Finite elements: computational engineering sciences
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester
Wiley
2012
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XX, 267 S. Ill., graph. Darst. |
| ISBN: | 9781119940500 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804149576825831424 |
|---|---|
| adam_text | Contents
Preface
xi
About the Author
xv
Notations
xvii
1
The Computational Engineering Sciences: an introduction
1
1.1
Engineering Simulation
1
1.2
A Problem-Solving Environment
3
1.3
Weak Formulation Essence
4
1.4
Decisions on Forming WSN
6
1.5
Discrete WS^Implementations
8
1.6
Chapter Summary
10
References
11
2
Problem Statements: in the engineering sciences
13
2.1
Engineering Simulation
13
2.2
Continuum Mechanics Viewpoint
14
2.3
Continuum Conservation Principle Forms
14
2.4
Constitutive Closure for Conservation Principle PDEs
16
2.5
Engineering Science Continuum Mechanics
20
References
21
3
Some Introductory Material: PDEs, BCs, solutions, discrete concepts
23
3.1
Example Linear Heat Conduction Solutions
23
3.2
Multidimensional PDEs, Separation of Variables
24
3.3
Mathematical Foundation Essence for GWSN
28
3.4
A Legacy FD Construction
29
3.5
An FD Approximate Solution
31
3.6 Lagrange
Interpolation Polynomials
32
viii Contents
3.7
Chapter Summary
33
Exercises
34
References
34
4
Heat Conduction: an FE weak statement tutorial
35
4.1
A Steady Heat Conduction Example
35
4.2
Weak Form Approximation, Error Extremization
36
4.3
GWSN Discrete Implementation, FE Trial Space Basis
38
4.4
Finite Element Matrix Statements
40
4.5
Assembly of
{WS},,
to form Algebraic GWS 1
42
4.6
Solution Accuracy, Error Distribution
44
4.7
Convergence, Boundary Heat Flux
45
4.8
Chapter Summary
46
Exercises
46
Reference
46
5
Steady Heat Transfer,
я
= 1:
GYVS*1 implemented with
{Nkiia)),
1 <
к
< 3,
accuracy, convergence, nonlinearity, templates
47
5.1
Introduction
47
5.2
Steady Heat Transfer,
и
= 1 48
5.3
FE k
= 1
Trial Space Basis Matrix Library
50
5.4
Object-Oriented GWS 1 Programming
53
5.5
Higher Completeness Degree Trial Space Bases
56
5.6
Global Theory, Asymptotic Error Estimate
59
5.7
Nonsmooth Data, Theory Generalization
63
5.8
Temperature-Dependent Conductivity, Nonlinearity
65
5.9
Static Condensation, p-Elements
68
5.10
Chapter Summary
70
Exercises
72
Computer Labs
72
References
73
6
Engineering Sciences,
я
= 1:
GWS*1 {Nk(&}
implementations in the computational engineering sciences
75
6.1
Introduction
75
6.2
The Euler-Bernoulli Beam Equation
76
6.3
Euler-Bernoulli Beam Theory GWS* Reformulation
81
6.4
Timoshenko Beam Theory
87
6.5
Mechanical Vibrations of a Beam
92
6.6
Fluid Mechanics, Potential Flow
100
6.7
Electromagnetic Plane Wave Propagation
104
6.8
Convection-Radiation Finned Cylinder Heat Transfer
105
6.9
Chapter Summary
113
Contents ¡x
Exercises
1
15
Computer Labs 5
References
116
7
Steady Heat
Transfer,
n
> 1:
и
= 2,3
GWS 1 for
D
E
+
BCs,
FE
bases,
convergence, error mechanisms
117
7.1
Introduction j
7.2
Multidimensional FE Bases and
DOF
118
7.3
Multidimensional FE Operations for
{Νλ(ζα)|
121
7.4
The NC
к
= 1,2
Basis FE Matrix Library
124
7.5
NC Basis {WS)e Template, Accuracy, Convergence
127
7.6
The Tensor Product Basis Element Family
130
7.7
Gauss Numerical Quadrature
Д
= 1
TP
Basis Library
132
7.8
Convection-Radiation
ВС
GWS^Implementa
tion
136
7.9
Linear Basis GWS Template Unification
140
7.10
Accuracy, Convergence Revisited
141
7.11
Chapter Summary I43
Exercises
144
Computer Labs
145
References
145
8
Finite Differences of Opinion: FE GWS*1 connections to
FD, FV
methods
147
8.1
The FD-FE Correlation 147
8.2
The FV-FE Correlation
150
8.3
Chapter Summary I54
Exercises
155
9
Convection-Diffusion,
и
= 1:
unsteady energy transport,
accuracy/convergence, dispersion error, numerical diffusion
157
9.1
Introduction
157
9.2
The Galerkin Weak Statement
158
9.3
G
WS 1
Completion for Time Dependence
160
9.4
GWS*1
+
ÖTS
Algorithm Templates
161
9.5
GWS
+
OTS Algorithm Asymptotic Error Estimates
163
9.6
Performance Verification Test Cases
164
9.7
Dispersive Error Characterization
167
9.8
A Modified Galerkin Weak Statement
171
9.9
Verification Problem Statements Revisited
174
9.10
Unsteady Heat Conduction
177
9.11
Chapter Summary
179
Exercises
180
Computer Labs
180
References
181
χ
Contents
10
Convection
-
Diffusion,
я
>1:
и
= 2, 3
GWS VmGWS 1
+
ÖTS,
stability, error characterization, linear algebra
183
10.1
The Problem Statement
183
10.2
G
WS 1 +
#TS Formulation Reprise
185
10.3
Matrix Library Additions, Templates
186
10.4
mPDE Galerkin Weak Forms, Theoretical Analyses
188
10.5
Verification, Benchmarking, and Validation
192
10.6
Mass Transport, the Rotating Cone Verification
193
10.7
The Gaussian Plume Benchmark
196
10.8
Steady
η-Ό
Peclet Problem Verification
197
10.9
Mass Transport, a Validated
η
= 3
Experiment
200
10.10
Numerical Linear Algebra, Matrix Iteration
203
10.11
Newton and AF
TP
Jacobian Templates
210
10.12
Chapter Summary
211
Exercises
213
Computer Labs
213
References
214
11
Engineering Sciences,
я
> 1:
GWS11 [Nk(lal
η;)>
implementations
in the
я
-D
computational engineering sciences
215
11.1
Introduction
215
11.2
Structural Mechanics
216
11.3
Structural Mechanics, Virtual Work FE Implementation
219
11.4
Plane Stress/Strain GWS Implementation
221
11.5
Plane Elasticity Computer Lab
224
11.6
Fluid Mechanics, Incompressible-Thermal Flow
226
11.7
Vorticity-Streamfunction GWS 1
+ ÖTS
Algorithm
231
11.8
An Isothermal INS Validation Experiment
234
11.9
Multimode Convection Heat Transfer
238
11.10
Mechanical Vibrations, Normal Mode GWS
242
11.11
Normal Modes of a Vibrating Membrane
245
11.12
Multiphysics Solid-Fluid Mass Transport
248
11.13
Chapter Summary
254
Exercises
257
Computer Labs
257
References
258
12
Conclusion
261
Index
263
FINITE
ELEMENTS
Computational
ENGINEERING SCIENCES
A. J. BAKER
Tennessee, USA
Uniting
weak form theory fundamentals with hands-on computer practice, this book
gives readers a firm appreciation of control of error mechanisms that underlie discrete
approximation algorithms in the engineering sciences. The focus is rigorous computable
formulations relevant to the computational engineering sciences, discretely implemented
via finite element
(FĽ)
trial space bases, tor a diverse range of topics including: solid
mechanics and vibrations; heat conduction and heat transfer; fluid mechanics and
heat/mass convective transport.
It provides a holistic view of the topic ranging from distinct engineering problem statements
that can be solved via weak form based FE algorithms, to each specific development
completely implemented for computing. Additional computational aspects of FE
methodology are provided at a companion website facilitating broadly coupled
• ;
multi-physics implementations.
Key features:
Avoids abstract mathematical concepts while emphasising the integration
of theory with discrete computational implementation via calculus
•
Takes a cross-discipline continuum mechanics viewpoint
Includes
MATLAB
toolbox and .m files, downloadable from a companion website,
immediately enabling hands-on computing in all covered disciplines
Website features eight topical lectures from the author s own academic course
He is an elected Fellow ot the International
Associât
ι
,.
,„л
tjjg
цѕ
Association for Computational
:
American Institute of Aeronautics and
Astronautici
www.wiley.com/go/baker/finite
Also available
as an
e
-book
|
| any_adam_object | 1 |
| author | Baker, Allen J. 1936- |
| author_GND | (DE-588)124829686 |
| author_facet | Baker, Allen J. 1936- |
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| callnumber-first | T - Technology |
| callnumber-label | TA347 |
| callnumber-raw | TA347.F5 |
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| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | SK 910 |
| ctrlnum | (OCoLC)816306898 (DE-599)BVBBV040500903 |
| dewey-full | 620.001/51825 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.001/51825 |
| dewey-search | 620.001/51825 |
| dewey-sort | 3620.001 551825 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV040500903 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:25:06Z |
| institution | BVB |
| isbn | 9781119940500 |
| language | English |
| lccn | 2012011745 |
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| physical | XX, 267 S. Ill., graph. Darst. |
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| spelling | Baker, Allen J. 1936- Verfasser (DE-588)124829686 aut Finite elements computational engineering sciences A. J. Baker 1. publ. Chichester Wiley 2012 XX, 267 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finite element method Computerunterstütztes Verfahren (DE-588)4139030-1 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Ingenieurwissenschaften (DE-588)4137304-2 s Computerunterstütztes Verfahren (DE-588)4139030-1 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025347683&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025347683&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Baker, Allen J. 1936- Finite elements computational engineering sciences Finite element method Computerunterstütztes Verfahren (DE-588)4139030-1 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4139030-1 (DE-588)4137304-2 (DE-588)4017233-8 |
| title | Finite elements computational engineering sciences |
| title_auth | Finite elements computational engineering sciences |
| title_exact_search | Finite elements computational engineering sciences |
| title_full | Finite elements computational engineering sciences A. J. Baker |
| title_fullStr | Finite elements computational engineering sciences A. J. Baker |
| title_full_unstemmed | Finite elements computational engineering sciences A. J. Baker |
| title_short | Finite elements |
| title_sort | finite elements computational engineering sciences |
| title_sub | computational engineering sciences |
| topic | Finite element method Computerunterstütztes Verfahren (DE-588)4139030-1 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Finite element method Computerunterstütztes Verfahren Ingenieurwissenschaften Finite-Elemente-Methode |
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