Preface |
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xiii | |
Authors |
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xvii | |
Chapter 1 Introduction |
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1 | (10) |
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1 | (1) |
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2 | (2) |
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4 | (2) |
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6 | (1) |
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7 | (4) |
Chapter 2 Method Of Weighted Residuals And Galerkin Approximations |
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11 | (20) |
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11 | (1) |
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12 | (2) |
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14 | (12) |
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26 | (1) |
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26 | (3) |
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29 | (2) |
Chapter 3 Finite Element Method In One Dimension |
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31 | (80) |
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31 | (1) |
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31 | (8) |
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32 | (3) |
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35 | (2) |
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37 | (2) |
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3.3 Steady Conduction Equation |
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39 | (16) |
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3.3.1 Galerkin Formulation |
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39 | (6) |
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3.3.2 Variable Conduction And Boundary Convection |
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45 | (10) |
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3.4 Axisymmetric Heat Conduction |
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55 | (5) |
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3.5 Natural Coordinate System |
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60 | (17) |
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77 | (13) |
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3.6.1 Spatial Discretization |
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79 | (2) |
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3.6.2 Time Discretization |
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81 | (9) |
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90 | (3) |
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93 | (9) |
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102 | (1) |
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103 | (6) |
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109 | (2) |
Chapter 4 Two-Dimensional Triangular Element |
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111 | (82) |
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111 | (1) |
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112 | (4) |
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116 | (7) |
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4.3.1 Linear Shape Functions |
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116 | (6) |
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4.3.2 Quadratic Shape Functions |
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122 | (1) |
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123 | (10) |
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4.5 Numerical Integration |
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133 | (5) |
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4.6 Conduction In A Triangular Element |
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138 | (5) |
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4.7 Steady-State Conduction With Boundary Convection |
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143 | (4) |
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4.8 The Axisymmetric Conduction Equation |
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147 | (3) |
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4.9 The Quadratic Triangular Element |
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150 | (16) |
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4.10 Time-Dependent Diffusion Equation |
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166 | (10) |
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176 | (5) |
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181 | (2) |
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183 | (1) |
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183 | (8) |
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191 | (2) |
Chapter 5 Two-Dimensional Quadrilateral Element |
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193 | (70) |
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193 | (1) |
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193 | (2) |
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195 | (5) |
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5.3.1 Bilinear Rectangular Element |
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195 | (2) |
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5.3.2 Quadratic Rectangular Element |
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197 | (3) |
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5.4 Natural Coordinate System |
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200 | (11) |
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5.5 Numerical Integration Using Gaussian Quadratures |
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211 | (4) |
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5.6 Steady-State Conduction Equation |
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215 | (11) |
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5.7 Steady-State Conduction With Boundary Convection |
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226 | (13) |
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5.8 The Quadratic Quadrilateral Element |
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239 | (14) |
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5.9 Time-Dependent Diffusion |
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253 | (1) |
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5.10 Computer Program Exercises |
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254 | (3) |
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257 | (1) |
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258 | (4) |
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262 | (1) |
Chapter 6 Isoparametric Two-Dimensional Elements |
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263 | (22) |
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263 | (1) |
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6.2 Natural Coordinate System |
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264 | (2) |
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266 | (7) |
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6.3.1 Bilinear Quadrilateral |
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266 | (2) |
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6.3.2 Eight-Noded Quadratic Quadrilateral |
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268 | (1) |
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269 | (1) |
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269 | (1) |
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6.3.5 Directional Cosines |
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270 | (3) |
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273 | (4) |
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6.5 Inviscid Flow Example |
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277 | (3) |
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280 | (1) |
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281 | (3) |
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284 | (1) |
Chapter 7 Three-Dimensional Element |
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285 | (44) |
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285 | (1) |
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285 | (3) |
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288 | (10) |
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288 | (7) |
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295 | (3) |
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7.4 Numerical Integration |
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298 | (3) |
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7.5 A One-Element Heat Conduction Problem |
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301 | (12) |
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303 | (4) |
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307 | (6) |
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7.6 Time-Dependent Heat Conduction With Radiation And Convection |
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313 | (7) |
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315 | (3) |
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318 | (2) |
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320 | (1) |
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321 | (5) |
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326 | (3) |
Chapter 8 Finite Elements In Solid Mechanics |
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329 | (44) |
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329 | (1) |
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8.2 Two-Dimensional Elasticity: Stress/Strain |
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329 | (4) |
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8.3 Galerkin Approximation |
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333 | (16) |
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349 | (7) |
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356 | (10) |
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8.6 Three-Dimensional Solid Elements |
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366 | (3) |
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369 | (1) |
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369 | (2) |
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371 | (2) |
Chapter 9 Applications To Convective Transport |
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373 | (82) |
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373 | (1) |
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373 | (18) |
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391 | (34) |
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9.4 Nonlinear Convective Transport |
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425 | (5) |
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430 | (16) |
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446 | (6) |
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452 | (1) |
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452 | (1) |
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453 | (2) |
Chapter 10 Introduction To Viscous Fluid Flow |
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455 | (42) |
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455 | (1) |
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10.2 Viscous Incompressible Flow With Heat Transfer |
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456 | (2) |
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10.3 The Penalty Function Algorithm |
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458 | (3) |
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10.4 Equal Order: Projection Method |
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461 | (2) |
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10.5 Application To Free And Forced Convection |
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463 | (31) |
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494 | (1) |
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494 | (1) |
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495 | (2) |
Chapter 11 Introduction To Boundary Elements |
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497 | (34) |
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497 | (1) |
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497 | (12) |
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509 | (16) |
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515 | (7) |
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522 | (3) |
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11.4 Three-Dimensional BEM |
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525 | (1) |
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11.5 Dual Reciprocity Method |
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526 | (1) |
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527 | (1) |
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528 | (1) |
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528 | (3) |
Chapter 12 Introduction To Meshless Methods |
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531 | (22) |
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531 | (1) |
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532 | (1) |
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12.3 Radial Basis Functions |
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533 | (3) |
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12.3.1 Global Versus Local RBFs |
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534 | (2) |
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536 | (4) |
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12.5 Implementation Of The Mem |
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540 | (10) |
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540 | (8) |
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548 | (2) |
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12.6 Smooth Particle Hydrodynamics |
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550 | (1) |
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550 | (1) |
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551 | (1) |
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551 | (2) |
Appendix A: Matrix Algebra |
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553 | (8) |
Appendix B: Units |
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561 | (2) |
Appendix C: Thermophysical Properties Of Some Common Materials |
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563 | (2) |
Appendix D: Nomenclature |
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565 | (4) |
Appendix E: Matlab® |
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569 | (10) |
Appendix F: Maple |
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579 | (10) |
Appendix G: Supplemental Routines Used In Maple And Matlab® Examples |
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589 | (12) |
Index |
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601 | |