| Notation |
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1 | (18) |
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1 | (2) |
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Problem Classification, Modeling, and Discretization |
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3 | (2) |
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Interpolation. Elements, Nodes, and D.O.F. |
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5 | (3) |
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Example Applications. History of FEA |
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8 | (3) |
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11 | (4) |
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15 | (4) |
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17 | (2) |
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One-Dimensional Elements and Computational Procedures |
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19 | (59) |
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19 | (1) |
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20 | (4) |
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24 | (5) |
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Bar and Beam Elements of Arbitrary Orientation |
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29 | (3) |
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32 | (4) |
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Properties of Stiffness Matrices |
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36 | (4) |
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40 | (2) |
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Exploiting Sparsity. Solving Equations |
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42 | (4) |
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Mechanical Loads. Stresses |
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46 | (6) |
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52 | (2) |
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54 | (3) |
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Review. Remarks Regarding Modeling |
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57 | (2) |
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59 | (19) |
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62 | (12) |
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74 | (4) |
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78 | (58) |
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78 | (5) |
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Interpolation and Shape Functions |
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83 | (5) |
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Formulas for Element Matricies |
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88 | (3) |
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91 | (4) |
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95 | (1) |
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96 | (4) |
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Quadratic Rectangle (Q8, Q9) |
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100 | (2) |
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Rectangular Solid Elements |
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102 | (2) |
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Choice of Interpolation Functions |
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104 | (2) |
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Improved Triangles and Quadrilaterals |
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106 | (5) |
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111 | (4) |
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115 | (3) |
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Nature of a Finite Element Solution |
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118 | (1) |
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Example: A Simple Stress Concentration Problem |
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119 | (2) |
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An Application with High Stress Gradient |
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121 | (15) |
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124 | (8) |
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132 | (4) |
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Formulation Techniques: Variational Methods |
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136 | (43) |
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136 | (1) |
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Principle of Stationary Potential Energy |
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137 | (3) |
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Problems Having Many D.O.F. |
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140 | (2) |
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Potential Energy of an Elastic Body |
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142 | (4) |
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146 | (3) |
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Comments Regarding the Rayleigh-Ritz Method |
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149 | (2) |
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Strong Form and Weak Form |
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151 | (5) |
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Finite Element Form of the Rayleigh-Ritz Method |
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156 | (5) |
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Convergence of Finite Element Solutions |
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161 | (4) |
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Additional Formulations. Hybrid Elements |
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165 | (14) |
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171 | (8) |
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Formulation Techniques: Galerkin and Other Weighted Residual Methods |
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179 | (23) |
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179 | (3) |
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Methods of Weighted Residuals (MWR) |
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182 | (4) |
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Galerkin Finite Element Method in One Dimension |
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186 | (5) |
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191 | (2) |
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Galerkin Finite Element Method in Two Dimensions |
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193 | (2) |
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195 | (7) |
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198 | (4) |
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202 | (57) |
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202 | (3) |
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Bilinear Quadrilateral (Q4) |
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205 | (4) |
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Quadrature: [k] Obtained by Numerical Integration |
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209 | (4) |
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Quadratic Quadrilaterals (Q8, Q9) |
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213 | (4) |
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Hexahedral Isoparametric Elements |
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217 | (2) |
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Incompatible Modes. Nodeless D.O.F. |
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219 | (2) |
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221 | (2) |
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Choices in Numerical Integration |
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223 | (4) |
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227 | (3) |
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230 | (4) |
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Effect of Element Geometry |
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234 | (3) |
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Validity of Isoparametric Elements |
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237 | (1) |
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238 | (2) |
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240 | (4) |
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244 | (15) |
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247 | (8) |
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255 | (4) |
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Isoparametric Triangles and Tetrahedra |
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259 | (12) |
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Reference Coordinates. Shape Functions |
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259 | (3) |
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Element Characteristic Matrices |
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262 | (2) |
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Analytical Integration. Area and Volume Coordinates |
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264 | (2) |
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266 | (5) |
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268 | (3) |
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Coordinate Transformation and Selected Analysis Options |
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271 | (29) |
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Transformation: Introduction and Vector Forms |
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271 | (2) |
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Strain, Stress, and Material Property Transformation |
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273 | (2) |
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Transformation of the Characteristic Matrix |
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275 | (1) |
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Changing the Directions of Restraints |
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276 | (2) |
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Connecting Dissimilar Elements. Rigid Elements |
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278 | (4) |
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Higher Derivatives as Nodal D.O.F. |
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282 | (1) |
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Fracture Mechanics. Singularity Elements |
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283 | (3) |
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Elastic Foundations. Infinite Media |
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286 | (6) |
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Structural Modification. Reanalysis |
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292 | (1) |
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293 | (7) |
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295 | (4) |
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299 | (1) |
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Error, Error Estimation, and Convergence |
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300 | (36) |
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300 | (2) |
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302 | (4) |
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306 | (2) |
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308 | (1) |
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309 | (1) |
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Discretization Error. Convergence Rate |
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310 | (5) |
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315 | (3) |
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318 | (2) |
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Gradient (Stress) Recovery and Smoothing |
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320 | (6) |
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A-Posteriori Error Estimate |
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326 | (3) |
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329 | (7) |
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331 | (4) |
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335 | (1) |
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Modeling Considerations and Software Use |
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336 | (37) |
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336 | (1) |
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Physical Behavior Versus Element Behavior |
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337 | (3) |
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Element Shapes and Interconnection |
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340 | (2) |
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Test Cases and Pilot Studies |
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342 | (2) |
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344 | (3) |
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347 | (1) |
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Connections in Structures |
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348 | (4) |
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352 | (2) |
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354 | (2) |
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Stress Concentrations. Submodels |
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356 | (2) |
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358 | (2) |
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360 | (3) |
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363 | (2) |
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365 | (1) |
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Critique of Computed Results |
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366 | (3) |
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369 | (1) |
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370 | (1) |
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371 | (2) |
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371 | (1) |
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372 | (1) |
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Finite Elements in Structural Dynamics and Vibrations |
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373 | (81) |
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373 | (1) |
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Dynamic Equations. Mass and Damping Matrices |
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374 | (3) |
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Mass Matrices: Consistent, Diagonal, and Other |
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377 | (6) |
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Natural Frequencies and Modes |
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383 | (5) |
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388 | (2) |
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Reduction of the Number of D.O.F. |
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390 | (4) |
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Response History: Modal Methods |
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394 | (4) |
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Response History: Ritz Vectors |
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398 | (2) |
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Component Mode Synthesis (CMS) |
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400 | (5) |
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405 | (2) |
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Response History: Direct Integration Methods |
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407 | (2) |
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Explicit Direct Integration |
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409 | (7) |
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Implicit Direct Integration |
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416 | (5) |
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Direct Integration: Stability and Accuracy Analysis |
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421 | (5) |
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Analysis by Response Spectra |
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426 | (3) |
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Remarks. Modeling Considerations |
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429 | (7) |
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An Application: Vibration and Harmonic Response |
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436 | (3) |
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An Application: Response History |
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439 | (15) |
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444 | (7) |
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451 | (3) |
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Heat Transfer and Selected Fluid Problems |
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454 | (35) |
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Heat Transfer: Introduction |
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454 | (5) |
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Finite Element Formulation |
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459 | (3) |
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Radiation. Nonlinear Heat Transfer Problems |
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462 | (2) |
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Transient Thermal Analysis |
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464 | (3) |
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Modeling Considerations. Remarks |
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467 | (2) |
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469 | (5) |
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Acoustic Frequencies and Modes |
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474 | (3) |
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Fluid-Structure Interaction |
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477 | (3) |
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Plane Incompressible Irrotational Flow |
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480 | (9) |
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482 | (4) |
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486 | (3) |
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Constraints: Penalty Forms, Locking, and Constraint Counting |
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489 | (19) |
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Explicit Constraints. Transformation Equations |
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489 | (3) |
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Lagrange Multipliers to Enforce Constraints |
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492 | (1) |
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Penalty Functions to Enforce Constraints |
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493 | (2) |
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Implicit Penalty Constraints and Locking |
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495 | (4) |
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499 | (3) |
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Remarks About Techniques for Incompressible Media |
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502 | (6) |
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504 | (4) |
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508 | (22) |
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Introduction. Elasticity Relations for Axial Symmetry |
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508 | (2) |
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Axisymmetric Solid Elements |
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510 | (2) |
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512 | (4) |
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Loads Without Axial Symmetry: Introduction |
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516 | (5) |
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Loads Without Axial Symmetry: Some Details of FEA |
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521 | (9) |
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524 | (3) |
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527 | (3) |
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530 | (31) |
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Introduction. Plate Behavior |
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530 | (6) |
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C1 (Kirchhoff) Plate Elements |
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536 | (6) |
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C0 (Mindlin) Plate Elements |
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542 | (5) |
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Mindlin Beam. More Devices for C0 Plate Elements |
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547 | (4) |
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Boundary Conditions. Test Problems |
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551 | (2) |
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553 | (8) |
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556 | (3) |
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559 | (2) |
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561 | (34) |
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561 | (2) |
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Circular Arches and Arch Elements |
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563 | (7) |
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570 | (4) |
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General Shells: Three- and Four-Node Elements |
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574 | (4) |
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General Shells: Curved Isoparametric Elements |
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578 | (5) |
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583 | (3) |
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An Axisymmetric Shell Application |
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586 | (9) |
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588 | (3) |
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591 | (4) |
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Nonlinearity: An Introduction |
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595 | (44) |
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595 | (1) |
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596 | (6) |
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602 | (4) |
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Plasticity: General Formulation for Small Strains |
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606 | (3) |
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Plasticity: Formulation for Von Mises Theory |
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609 | (3) |
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Plasticity: Some Computational Procedures |
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612 | (4) |
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Nonlinear Dynamic Problems |
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616 | (3) |
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Problems of Gaps and Contact |
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619 | (2) |
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621 | (5) |
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Modeling Considerations. Remarks |
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626 | (13) |
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630 | (6) |
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636 | (3) |
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Stress Stiffness and Buckling |
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639 | (24) |
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Introduction. Energy Considerations |
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639 | (3) |
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642 | (3) |
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645 | (1) |
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646 | (2) |
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Calculation of Buckling Loads |
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648 | (2) |
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Remarks on Stress Stiffness and Its Uses |
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650 | (3) |
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653 | (10) |
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656 | (5) |
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661 | (2) |
| Appendix A MATRICES: SELECTED DEFINITIONS AND MANIPULATIONS |
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663 | (5) |
| Appendix B SIMULTANEOUS ALGEBRAIC EQUATIONS |
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668 | (7) |
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668 | (1) |
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668 | (3) |
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671 | (4) |
| Appendix C EIGENVALUES AND EIGENVECTORS |
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675 | (7) |
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675 | (1) |
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C.2 The Standard Eigenproblem |
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675 | (1) |
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C.3 The General Eigenproblem |
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676 | (3) |
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679 | (3) |
| References |
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682 | (29) |
| Index |
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711 | |