Finite Elements Their Design and Performance 0824791622

Table of contents :
MacNeal R.H. Finite Elements Their Design and Performance (Mechanical Engineering, Vol. 89)(Marcel Dekker,1993)(ISBN 0824791622)(600dpi)(547p) 4......Page 4
Copyright 5......Page 5
Contents xi 12......Page 12
PREFACE v 7......Page 7
1.1 Dominance of the Finite Element Method 1 16......Page 16
1.2 Reasons for the Popularity of the Finite Element Method 7 22......Page 22
1.3 Reasons for Studying the Design of Finite Elements 9 24......Page 24
1.4 Classification of Finite Element Characteristics 15 30......Page 30
References 18 33......Page 33
2.1 Physics 21 36......Page 36
2.2 Basic Assumptions 35 50......Page 50
2.3 The Basic Stiffness Formulation 37 52......Page 52
2.4 The Strain-Displacement Matrix for the Constant Strain Triangle Evaluated by Three Methods 45 60......Page 60
2.5 Hybrid Methods 55 70......Page 70
References 61 76......Page 76
3 ASSUMED DISPLACEMENT FIELDS 63 78......Page 78
3.1 Shape Functions and Basis Functions 64 79......Page 79
3.2 Node Locations and the Selection of Basis Functions 71 86......Page 86
3.3 Inventories of Degrees of Freedom 86 101......Page 101
3.4 The Issue of Inter-Element Continuity 93 108......Page 108
3.5 Parametric Mapping 100 115......Page 115
References 111 126......Page 126
4.1 The Calculation of Shape Functions 113 128......Page 128
4.2 The Strain-Displacement Matrix 129 144......Page 144
4.3 Numerical Integration 134 149......Page 149
4.4 Loads, Masses, and Output 149 164......Page 164
4.5 Hierarchical Elements 157 172......Page 172
4.6 Higher Order Versus Lower Order Elements 163 178......Page 178
References 176 191......Page 191
5 THE PATCH TEST 179 194......Page 194
5.1 Patch Tests as Numerical Experiments 180 195......Page 195
5.2 The Patch Test as Proof of Convergence 185 200......Page 200
5.3 How to Pass the Patch Test 189 204......Page 204
5.4 Isoparametric Elements and the Patch Test 194 209......Page 209
5.5 A New Order of Respectability 199 214......Page 214
References 201 216......Page 216
6 INTERPOLATION FAILURE: LOCKING AND SHAPE SENSITIVITY 203 218......Page 218
6.1 Aliasing 205 220......Page 220
6.2 Locking of the Four-Node Rectangle 212 227......Page 227
6.3 Locking of the Constant Strain Triangle 224 239......Page 239
6.4 Locking in Other Rectangular Elements 227 242......Page 242
6.5 Locking in Other Disciplines 240 255......Page 255
6.6 Shape Sensitivity 241 256......Page 256
6.A Skewed Strain Components 255 270......Page 270
References 257 272......Page 272
7 REDUCED INTEGRATION AND SPURIOUS MODES 261 276......Page 276
7.1 The Benefits of Reduced Integration 262 277......Page 277
7.2 The Spurious Modes of an Element 266 281......Page 281
7.3 Spurious Modes in Fields of Elements 272 287......Page 287
7.4 Near Mechanisms 277 292......Page 292
7.5 Zero Energy Modes in Magnetostatics 281 296......Page 296
7.6 Selective Underintegration 287 302......Page 302
7.7 Assumed Strain Hybrid Formulations 29S 310......Page 310
7.8 Spurious Mode Stabilization 310 325......Page 325
References 314 329......Page 329
8 MORE REMEDIES FOR LOCKING 317 332......Page 332
8.1 Bubble Functions 318 333......Page 333
8.2 Drilling Freedoms 330 345......Page 345
8.3 Metric Interpolation 348 363......Page 263
8.4 Direct Assumed Strain Formulations 354 369......Page 369
References 366 381......Page 381
9 PLATE BENDING ELEMENTS 369 384......Page 384
9.1 Plate Theory 370 385......Page 385
9.2 Kirchhoff Plate Elements 378 393......Page 393
9.3 Mindlin Plate Elements 388 403......Page 403
9.4 Transverse Shear Locking 392 407......Page 407
9.5 Residual Bending Flexibility 406 421......Page 421
References 414 429......Page 429
10.1 Shell Theory 419 434......Page 434
10.2 The Use of Flat Plate Elements and Solid Elements in Shell Analysis 435 450......Page 450
10.3 Comparison of Performance in Curved Shell Applications 444 459......Page 459
10.4 Membrane Locking 450 465......Page 465
10.5 Curved Shell Elements 462 477......Page 477
References 481 496......Page 496
11.1 The Medical Analogy 485 500......Page 500
11.2 Remedies for Finite Element Disorders and Their Side Effects 486 501......Page 501
11.3 Diagnostic Tests and Other Tests 492 507......Page 507
11.4 The Limits of Finite Element Perfectibility 499 514......Page 514
References 517 532......Page 532
AUTHOR INDEX 521 536......Page 536
SUBJECT INDEX 525 540......Page 540
cover 1......Page 1
back cover 532 547......Page 547