Structural Analysis with Finite Elements

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Springer Science & Business Media, Jan 30, 2007 - Technology & Engineering - 598 pages
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Structural Analysis with Finite Elements, 2nd Edition provides a solid introduction to the foundation and the application of the finite element method in structural analysis. It offers new theoretical insight and practical advice on why finite element results are 'wrong,' why support reactions are relatively accurate, why stresses at midpoints are more reliable, why averaging the stresses sometimes may not help or why the equilibrium conditions are violated. This second edition contains additional sections on sensitivity analysis, on retrofitting structures, on the Generalized FEM (X-FEM) and on model adaptivity. An additional chapter treats the boundary element method, and related software is available at www.winfem.de.

 

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Contents

Plane problems
327
42 Strains and stresses
334
43 Shape functions
337
44 Plane elements
338
45 The patch test
344
46 Volume forces
346
47 Supports
347
48 Nodal stresses and element stresses
357

110 Least squares
33
111 Distance inside distance outside
37
112 Scalar product and weak solution
40
113 Equivalent nodal forces
42
114 Concentrated forces
44
115 Greens functions
51
116 Practical consequences
55
117 Why finite element results are wrong
57
118 Proof
64
119 Influence functions
69
120 Accuracy
80
121 Why resultant stresses are more accurate
86
122 Why stresses at midpoints are more accurate
88
123 Why stresses jump
99
125 Gauss points
104
126 The Dirac energy
110
127 How to predict changes
113
128 The influence of a single element
126
129 Retrofitting structures
130
130 Local errors and pollution
136
131 Adaptive methods
147
132 St Venants principle
172
133 Singularities
175
134 Actio reactio?
177
135 The output
181
136 Support conditions
183
137 Equilibrium
184
138 Temperature changes and displacement of supports
187
139 Stability problems
193
140 Interpolation
197
141 Polynomials
199
142 Infinite energy
208
143 Conforming and nonconforming shape functions
209
144 Partition of unity
211
145 Generalized finite element methods
213
146 Elements
220
147 Stiffness matrices
221
148 Coupling degrees of freedom
224
149 Numerical details
226
150 Warning
235
What are boundary elements?
239
21 Influence functions or Bettis theorem
240
22 Structural analysis with boundary elements
247
23 Comparison finite elementsboundary elements
262
Frames
269
32 The FE approach
270
33 Finite elements and the slope deflection method
289
34 Stiffness matrices
292
35 Approximations for stiffness matrices
298
36 Cables
305
37 Hierarchical elements
309
38 Sensitivity analysis
313
49 Truss and frame models
363
410 Twobay wall
365
412 Shear wall with suspended load
370
413 Shear wall and horizontal load
375
414 Equilibrium of resultant forces
378
415 Adaptive mesh refinement
383
416 Plane problems in soil mechanics
386
417 Incompressible material
393
419 Influence functions for mixed formulations
399
420 Error analysis
401
Slabs
415
51 Kirchhoff plates
416
52 The displacement model
421
53 Elements
422
54 Hybrid elements
425
55 Singularities of a Kirchhoff plate
429
56 ReissnerMindlin plates
431
57 Singularities of a ReissnerMindlin plate
436
58 ReissnerMindlin elements
439
59 Supports
441
510 Columns
443
511 Shear forces
451
512 Variable thickness
452
513 Beam models
459
514 Wheel loads
460
515 Circular slabs
461
516 T beams
462
517 Foundation slabs
469
518 Direct design method
476
519 Point supports
477
520 Study
480
Shells
485
62 Shells of revolution
488
63 Volume elements and degenerate shell elements
490
64 Circular arches
491
65 Flat elements
493
66 Membranes
498
Theoretical details
503
72 Greens identities
508
73 Greens functions
516
74 Generalized Greens functions
519
75 Nonlinear problems
526
76 The derivation of influence functions
529
77 Weak form of influence functions
535
78 Influence functions for other quantities
539
79 Shifted Greens functions
541
710 The dual space
552
711 Some concepts of error analysis
560
712 Important equations and inequalities
568
References
578
Index
593
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