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| موضوع: كتاب Using Finite Elements in Mechanical Design السبت 14 أغسطس 2021, 1:57 am | |
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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 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 Using Finite Elements in Mechanical Design رابط مباشر لتنزيل كتاب Using Finite Elements in Mechanical Design
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