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عدد المساهمات : 18962 التقييم : 35392 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Finite Element Analysis with Error Estimators الإثنين 30 أبريل 2012, 6:43 pm | |
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أخوانى فى الله أحضرت لكم كتاب Finite Element Analysis with Error Estimators An Introduction to the FEM and Adaptive Error Analysis for Engineering Students J. E. Akin
ويتناول الموضوعات الأتية :
Contents Preface . xi Notation xiii 1. Introduction . 1 1.1 Finite element methods . 1 1.2 Capabilities of FEA . 3 1.3 Outline of finite element procedures . 8 1.4 Assembly into the system equations . 12 1.5 Error concepts . 21 1.6 Exercises . 22 1.7 Bibliography . 24 2. Mathematical preliminaries . 26 2.1 Introduction . 26 2.2 Linear spaces and norms . 28 2.3 Sobolev norms* 29 2.4 Dual problems, self-adjointness 29 2.5 Weighted residuals 31 2.6 Boundary condition terms . 35 2.7 Adding more unknowns 39 2.8 Numerical integration . 39 2.9 Integration by parts . 41 2.10 Finite element model problem 41 2.11 Continuous nodal flux recovery 56 2.12 A one-dimensional example error analysis . 59 2.13 General boundary condition choices . 67 2.14 General matrix partitions 69 2.15 Elliptic boundary value problems . 70 2.16 Initial value problems . 77 2.17 Eigen-problems . 80vi Contents 2.18 Equivalent forms* . 83 2.19 Exercises . 86 2.20 Bibliography . 90 3. Element interpolation and local coordinates 92 3.1 Introduction . 92 3.2 Linear interpolation . 92 3.3 Quadratic interpolation . 96 3.4 Lagrange interpolation 97 3.5 Hermitian interpolation . 98 3.6 Hierarchial interpolation . 101 3.7 Space-time interpolation* . 106 3.8 Nodally exact interpolations* . 106 3.9 Interpolation error* . 107 3.10 Gradient estimates* 110 3.11 Exercises . 113 3.12 Bibliography . 115 4. One-dimensional integration . 116 4.1 Introduction . 116 4.2 Local coordinate Jacobian . 116 4.3 Exact polynomial integration* 117 4.4 Numerical integration . 119 4.5 Variable Jacobians . 123 4.6 Exercises . 126 4.7 Bibliography . 126 5. Error estimates for elliptic problems 127 5.1 Introduction . 127 5.2 Error estimates 131 5.3 Hierarchical error indicator . 132 5.4 Flux balancing error estimates 136 5.5 Element adaptivity 138 5.6 H adaptivity . 139 5.7 P adaptivity . 139 5.8 HP adaptivity 140 5.9 Exercises . 141 5.10 Bibliography . 143Contents vii 6. Super-convergent patch recovery 146 6.1 Patch implementation database . 146 6.2 SCP nodal flux averaging 158 6.3 Computing the SCP element error estimate 164 6.4 Hessian matrix* 166 6.5 Exercises . 176 6.6 Bibliography . 176 7. Variational methods 178 7.1 Introduction . 178 7.2 Structural mechanics . 179 7.3 Finite element analysis 180 7.4 Continuous elastic bar . 185 7.5 Thermal loads on a bar* . 192 7.6 Reaction flux recovery for an element* 196 7.7 Heat transfer in a rod . 199 7.8 Element validation* 202 7.9 Euler’s equations of variational calculus* 208 7.10 Exercises . 210 7.11 Bibliography . 213 8. Cylindrical analysis problems 215 8.1 Introduction . 215 8.2 Heat conduction in a cylinder . 215 8.3 Cylindrical stress analysis . 225 8.4 Exercises . 229 8.4 Bibliography . 229 9. General interpolation 231 9.1 Introduction . 231 9.2 Unit coordinate interpolation 231 9.3 Natural coordinates . 238 9.4 Isoparametric and subparametric elements . 239 9.5 Hierarchical interpolation . 247 9.6 Differential geometry* 252 9.7 Mass properties* . 256 9.9 Interpolation error* . 257 9.9 Element distortion . 258 9.10 Space-time interpolation* . 260 9.11 Exercises . 262 9.12 Bibliography . 263viii Contents 10. Integration methods 265 10.1 Introduction . 265 10.2 Unit coordinate integration . 265 10.3 Simplex coordinate integration . 267 10.4 Numerical integration . 270 10.5 Typical source distribution integrals* . 273 10.6 Minimal, optimal, reduced and selected integration* . 276 10.7 Exercises . 279 10.8 Bibliography . 280 11. Scalar fields 281 11.1 Introduction . 281 11.2 Variational formulation . 281 11.3 Element and boundary matrices 284 11.4 Linear triangle element . 289 11.5 Linear triangle applications . 291 11.6 Bilinear rectangles* 316 11.7 General 2-d elements 318 11.8 Numerically integrated arrays . 319 11.9 Strong diagonal gradient SCP test case 322 11.10 Orthtropic conduction . 337 11.11 Axisymmetric conduction . 344 11.12 Torsion 350 11.13 Introduction to linear flows . 358 11.14 Potential flow 358 11.15 Axisymmetric plasma equilibria* . 365 11.16 Slider bearing lubrication 370 11.17 Transient scalar fields 377 11.18 Exercises . 381 11.19 Bibliography . 382 12. Vector fields . 384 12.1 Introduction . 384 12.2 Displacement based stress analysis . 384 12.3 Planar models 389 12.4 Matrices for the constant strain triangle 395 12.5 Stress and strain transformations* 407 12.6 Axisymmetric solid stress* . 412 12.7 General solid stress* . 413 12.8 Anisotropic materials* 413Contents ix 12.9 Circular hole in an infinite plate 416 12.10 Dynamics of solids 428 12.11 Exercises . 435 12.11 Bibliography . 435 Index .
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Admin مدير المنتدى
عدد المساهمات : 18962 التقييم : 35392 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: رد: كتاب Finite Element Analysis with Error Estimators الخميس 03 يناير 2013, 11:13 pm | |
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