 48- 49. 52. 61, 76-77, 81, 92, 260
intensity, 96I N D E X 275
from laminate. 196-197. 204- 208
local. 209
mean, 6. 244
normal, (see Stress, axial)
peak, 43. 117, 212, 227
peel, 205
plane. 13, 40-41. 61 64, 80. 161 174
plots, 78, 96. 154, 158-159. 167-173.
184-191, 226-230, 239-240. 244-245.
Taylor series. 24, 26-27
Thermal. 4. 6, 43. 81-82, 102, 127. 160. 260
conductivity. 29
effects on structure, 4. 81. 109, 252. 260
elements, 55. 81
Poisson's equation. 260
Three dimensions:
modification from two dimensions, 55-56,
120, 129
248 numerical integration, 72
principal values, 23, 28. 36, 78. 160. 185-189.
206. 227-229
Time:
dependence, 18. 30. 43, 81. 101-102. 140,
210, 252-255
Explicit methods. 253
Implicit methods, 89. 253
variation. 56, 85, 254-255
Topology, of mesh. 125-126, 136
Torsion. 9. 19, 39. 249
dement, 214
Tractions, surface, .37, 48-49. 52. 77
Transformation:
axis, 23. 28. 61, 78, 125, 157, 194
consistent, 51-52, 61-62, 75-77, 146, 180
Tresca criterion, 36
Troubleshooting, 140, 150-151
proof , 35
range, 6, 183
residual
. 48, 81
resultants. 194
shear, (see Strain, shear)
- strain relationships, 6, 8. 30-34, 48. 50, 61,
64
, 79. 81, 168. 172, 194, 260
superaccurate, 78
superconvergent. 78
tensor, 21
total, 21
von Mises’, 154, 159, 160, 168. 206. 222,
229-230. 239. 244
yield, (see Strength, yield)
Structured mesh, (see Mesh, mapped)
Structures:
load-bearing, 18-20
Sub-:
region model. 9-13, 69, 92
parametric element, 65
structuring, 108, 121, 191-192, 210, 215, 218.
220-230
Universities, I. 7, 14, 71, 110
Unstructured mesh, (see Mesh, free)
Up-direction, 155-156
User, 96, 98, 100, 107, 137, 145, 150, 200
current, 105
end-, 110
experience, 93-95, 104, 111, 127, 135
friendliness, 95, 104-105
or graphics, 152-159
interface, 96, 104
multi-
, 97-98
single-, 97
programmed-, 152
successful-, 108-111
support, 16, 34, 71, 79, 104-106, 110
Utility programs, 94, 96-97
Successive overtaxation method. 88
Supercomputers, 88. 98, 101, 107
mini-, 98. 101, 152
Super-parametric element, 65
Superposition, principle of 32
Surface:
descriptions, 44, 73-74, 112-117, 128-129,
177, 234-235, 247
Bezier
. 114-115, 129
Coons, 114, 129
Non-uniform rational B-spline (NURBS),
115, 129
tractions, 37. 48-49, 51-52, 76-77
Suspension arm example, 246-249
Symmetry. 108. 117-118. 161. 164-166.
173-174, 176-177, 180, 182-183. 194,
199, 211, 225, 241
Vandermode matrix, (see Matrix, Vandermode)
Variational formulation method, 9-10, 12, 15
Variational, Calculus of, 9-10, 12
Visual Display Unit (VDU), 95, 153
Vector plots, 96, 154, 158-159, 167
Vehicle body shell example, 249-251
Vibration, 4. 43. 81, 101, 109, 127, 210, 213.
227, 249, 254-255
mode of, 255
View area, 156
Visual display system , (see Visual Display Unit)
Visualization, 108, 117, 134, 139
of results, 23, 152-153
Volume clipping, 157
Volume fraction. 141, 195
axial, 118
boundary condition , 1 18, 165, 182, 201-202,
243
cvclic, 118
mirror, 118, 162, 174. 176, 199, 243
repetitive, 118
Target position. 155-156276 INDEX
Yield, 35-36, 160, 163, 168, 229
criteria, 36, 78, 154, 160, 168, 229
point, 35-36
lower, 35
upper. 35
strength, (JW Strength, yield)
stress, ( see Strength, yield)
Young’s modulus, (see Modulus, Young’s)
von Mises’:
criterion. 36, 78, 154, 160, 168, 229
stress, 154, 159, 160. 168, 206, 222, 229-230,
239, 244
Weight, (see Load, dead)
Weighted :
residual method, 10, 15
Welded joints, 175, 209-231
Windows. Icons. Menus, Pull-Down Screens
(WIMPS). 95
Workstations. 97-98, 101. 107. 145. 152-153
Zooming-in, 153, 156, 227
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