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| موضوع: كتاب The Finite Element Method - A Practical Course الخميس 19 أبريل 2012, 4:31 am | |
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أخواني في الله أحضرت لكم كتاب The Finite Element Method - A Practical Course C.R. Liu & S.S. Quek
و المحتوى كما يلي :
CONTENTS Biographical Information ix Preface xi 1 Computational Modelling 1 1.1 Introduction 1 1.2 Physical Problems in Engineering 3 1.3 Computational Modelling using the FEM 4 1.4 Simulation 7 1.5 Visualization 9 2 Introduction to Mechanics for Solids and Structures 12 2.1 Introduction 12 2.2 Equations for Three-Dimensional Solids 13 2.3 Equations for Two-Dimensional Solids 19 2.4 Equations for Truss Members 22 2.5 Equations for Beams 24 2.6 Equations for Plates 28 2.7 Remarks 34 3 Fundamentals for Finite Element Method 35 3.1 Introduction 35 3.2 Strong and Weak Forms 36 3.3 Hamilton’s Principle 37 3.4 FEM Procedure 38 3.5 Static Analysis 58 3.6 Analysis of Free Vibration (Eigenvalue Analysis) 58 3.7 Transient Response 60 3.8 Remarks 64 3.9 Review Questions 65 vvi CONTENTS 4 FEM for Trusses 67 4.1 Introduction 67 4.2 FEM Equations 67 4.3 Worked Examples 76 4.4 High Order One-Dimensional Elements 87 4.5 Review Questions 88 5 FEM for Beams 90 5.1 Introduction 90 5.2 FEM Equations 90 5.3 Remarks 95 5.4 Worked Examples 95 5.5 Case study: Resonant Frequencies of Micro Resonant Transducer 98 5.6 Review Questions 107 6 FEM for Frames 108 6.1 Introduction 108 6.2 FEM Equations for Planar Frames 109 6.3 FEM Equations for Space Frames 114 6.4 Remarks 120 6.5 Case Study: Finite Element Analysis of a Bicycle Frame 121 6.6 Review Questions 127 7 FEM for Two-Dimensional Solids 129 7.1 Introduction 129 7.2 Linear Triangular Elements 131 7.3 Linear Rectangular Elements 141 7.4 Linear Quadrilateral Elements 148 7.5 Higher Order Elements 153 7.6 Elements with Curved Edges 160 7.7 Comments on Gauss Integration 161 7.8 Case Study: Side Drive Micro-Motor 162 7.9 Review Questions 171 8 FEM for Plates and Shells 173 8.1 Introduction 173 8.2 Plate Elements 173 8.3 Shell Elements 180 8.4 Remarks 184 8.5 Case Study: Natural Frequencies of Micro-Motor 185 8.6 Case Study: Transient Analysis of a Micro-Motor 192 8.7 Review Questions 198CONTENTS vii 9 FEM for 3D Solids 199 9.1 Introduction 199 9.2 Tetrahedron Element 200 9.3 Hexahedron Element 209 9.4 Higher Order Elements 216 9.5 Elements with Curved Surfaces 222 9.6 Case Study: Stress and Strain Analysis of a Quantum Dot Heterostructure 223 9.7 Review Questions 232 10 Special Purpose Elements 233 10.1 Introduction 233 10.2 Crack Tip Elements 234 10.3 Methods for Infinite Domains 236 10.4 Finite Strip Elements 242 10.5 Strip Element Method (SEM) 245 11 Modelling Techniques 246 11.1 Introduction 246 11.2 CPU Time Estimation 247 11.3 Geometry Modelling 248 11.4 Meshing 250 11.5 Mesh Compatibility 254 11.6 Use of Symmetry 256 11.7 Modelling of Offsets 265 11.8 Modelling of Supports 270 11.9 Modelling of Joints 271 11.10 Other Applications of MPC Equations 274 11.11 Implementation of MPC Equations 278 11.12 Review Questions 280 12 FEM for Heat Transfer Problems 282 12.1 Field Problems 282 12.2 Weighted Residual Approach for FEM 288 12.3 1D Heat Transfer Problem 289 12.4 2D Heat Transfer Problem 303 12.5 Summary 316 12.6 Case Study: Temperature Distribution of Heated Road Surface 318 12.7 Review Questions 321viii CONTENTS 13 Using ABAQUS 324 13.1 Introduction 324 13.2 Basic Building Block: Keywords and Data Lines 325 13.3 Using Sets 326 13.4 ABAQUS Input Syntax Rules 327 13.5 Defining a Finite Element Model in ABAQUS 329 13.6 General Procedures 339 References 342 Index 34 INDEX ABAQUS input file, 327, 329 calculate eigenvalues of beam, 100 calculate low speed impact on bicycle frame, 122 calculation of 2D heat transfer, 318 calculation of stress distribution in quantum dot structure, 227 cantilever beam with downward force, 337 eigenvalue analysis of micro-motor, 186 static analysis of mico-motor, 165 transient analysis of micro-motor, 193 ABAQUS input syntax rules, 327 Acoustic, 287 Admissible displacement, 37 Area coordinates, 137–138 Axisymmetric elements, 262 loading, 250 mesh, 8 model, 224 solids, 250 Bandwidth, 247 Beam element(s), 90–107, 108 Beam(s), 5, 24, 90 Bending of beams, 24 Bending of plates, 28 Boundary conditions cyclic, 264 essential,13, 18–19, 309 for 2D heat transfer, 308, homogenuous, 19 in abaqus input file, 330, 334 infinite, 245 inhomogenuous, 19 natural, 13, 18–19 symmetric, 258, 274 Boundary element method (BEM), 242, 324 Central difference algorithm, 60 Comment lines, 327 Compatibility equations, 37 of displacements, 243 of mesh, 254, 274 Complexity of linear algebraic system, 247 Computational modelling, 4 Conforming element, 177, 180 Consistency, 44–46, 65 Constant strain element, 204 Constant stress element, 204 Constitutive equations beam, 26 plate, 30 one-dimensional solid, 24 three-dimensional solid, 16 two-dimensional solid, 21 Constraints, 57, 330 Continuity, 36, 254–255 Convective boundary condition, 310 Convergence, 78–79, 100 Coordinate mapping, 142, 148–149 Coordinate transformation, 55, 71, 73–74, 112–113, 116–117 CPU time, 247 Crack-like behaviour, 254 Crack tip elements, 233–234 Cubic element(s), 88, 160, 218–219, 222 345346 INDEX Damping, 242 coefficients, 60 Data lines, 325, 328 Delta function property, 46–52, 64 Direct assembly, 82, 84, 294 Direct integration method, 58, 60, 195–196 Discrete system equations, 8, 38 Discretization, 4, 38–39 Displacement constraints, 57 Displacement interpolation, 39 Displacement method, 41 Dynamic equilibrium equation, 17–18, 24, 28, 32 Effort to accuracy ratio, 246 Eigenvalue analysis, 58–60, 102, 186 Element distortion, 250–252 Element force vector, 55, 307, 308 Element mass matrix, 111, 140, 146–147, 152, 178 Element matrices 2D solid element, 140–141, 145, 152 3D solid element, 204–208, 213–215 beam element, 93–94 frame element, 109–112, 115–116 heat transfer element, 294, 296–297, 300, 302–303, 308 plate element, 178 shell element, 180–183 truss element, 71 Element stiffness matrix, 53, 71, 140, 145, 152, 178–179, 230, 251, 299, 305 Elements with curved edges, 160, 223 Elements with curved surfaces, 222 Euler–Bernoulli beam theory, 25, 121 Field problems, 282 Finite difference method, 8, 36, 60 Fin one-dimensional, 284, 289 two-dimensional, 282–283 Finite element method (FEM) equations, 67, 90, 109, 114 procedure, 38, 64 Finite strip elements, 233, 242 Finite strip method, 243 Finite volume method (FVM), 8, 324 Flexural vibration modes, 185–186, 188 Fluid flow, 287 Force boundary condition, 19 Fourier series, 195–196 superimposition, 263 Frame element, 108 Frame structure, 108, 112 Free vibration, 58 Functional, 37, 54, 279 Galerkin method, 289 Gauss elimination, 9, 58 Gauss integration, 145, 161, 213 Gauss points, 145–146, 161 Gauss’s divergence theorem, 303 Geometry modelling, 248 Global coordinate system, 55–56, 71–74, 112–114, 116–117, 184 h-adaptivity, 79 Hamilton’s principle, 37–39 Heat insulation boundary, 310 Heat source/sink, 314–315 Heat transfer 1D problem, 289 2D problem, 303 across a composite wall, 285, 298 in a long two-dimensional body, 283 in a one-dimensional fin, 284, 289, 296 in a two-dimensional fin, 282 Helmholtz equation, 282 Hexahedron element, 209 Higher order elements brick, 218 one-dimensional, 87 plate, 180 rectangular, 156 tetrahedron, 216 triangular, 153 History data, 329, 331 Homogeneous equation, 58 Implicit method, 63 Infinite domains, 233, 236INDEX 347 Infinite element, 237 Initial conditions, 4, 61, 246, 330 Integration by parts, 290 Irrotational fluid flow, 287 Isoparametric element, 152 Jacobian matrix, 151–152, 207, 212–213 Joints modelling, 271 Keyword lines, 326, 328 Kinetic energy, 37, 53, 177 Lagrange interpolants, 87 Lagrange multiplier method, 279 Lagrange type elements, 156, 218 Lagragian functional, 37, 54 Lamb waves, 240 Linear element(s), 70, 130 Linear field reproduction, 47, 50–52, 64–65 Linear independence, 46 Linear quadrilateral elements, 148 Linear rectangular elements, 141 Linear triangular elements, 131 Mass matrix, 53 2D solid element, 140, 146–147, 152 3D solid element, 204–205, 213- 215 beam element, 94 frame element, 111, 116 plate element, 178 shell element, 183 truss element, 71, 74 Matrix inversion, 63 Mechanics for solids and structures, 3, 12 Membrane effects, 182–184 Mesh compatibility, 254–255, 274, 276 density, 250, 276 generation, 6 Mindlin plate, 28, 32–33, 174–175 Modal analysis, 58–59 Model data, 329–330 Moments, 26–28, 30–31 Multi-point constraints (MPC), 267, 271, 273–279 Natural coordinates, 91, 142 Newmark’s method, 63 Nodal interpolation functions, see shape functions Non-conforming, 174 Order of elements, 254 Offsets, 265–269 p-adaptivity, 79 Partitions of unity, 47–49, 52, 64–65 Pascal pyramid, 42 Pascal triangle, 41–42 Penalty method, 279 Planar frame element, 109, 110 Planar truss, 74 Plane strain, 20–22, 129–130 Plane stress, 20–21, 129–130 Plate element(s), 5, 28–29, 173–180 Poisson’s equation, 286, 287 Polynomial basis functions, 43 integrand, 145, 161 interpolation, 39 Potential energy, 37 Quadratic element(s), 130, 157, 216, 219 Quadrilateral element(s), 6, 148–149, 151 Rate of convergence, 79 Rectangular element(s), 141–148, 156–158, 307–308 Reproduction property, 44–45, 50, 65, 78 Serendipity type elements, 157, 219 Shape functions properties, 44, 65 standard procedure for constructing, 41 sufficient requirements, 64 Single point constraint, 51, 258 Singularity point, 234348 INDEX Singularity elements, see crack tip elements Space frame, 108–109, 114–120 Space truss(es), 67 Static analysis, 58 Steady state heat transfer, 282, 289 Straddling elements, 255 Strain displacement relation/relationship(s), 16, 21, 23 Strain energy, 37, 52, 179 Strain matrix, 53, 291 beam element, 93 hexahedron element, 209 linear quadrilateral element, 151 linear rectangular element, 144, 307 linear triangular element, 139, 306 mindlin plate element, 179 tetrahedron element, 200 truss element, 70 Streamline function, 287 Stress intensity factor, 234 Strip element method (SEM), 240, 242, 245 Strong form, 36, 38 Subparametric elements, 153 Subspace iteration, 59 Superparametric elements, 153 Supports modelling, 270 Symmetric positive definite (SPD), 57, 59 Symmetry, 256 axial, 262 cyclic, 264 mirror, 256 repetitive, 264 Tetrahedron element, 200–207, 216–218 Torsional deformation, 282, 286 element, 115 Transformation matrix, 56, 72, 74, 113, 117, 184 Transient analysis, 192 dynamic analysis, 336, 341 response, 60 Triangular element(s), 131–141, 153–156, 289, 305–306 Truss(es), 22–24, 67–89 Two-dimensional (2D) heat transfer, 303, 318 Variational principle(s), 36, 38 Vibration, 12 modes, 59 problems, 240 Visualization, 1, 9 Volume coordinates, 201–202 Wave propagation, 240, 242 Weak form, 19, 36 Weighted residual approach, 305 method, 8, 36 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 The Finite Element Method - A Practical Course رابط مباشر لتنزيل كتاب The Finite Element Method - A Practical Course
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