The finite element method . v.2 , Solid and fluid mechanics, dynamics and non-linearity

목차 (Table of Contents)

• CONTENTS
• PREFACE = xiii
• CHAPTER 1 PLATE AND SHELL BENDING APPROXIMATION : THN(KlRCHHOFF) PLATES AND C$$_1$$ CONTINUITY REQUIREMENTS = 1
• 1.1 Introduction = 1
• 1.2 The plate problem : thick and thin formulations = 3
• 1.3 Rectangular element with corner nodes(12 DOF) = 15
• 1.4 Quadrilateral and parallelogram elements = 20
• 1.5 Triangular element with corner nodes(9 DOF) = 23
• 1.6 Triangular element of the simplest form(6 DOF) = 27
• 1.7 The patch test-an analytical requirement = 29
• 1.8 Numerical examples = 30
• 1.9 General remarks = 34
• 1.10 Singular shape functions for the simple triangular element = 40
• 1.11 An 18 degree of freedom triangular element with conforming shape functions = 45
• 1.12 Compatible quadrilateral elements = 45
• 1.13 Quasi-couforming elements = 47
• 1.14 Hermitian rectangle shape function = 47
• 1.15 The 21 and 18 degree of freedom triangles = 49
• 1.16 Mixed formulations-general remarks = 51
• 1.17 Hybrid plate elements = 54
• 1.18 Discrete Kirchhoff constraints = 56
• 1.19 Concluding remarks-which elements? = 60
• CHAPTER 2 'THICK' REISSNER-MINDLIN PLATES-IRREDUCIBLE AND MIXED FORMULATIONS = 66
• 2.1 Introduction = 66
• 2.2 The irreducible formulation-reduced integration = 69
• 2.3 Mixed formulation for thick plates and numerical integration equivalence = 73
• 2.4 The patch test for plate bending elements = 76
• 2.5 Elements with discrete collocation constraints = 82
• 2.6 Performance of various'thick'plate elements-limitations of thin plate theory = 92
• 2.7 Concluding remarks-adaptive refinement = 98
• CHAPTER 3 SHELLS AS AN ASSEMBLY OF FLAT ELEMENTS = 103
• 3.1 Introduction = 103
• 3.2 Stiffness of a plane element in local coordinates = 105
• 3.3 Transformation to global coordinates and assembly of the elements = 108
• 3.4 Local direction cosines = 110
• 3.5 'Drilling' rotational stillness-6 degree of freedom assembly = 114
• 3.6 Elements with mid-side slope connections only = 120
• 3.7 Choice of element = 121
• 3.8 Some practical examples = 121
• CHAPTER 4 AXISYMMETRIC SHELLS = 135
• 4.1 Introduction = 135
• 4.2 Element characteristics-axisymmetrical loads-straight elements = 137
• 4.3 Examples and accuracy = 140
• 4.4 Curved elements and their shape functions = 140
• 4.5 Strain expressions and properties of curved elements = 145
• 4.6 Additional nodeless variables = 148
• 4.7 Independent slope-displacement interpolation with penalty functions(thick or thin shell formulations) = 149
• CHAPTER 5 SMELLS AS A SPECIAL CASE OF THREE-DIMENSIONAL ANALYSIS-REISSNER-MINDLIN ASSUMPTIONS = 159
• 5.1 Introduction = 159
• 5.2 Geometric definition of the element = 161
• 5.3 Displacement field = 164
• 5.4 Definition of strains and stresses = 165
• 5.5 Element properties and necessary transformations = 167
• 5.6 Some remarks on stress representation = 169
• 5.7 Special case of axisymmetric, curved, thick shells = 170
• 5.8 Special case of thick plates = 174
• 5.9 Convergence = 174
• 5.10 Some shell examples = 175
• 5.11 Concluding remarks = 181
• CHAPTER 6 SEMI-ANALYTICAL FINITE ELEMENT PROCESSES USE OF ORTHOGOUAL FUNCTIONS AND 'FINITE STRIP' METHODS = 185
• 6.1 Introduction = 185
• 6.2 Prismatic bar = 188
• 6.3 Thin membrane box structures = 192
• 6.4 Plates and boxes with flexure = 193
• 6.5 Axisymmetric solids with non-symmetrical load = 195
• 6.6 Axisymmetric shells with non-symmetric loading = 199
• 6.7 Finite strip method-incomplete decoupling = 202
• 6.8 Concluding remarks = 206
• CHAPTER 7 NON-LINEAR PROBLEMS-PLASTICITY, CREEP (VISCOPLASTICITY), NON-LINEAR FIELD PROBLEMS, ETC. = 211
• 7.1 Introduction = 211
• 7.2 Iterative techniques = 214
• 7.3 Acceleration of convergence and line search procedures = 220
• 7.4 'Softening' behaviour and displacement control = 221
• 7.5 Convergence criteria = 223
• 7.6 General remarks-incremental methods = 224
• 7.7 General remarks-non-linear elasticity = 225
• 7.8 Plasticity = 228
• 7.9 Computation of stress increments = 239
• 7.10 Some examples of plastic computation = 244
• 7.11 The basic formulation of creep problems = 250
• 7.12 Viscoplasticity = 253
• 7.13 Viscoplasticity-history dependence of creep = 260
• 7.14 Some special problems of rock, concrete, etc. = 262
• 7.15 Non-uniqueness and localization in solid mechanics-some outstanding problems = 266
• 7.16 Non-linear quasi-harmonic field problems = 271
• CHAPTER 8 GEOMETRICALLY NON-LINEAR PROBLEMS LARGE DISPLACEMENT AND STRUCTURAL INSTABILITY = 284
• 8.1 Introduction = 284
• 8.2 General considerations = 285
• 8.3 Large deflection and 'initial' stability of plates = 290
• 8.4 shells = 299
• 8.5 General, large strain and displacement formulation = 300
• 8.6 Concluding remarks = 304
• CHAPTER 9 THE TIME DIMEHSION-SEMI-DISCRETIZATION OF FIELD AND DYNAMIC PROBLEMS AHD ANALYTICAL SOLUTION PROCEDURES = 312
• 9.1 Introduction = 312
• 9.2 Direct formulation of time-dependent problems with spatial finite element subdivision = 313
• 9.3 General classification = 323
• 9.4 Free response-eigenvalues for second-order problems and dynamic vibrations = 324
• 9.5 Free response-eigenvalues for first-order problems and heat conduction, etc. = 334
• 9.6 Free response-damped dynamic eigenvalues = 335
• 9.7 Forced periodic response = 336
• 9.8 Transient response by analytical procedures = 337
• 9.9 Symmetry and repeatability = 341
• CHAPTER 10 THE TIME DIMENSION-DISCRETE APPROXIMATION IN TIME = 346
• 10.1 Introduction = 346
• 10.2 Simple time-step algorithms for the first-order equation = 348
• 10.3 General single-step algorithms for first- and second-order equations = 362
• 10.4 Multistep recurrence algorithms = 378
• 10.5 Some remarks on general performance of numerical algorithms = 385
• 10.6 Non-linear problems = 388
• 10.7 Concluding remarks = 400
• CHAPTER 11 COUPLED SYSTEMS = 404
• 11.1 Coupled problems-definition and classification = 404
• 11.2 Fluid-structure interaction(class I problem) = 407
• 11.3 Soil-pore fluid interaction(class Ⅱ problem) = 420
• 11.4 Partitioned single-phase systems-implicit-explicit partitions(class I problems) = 425
• 11.5 Staggered solution = processes = 429
• CHAPTER 12 CONVECTION DEMINATED PROBLEMS = 438
• 12.1 Introduction = 438
• 12.2 The steady-state problem in one dimension-some preliminaries and Petrov-Galerkin methods = 440
• 12.3 The steady-state problem in one dimension-balancing diffusion = 448
• 12.4 The steady-state problem in one dimension-a variational Principle = 448
• 12.5 Least square-Galerkin approximation = 451
• 12.6 Higher-order approximations = 453
• 12.7 Extension to two(or three) dimensions = 453
• 12.8 Steady state-concluding remarks = 456
• 12.9 Transients-introductory remarks = 459
• 12.10 Transient formulation of the variational and Petrov-Galerkin procedures = 461
• 12.11 Least squares and space-time Petrov-Galerkin methods = 467
• 12.12 Characteristic-based methods = 471
• 12.13 Approximations of a higher time order and generalization to vector variables = 484
• 12.14 Non-linear waves and shocks = 494
• 12.15 Summary and concluding remarks = 499
• CHAPTER 13 FLUID MECHANICS-GOVERNING EQUATIONS AND INCOMPRESSIBLE FLOW NEWTONIAN AND NON-NEWTONIAN VISCOUS FLOWS = 506
• 13.1 Introduction = 506
• 13.2 The governing equations of fluid mechanics = 507
• 13.3 Governing equations = 513
• 13.4 Inviscid, incompressible flow-potential formulation = 514
• 13.5 Slow(creeping) fully incompressible viscous flow-the Stokes problem = 518
• 13.6 Slow non-newtonian flows-metal and polymer forming = 522
• 13.7 The Navier-Stokes problem and convective acceleration offsets-steady-state solutions = 534
• 13.8 The Navier-Stokes problem-transient solution procedures = 542
• 13.9 Concluding remarks = 550
• CHAPTER 14 COMPRESSIBLE HIGH-SPEED GAS FLOW = 557
• 14.1 Introduction = 557
• 14.2 The governinge quations = 558
• 14.3 Boundary conditions-subsonic and supersonic flow = 560
• 14.4 Numerical approximation and solution algorithms = 562
• 14.5 Shock formation and artificial diffusion = 564
• 14.6 Some Preliminary examples for the Euler equation = 565
• 14.7 Adaptive refinement and'shock capture' in the Euler Problem = 568
• 14.8 The Navier-Stockes problem-boundary layer refinement = 584
• 14.9 Some examples of viscous compressible flow computation = 589
• 14.10 Compressible and incompressible behaviour = 589
• 14.11 Concluding remarks = 597
• CHAPTER 15 SHALLOW WATER EQUATIONS AND WAVES = 602
• 15.1 Introduction = 602
• 15.2 The basis of shallow water equations = 603
• 15.3 Numerical approximation = 608
• 15.4 Examples of application = 609
• 15.5 Drying areas = 620
• 15.6 Shallow water transport = 620
• 15.7 Introduction and equations = 622
• 15.8 Waves in closed basins-finite element models = 624
• 15.9 Waves in unbounded domains(exterior surface wave problems) = 626
• 15.10 Boundary dampers = 630
• 15.11 Linking to exterior solutions = 630
• 15.12 Infinite elements = 635
• 15.13 Three-dimensional effects = 642
• 15.14 Large-amplitude waves = 643
• CHAPTER 16 COMPUTER PROCEDURES FOR FINITE ELEMENT ANALYSIS = 651
• 16.1 Introduction = 651
• 16.2 User instructions-description of additional program features = 653
• 16.3 Example problem descriptions = 654
• 16.4 Solution of non-linear problems = 661
• 16.5 Restart option = 665
• 16.6 Solution of transient linear and non-linear problems = 665
• 16.7 Eigensolutions = 673
• 16.8 Description of elements = 677
• 16.9 Solution of example problems = 683
• 16.10 Installation information and listings for program modules = 695
• AUTHOR INDEX = 758
• SUBJECT INDEX = 770