A first course in the finite element method:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stamford, CT
Cengage Learning
2011
|
| Edition: | 4. ed. SI |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 798 S. Ill., graph. Darst. |
| ISBN: | 9780495667919 0495667919 |
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MARC
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| 100 | 1 | |a Logan, Daryl L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A first course in the finite element method |c Daryl L. Logan |
| 250 | |a 4. ed. SI | ||
| 264 | 1 | |a Stamford, CT |b Cengage Learning |c 2011 | |
| 300 | |a XX, 798 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020342116 | ||
Record in the Search Index
| _version_ | 1804142966159179776 |
|---|---|
| adam_text | Contents
1
Introduction
Prologue
1
1.1
Brief History
2
1.2
Introduction to Matrix Notation
4
1.3
Role of the Computer
6
1.4
General Steps of the Finite Element Method
7
1.5
Applications of the Finite Element Method
15
1.6
Advantages of the Finite Element Method
19
1.7
Computer Programs for the Finite Element Method
23
References
24
Problems
27
2
Introduction to the Stiffness (Displacement) Method
28
Introduction
28
2.1
Definition of the Stiffness Matrix
28
2.2
Derivation of the Stiffness Matrix for a Spring Element
29
2.3
Example of a Spring Assemblage
34
2.4
Assembling the Total Stiffness Matrix by Superposition
(Direct Stiffness Method)
37
2.5
Boundary Conditions
39
2.6
Potential Energy Approach to Derive Spring Element Equations
52
III
vi
▲ Contents
7.3
Convergence
of
Solution
367
7.4
Interpretation of
Stresses
368
7.5
Static Condensation
369
7.6
Flowchart for the Solution of Plane Stress/Strain Problems
374
7.7
Computer Program Assisted Step-by-Step Solution, Other Models,
and Results for Plane Stress/Strain Problems
374
References
381
Problems
382
8
Development of the Linear-Strain Triangle Equations
398
Introduction
398
8.1
Derivation of the Linear-Strain Triangular Element
Stiffness Matrix and Equations
398
8.2
Example LST Stiffness Determination
403
8.3
Comparison of Elements
406
References
409
Problems
409
9
Axisymmetric Elements
412
Introduction
412
9.1
Derivation of the Stiffness Matrix
412
9.2
Solution of an Axisymmetric Pressure Vessel
422
9.3
Applications of Axisymmetric Elements
428
References
433
Problems
434
10
Isoparametric Formulation
443
Introduction
443
10.1
Isoparametric Formulation of the Bar Element Stiffness Matrix
444
10.2
Rectangular Plane Stress Element
449
10.3
Isoparametric Formulation of the Plane Element Stiffness Matrix
452
10.4
Gaussian and Newton-Cotes Quadrature (Numerical Integration)
463
10.5
Evaluation of the Stiffness Matrix and Stress Matrix
by Gaussian Quadrature
469
Contents ▲
vii
10.6
Higher-Order Shape Functions
475
References
484
Problems
484
11
Three-Dimensional Stress Analysis
490
Introduction
490
1
1.1
Three-Dimensional Stress and Strain
490
11.2
Tetrahedral Element
493
11.3
Isoparametric Formulation
501
References
508
Problems
509
12
Plate Bending Element
514
Introduction
514
12.1
Basic Concepts of Plate Bending
514
12.2
Derivation of a Plate Bending Element Stiffness Matrix
and Equations
519
12.3
Some Plate Element Numerical Comparisons
523
12.4
Computer Solution for a Plate Bending Problem
524
References
528
Problems
529
13
Heat Transfer and Mass Transport
534
Introduction
534
13.1
Derivation of the Basic Differential Equation
535
13.2
Heat Transfer with Convection
538
13.3
Typical Units; Thermal Conductivities, K; and Heat-Transfer
Coefficients,
h
539
13.4
One-Dimensional Finite Element Formulation Using
a Variational Method
540
13.5
Two-Dimensional Finite Element Formulation
555
13.6
Line or Point Sources
564
13.7
Three-Dimensional Heat Transfer Finite Element Formulation
566
13.8
One-Dimensional Heat Transfer with Mass Transport
569
viii
▲ Contents
13.9
Finite Element
Formulation
of Heat Transfer with Mass Transport
by Galerkin s Method
569
lß.lOFlowchart
and Examples of a Heat-Transfer Program
574
References
577
Problems
577
14
Fluid Flow
593
Introduction
593
14.1
Derivation of the Basic Differential Equations
594
14.2
One-Dimensional Finite Element Formulation
598
14.3
Two-Dimensional Finite Element Formulation
606
14.4
Flowchart and Example of a Fluid-Flow Program
611
References
612
Problems
613
15
Thermal Stress
617
Introduction
617
15.1
Formulation of the Thermal Stress Problem and Examples
617
Reference
640
Problems
641
1
б
Structural Dynamics and Time-Dependent Heat Transfer
647
Introduction
647
16.1
Dynamics of a Spring-Mass System
647
16.2
Direct Derivation of the Bar Element Equations
649
16.3
Numerical Integration in Time
653
16.4
Natural Frequencies of a One-Dimensional Bar
665
16.5
Time-Dependent One-Dimensional Bar Analysis
669
16.6
Beam Element Mass Matrices and Natural Frequencies
674
16.7
Truss, Plane Frame, Plane Stress/Strain, Axisymmetric,
and Solid Element Mass Matrices
681
16.8
Time-Dependent Heat Transfer
686
Contents
16.9 Computer Program
Example
Solutions
for Structural
Dynamics 693
References
702
Problems 702
Appendix
A
Matrix Algebra 708
Introduction
708
Α.
1 Definition
of
a
Matrix 708
Α.
2 Matrix
Operations
709
Α.
3
Cofactor or Adjoint Method to Determine the Inverse of a Matrix
716
A.4 Inverse of a Matrix by Row Reduction
718
References
720
Problems
720
Appendix
В
Methods for Solution
of Simultaneous Linear Equations
722
Introduction
722
B.I General Form of the Equations
722
B.2 Uniqueness, Nonuniqueness, and Nonexistence of Solution
723
B.3 Methods for Solving Linear Algebraic Equations
724
B.4 Banded-Symmetric Matrices, Bandwidth, Skyline.
and
Wavefront
Methods
735
References
741
Problems
742
AppendixC Equations
f
rom
Elasticity Theory
744
Introduction
744
C.I Differential Equations of Equilibrium
744
C.2 Strain/Displacement and Compatibility Equations
746
C.3 Stress/Strain Relationships
748
Reference
751
χ
▲ Contents
Appendix D
Equivalent
Nodal
Forces
752
Problems 752
Appendix E
Principle of Virtual Work
755
References
758
Appendix
F
Geometric Properties of Structural
Steel Wide Flange Sections
759
Answers to Selected Problems
763
Index
789
|
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| indexdate | 2024-07-09T22:40:09Z |
| institution | BVB |
| isbn | 9780495667919 0495667919 |
| language | English |
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| physical | XX, 798 S. Ill., graph. Darst. |
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| publisher | Cengage Learning |
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| spelling | Logan, Daryl L. Verfasser aut A first course in the finite element method Daryl L. Logan 4. ed. SI Stamford, CT Cengage Learning 2011 XX, 798 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020342116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Logan, Daryl L. A first course in the finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4123623-3 |
| title | A first course in the finite element method |
| title_auth | A first course in the finite element method |
| title_exact_search | A first course in the finite element method |
| title_full | A first course in the finite element method Daryl L. Logan |
| title_fullStr | A first course in the finite element method Daryl L. Logan |
| title_full_unstemmed | A first course in the finite element method Daryl L. Logan |
| title_short | A first course in the finite element method |
| title_sort | a first course in the finite element method |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Finite-Elemente-Methode Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020342116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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