Concepts and applications of finite element analysis:
Gespeichert in:
| Vorheriger Titel: | Cook, Robert Davis Concepts and applications of finite element analysis |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ [u.a.]
Wiley
2002
|
| Ausgabe: | 4. ed. |
| Schlagworte: | |
| Online-Zugang: | Table of Contents Inhaltsverzeichnis |
| Beschreibung: | XVI, 719 S. zahlr. graph. Darst. |
| ISBN: | 0471356050 9780471356059 |
Internformat
MARC
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| 245 | 1 | 0 | |a Concepts and applications of finite element analysis |c Robert D. Cook ... |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Hoboken, NJ [u.a.] |b Wiley |c 2002 | |
| 300 | |a XVI, 719 S. |b zahlr. graph. Darst. | ||
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| 650 | 4 | |a Finite-Elemente-Methode - Anwendung | |
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Datensatz im Suchindex
| _version_ | 1804129235792560128 |
|---|---|
| adam_text | CONTENTS
NOTATION
Chapter I INTRODUCTION
1
1.1
Finite Element Analysis
1
1.2
Problem Classification, Modeling, and Discretization
3
1.3
Interpolation. Elements, Nodes, and D.O.F.
5
1.4
Example Applications. History of
FEA
8
1.5
Solving a Problem by
FEA
11
1.6
Learning and Using
FEA
15
Analytical Problems
17
Chapter
2
ONE-DIMENSIONAL ELEMENTS AND COMPUTATIONAL
PROCEDURES
19
2.1
Introduction
19
2.2
Bar Element
20
2.3
Beam Element
24
2.4
Bar and Beam Elements of Arbitrary Orientation
29
2.5
Assembly of Elements
32
2.6
Properties of Stiffness Matrices
36
2.7
Boundary Conditions
40
2.8
Exploiting Sparsity. Solving Equations
42
2.9
Mechanical Loads. Stresses
46
2.10
Thermal Loads. Stresses
52
2.11
Structural Symmetry
54
2.12
Review. Remarks Regarding Modeling
57
2.13
An Application
59
Analytical Problems
62
Computational Problems
74
Chapter
3
BASIC ELEMENTS
78
3.1
Preliminaries
78
3.2
Interpolation and Shape Functions
83
3.3
Formulas for Element Matricies
88
3.4
Linear Triangle (CST)
91
3.5
Quadratic Triangle (LST)
95
3.6
Bilinear Rectangle (Q4)
96
3.7
Quadratic Rectangle (Q8, Q9)
100
3.8
Rectangular Solid Elements
102
3.9
Choice of Interpolation Functions
104
3.10
Improved Triangles and Quadrilaterals
106
ix
Contents
3.11
Nodal Loads 111
3.12
Stress Calculation
115
3.13
Nature of a Finite Element Solution
118
3.14
Example: A Simple Stress Concentration Problem
119
3.15
An Application with High Stress Gradient
121
Analytical Problems
124
Computational Problems
132
Chapter
4
FORMULATION TECHNIQUES: VARIATIONAL
METHODS
136
4.1
Introduction
136
4.2
Principle of Stationary Potential Energy
137
43
Problems Having Many D.O.F.
140
4.4
Potential Energy of an Elastic Body
142
4.5
The Rayleigh-Ritz Method
146
4.6
Comments Regarding the Rayleigh-Ritz Method
149
4.7
Strong Form and Weak Form
151
4.8
Finite Element Form of the Rayleigh-Ritz Method
156
4.9
Convergence of Finite Element Solutions
161
4.10
Additional Formulations. Hybrid Elements
165
Analytical Problems
171
Chapter
5
FORMULATION TECHNIQUES: GALERKIN
AND OTHER WEIGHTED RESIDUAL METHODS
179
5.1
Galerkin Method
179
5.2
Methods of Weighted Residuals (MWR)
182
5.3
Galerkin Finite Element Method in One Dimension
186
5.4
Integration by Parts
191
5.5
Galerkin Finite Element Method in Two Dimensions
193
5.6
A Mixed Formulation
195
Analytical Problems
198
Chapter
6
ISOPARAMETRIC ELEMENTS
202
6.1
Introduction
202
6.2
Bilinear Quadrilateral (Q4)
205
6.3
Quadrature: [k] Obtained by Numerical Integration
209
6.4
Quadratic Quadrilaterals (Q8, Q9)
213
63
Hexahedral Isoparametric Elements
217
6.6
Incompatible Modes. Nodeless D.O.F.
219
6.7
Static Condensation
221
6.8
Choices in Numerical Integration
223
6.9
Load Considerations
227
6.10
Stress Calculation
230
6.11
Effect of Element Geometry
234
6.12
Validity of Isoparametric Elements
237
6.13
Patch Test
238
Contents xi
6.14
A 2D
Application 240
6.15
A
3D Application 244
Analytical
Problems 247
Computational
Problems 255
Chapter
7
ISOPARAMETRIC TRIANGLES AND TETRAHEDRA
259
7.1
Reference Coordinates. Shape Functions
259
7.2
Element Characteristic Matrices
262
7.3
Analytical Integration. Area and Volume Coordinates
264
7.4
Numerical Integration
266
Analytical Problems
268
Chapter
8
COORDINATE TRANSFORMATION AND SELECTED
ANALYSIS OPTIONS
271
8.1
Transformation: Introduction and Vector Forms
271
8.2
Strain, Stress, and Material Property Transformation
273
8.3
Transformation of the Characteristic Matrix
275
8.4
Changing the Directions of Restraints
276
8.5
Connecting Dissimilar Elements. Rigid Elements
278
8.6
Higher Derivatives as Nodal D.O.F.
282
8.7
Fracture Mechanics. Singularity Elements
283
8.8
Elastic Foundations. Infinite Media
286
8.9
Structural Modification. Reanalysis
292
8.10
Tests of Element Quality
293
Analytical Problems
295
Computational Problems
299
Chapter
9
ERROR, ERROR ESTIMATION, AND CONVERGENCE
300
9.1
Sources of Error
300
9.2
Ill-Conditioning
302
9.3
The Condition Number
306
9.4
Diagonal Decay Test
308
9.5
Residuals
309
9.6
Discretization Error. Convergence Rate
310
9.7
Multimesh Extrapolation
315
9.8
Mesh Revision Methods
318
9.9
Gradient (Stress) Recovery and Smoothing
320
9.10
А
-Posteriori
Error Estimate
326
9.11
Adaptive Meshing
329
Analytical Problems
331
Computational Problems
335
Chapter
10
MODELING CONSIDERATIONS AND SOFTWARE USE
336
10.1
Introduction
336
10.2
Physical Behavior Versus Element Behavior
337
10.3
Element Shapes and Interconnection
340
xii
Contents
10.4
Test Cases and Pilot Studies
342
10.5
Material Properties
344
10.6
Loads and Reactions
347
10.7
Connections in Structures
348
10.8
Boundary Conditions
352
10.9
Repetitive Symmetry
354
10.10
Stress Concentrations. Submodels
356
10.11
Substructures
358
10.12
Planning an Analysis
360
10.13
Common Mistakes
363
10.14
Checking the Model
365
10.15
Critique of Computed Results
366
10.16
Design Optimization
369
10.17
Software
370
10.18
Concluding Remarks
371
Analytical Problems
371
Computational Problems
372
Chapter
11
FINITE ELEMENTS IN STRUCTURAL DYNAMICS
AND VIBRATIONS
373
11.1
Introduction
373
11.2
Dynamic Equations. Mass and Damping Matrices
374
11.3
Mass Matrices: Consistent, Diagonal, and Other
377
11.4
Natural Frequencies and Modes
383
11.5
Damping
388
11.6
Reduction of the Number of D.O.F.
390
11.7
Response History: Modal Methods
394
11.8
Response History:
Ritz
Vectors
398
11.9
Component Mode Synthesis (CMS)
400
11.10
Harmonic Response
405
11.11
Response History: Direct Integration Methods
407
11.12
Explicit Direct Integration
409
11.13
Implicit Direct Integration
416
11.14
Direct Integration: Stability and Accuracy Analysis
421
11.15
Analysis by Response Spectra
426
11.16
Remarks. Modeling Considerations
429
11.17
An Application: Vibration and Harmonic Response
436
11.18
An Application: Response History
439
Analytical Problems
444
Computational Problems
451
Chapter
12
HEAT TRANSFER AND SELECTED FLUID PROBLEMS
454
12.1
Heat Transfer: Introduction
454
12.2
Finite Element Formulation
459
12.3
Radiation. Nonlinear Heat Transfer Problems
462
12.4
Transient Thermal Analysis
464
12.5
Modeling Considerations. Remarks
467
Contents
xiii
12.6
An Application
469
12.7
Acoustic Frequencies and
Modes
474
12.8
Fluid-Structure
Interaction
477
12.9
Plane Incompressible Irrotational
Flow
480
Analytical Problems
482
Computational Problems
486
Chapter
13
CONSTRAINTS: PENALTY FORMS, LOCKING, AND
CONSTRAINT COUNTING
489
13.1
Explicit Constraints. Transformation Equations
489
13.2 Lagrange
Multipliers to Enforce Constraints
492
13.3
Penalty Functions to Enforce Constraints
493
13.4
Implicit Penalty Constraints and Locking
495
13.5
Constraint Counting
499
13.6
Remarks About Techniques for Incompressible Media
502
Analytical Problems
504
Chapter
14
SOLIDS OF REVOLUTION
508
14.1
Introduction. Elasticity Relations for Axial Symmetry
508
14.2
Axisymmetric Solid Elements
510
14.3
An Application
512
14.4
Loads Without Axial Symmetry: Introduction
516
14.5
Loads Without Axial Symmetry: Some Details of
FEA
521
Analytical Problems
524
Computational Problems
527
Chapter
15
PLATE BENDING
530
15.1
Introduction. Plate Behavior
530
15.2
C1
(Kirchhoff)
Plate Elements
536
15.3
C° (Mindlin) Plate Elements
542
15.4
Mindlin Beam. More Devices for C° Plate Elements
547
15.5
Boundary Conditions. Test Problems
551
15.6
An Application
553
Analytical Problems
556
Computational Problems
559
Chapter
16
SHELLS
561
16.1
Introduction
561
16.2
Circular Arches and Arch Elements
563
16.3
Shells of Revolution
570
16.4
General Shells: Three- and Four-Node Elements
574
16.5
General Shells: Curved Isoparametric Elements
578
16.6
Test Cases. Remarks
583
16.7
An Axisymmetric Shell Application
586
Analytical Problems
588
Computational Problems
591
xjv Contents
Chapter
17
NONLINEARITY: AN INTRODUCTION
595
17.1
Nonlinear Problems
595
17.2
Some Solution Methods
596
17.3
Plasticity: Introduction
602
17.4
Plasticity: General Formulation for Small Strains
606
17.5
Plasticity: Formulation for
Von
Mises
Theory
609
17.6
Plasticity: Some Computational Procedures
612
17.7
Nonlinear Dynamic Problems
616
17.8
Problems of Gaps and Contact
619
17.9
Geometric Nonlinearity
621
17.10
Modeling Considerations. Remarks
626
Analytical Problems
630
Computational Problems
636
Chapter
18
STRESS STIFFNESS AND BUCKLING
639
18.1
Introduction. Energy Considerations
639
18.2
Bar and Beam Elements
642
18.3
Plate Elements
645
18.4
A General Formulation
646
18.5
Calculation of Buckling Loads
648
18.6
Remarks on Stress Stiffness and Its Uses
650
18.7
Remarks and Examples
653
Analytical Problems
656
Computational Problems
661
Appendix A MATRICES: SELECTED DEFINITIONS AND
MANIPULATIONS
663
Appendix
В
SIMULTANEOUS ALGEBRAIC EQUATIONS
668
B.I Overview
668
B.2 Direct Solvers
668
B.3 Iterative Solvers
671
AppendixC EIGENVALUES AND EIGENVECTORS
675
C.I Overview
675
C.2 The Standard
Eigenproblem 675
C.3 The General
Eigenproblem 676
C.4 Solution Algorithms
679
REFERENCES
682
INDEX
711
|
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| ctrlnum | (OCoLC)248021568 (DE-599)BVBBV014340896 |
| dewey-full | 624.171 |
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| dewey-search | 624.171 |
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| dewey-tens | 620 - Engineering and allied operations |
| discipline | Bauingenieurwesen Mathematik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV014340896 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:01:55Z |
| institution | BVB |
| isbn | 0471356050 9780471356059 |
| language | English |
| lccn | 2001033009 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009835292 |
| oclc_num | 248021568 |
| open_access_boolean | |
| owner | DE-703 DE-1047 DE-91G DE-BY-TUM DE-824 DE-573 DE-860 DE-634 DE-83 DE-1050 |
| owner_facet | DE-703 DE-1047 DE-91G DE-BY-TUM DE-824 DE-573 DE-860 DE-634 DE-83 DE-1050 |
| physical | XVI, 719 S. zahlr. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Wiley |
| record_format | marc |
| spelling | Concepts and applications of finite element analysis Robert D. Cook ... 4. ed. Hoboken, NJ [u.a.] Wiley 2002 XVI, 719 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finite-Elemente-Methode - Anwendung Finite-Elemente-Methode - Baustatik Finite element method Structural analysis Engineering Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf Baustatik (DE-588)4112679-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s Anwendung (DE-588)4196864-5 s DE-604 Baustatik (DE-588)4112679-8 s Partielle Differentialgleichung (DE-588)4044779-0 s Numerische Mathematik (DE-588)4042805-9 s 1\p DE-604 Cook, Robert D. Sonstige oth 3. Auflage Cook, Robert Davis Concepts and applications of finite element analysis http://www.loc.gov/catdir/toc/onix05/2001033009.html Table of Contents Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009835292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Concepts and applications of finite element analysis Finite-Elemente-Methode - Anwendung Finite-Elemente-Methode - Baustatik Finite element method Structural analysis Engineering Partielle Differentialgleichung (DE-588)4044779-0 gnd Anwendung (DE-588)4196864-5 gnd Baustatik (DE-588)4112679-8 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4196864-5 (DE-588)4112679-8 (DE-588)4017233-8 (DE-588)4042805-9 |
| title | Concepts and applications of finite element analysis |
| title_auth | Concepts and applications of finite element analysis |
| title_exact_search | Concepts and applications of finite element analysis |
| title_full | Concepts and applications of finite element analysis Robert D. Cook ... |
| title_fullStr | Concepts and applications of finite element analysis Robert D. Cook ... |
| title_full_unstemmed | Concepts and applications of finite element analysis Robert D. Cook ... |
| title_old | Cook, Robert Davis Concepts and applications of finite element analysis |
| title_short | Concepts and applications of finite element analysis |
| title_sort | concepts and applications of finite element analysis |
| topic | Finite-Elemente-Methode - Anwendung Finite-Elemente-Methode - Baustatik Finite element method Structural analysis Engineering Partielle Differentialgleichung (DE-588)4044779-0 gnd Anwendung (DE-588)4196864-5 gnd Baustatik (DE-588)4112679-8 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Finite-Elemente-Methode - Anwendung Finite-Elemente-Methode - Baustatik Finite element method Structural analysis Engineering Partielle Differentialgleichung Anwendung Baustatik Finite-Elemente-Methode Numerische Mathematik |
| url | http://www.loc.gov/catdir/toc/onix05/2001033009.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009835292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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