A pragmatic introduction to the finite element method for thermal and stress analysis: with the Matlab Toolkit SOFEA
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2006
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XII, 278 S. Ill., graph. Darst. |
| ISBN: | 9812704116 981256876X |
Internformat
MARC
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| 100 | 1 | |a Krysl, Petr |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A pragmatic introduction to the finite element method for thermal and stress analysis |b with the Matlab Toolkit SOFEA |c Petr Krysl |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2006 | |
| 300 | |a XII, 278 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| _version_ | 1804138999418191872 |
|---|---|
| adam_text | Contents
Preface v
1.
Model
of a Taut Wire
1
1.1
Deriving the PDE model
................... 1
1.2
Balance equation
........................ 2
1.3
Boundary conditions
..................... 2
1.4
Boundary conditions (in space)
................ 3
1.5
Initial conditions (boundary conditions in time)
...... 4
1.6
Anything else?
......................... 5
2.
The Method of
Galer
kin
7
2.1
Residual of the balance equation
............... 7
2.2
Integral test of the residual
.................. 8
2.3
Test function
.......................... 8
2.4
Trial function
.......................... 10
2.5
Manipulation of the residuals
................. 11
2.6
Stiffness and mass matrix
................... 13
2.7
Piecewise linear basis functions
................ 15
2.8
How are the Galerkin and Finite Element Methods Related
17
2.9
Numerical quadrature
..................... 18
2.10
Putting it together: system of ODE s
............ 21
Exercises
............................... 22
3.
Statics and Dynamics Examples for the Wire Model
27
3.1
Statics
............................. 28
3.2
Statics: uniform load
..................... 28
VII
viii A Pragmatic
Introduction to the Finite Element Method
3.3
Free vibration
......................... 32
3.4
Integration of transient motion
................ 33
3.4.1
Using built-in
Matlab
solver
............. 34
3.4.2
Using the Trapezoidal integrator
........... 35
Exercises
............................... 38
4.
Boundary Conditions for the Model of a Taut Wire
41
4.1
Mixed essential and natural boundary conditions
...... 42
4.2
Essential boundary conditions only
............. 43
4.3
Natural boundary conditions only
.............. 43
4.4
Overspecified boundary conditions
.............. 44
5.
Model of Heat Conduction
49
5.1
Balance equation
........................ 49
5.2
Constitutive equation
..................... 52
5.3
Boundary conditions
...................... 53
5.3.1
On the sufficiency of boundary conditions
...... 54
5.4
Initial condition
........................ 55
5.5
Summary of the PDE model of heat conduction
...... 56
Exercises
............................... 56
6.
Galerkin Method for the Model of Heat Conduction
57
6.1
Weighted residual formulation
................ 57
6.2
Reducing the model dimension
................ 59
6.3
Test and trial functions: basis functions on
triangulations
......................... 61
6.4
Basis functions on the standard triangle
........... 63
6.5
Discretizing the weighted residual equation
......... 66
6.6
Derivatives of the basis functions; Jacobian
......... 70
6.7
Numerical integration
..................... 74
6.8
Conductivity matrix
...................... 76
6.9
Surface heat transfer matrix and load
............ 80
Exercises
............................... 86
7.
Steady-state Heat Conduction Solutions
89
7.1
Steady-state heat conduction equation
............ 89
7.2
Thick-walled tube
....................... 89
7.3
Orthotropic insert
....................... 93
Contents ix
7.4 The
Т4
NAFEMS Benchmark
................ 96
8.
Transient Heat Conduction Solutions
101
8.1
Discretization in time for transient heat conduction
.... 101
8.2
The T3 NAFEMS Benchmark
................ 104
8.3
Transient cooling in a shrink-fitting application
....... 107
9.
Expanding the Library of Element Types 111
9.1
Quadratic triangle T6
..................... 112
9.2
Quadratic 1-D element L3
.................. 114
9.3
Point element PI
........................ 114
9.4
Integrating over
n-dimensional
domains
........... 115
9.5
Tetrahedron T4
........................ 120
9.6
Simplex elements
........................ 122
9.7
Quadrilateral Q4
........................ 123
9.8
Hexahedron H8
........................ 124
9.9
Extracting the mesh boundary
................ 124
Exercises
............................... 126
10.
Discretization Error, Error Control, and Convergence
129
10.1
Interpolation errors
...................... 129
10.1.1
Interpolation error for temperature
......... 129
10.1.2
Interpolation error for temperature gradient
.... 132
10.1.3
Controlling the error; Convergence rate
....... 134
10.2
Richardson extrapolation
................... 136
10.3
The T4 NAFEMS Benchmark revisited
........... 138
10.4
Graded meshes
......................... 139
10.5
Shrink fitting revisited
.................... 139
10.6
Representing functions by interpolation
........... 141
Exercises
............................... 143
11.
Model of Elastodynamics
145
11.1
Balance of linear momentum
................. 145
11.2
Stress
.............................. 147
11.2.1
Balance of angular momentum and stress symmetry.
150
11.3
Local equilibrium
....................... 152
11.3.1
Change of linear momentum
............. 152
11.3.2
Stress divergence
.................... 152
χ Α
Pragmatic Introduction to the Finite Element Method
11.3.3
All together now
.................... 156
11.4
Strains and displacements
................... 156
11.5
Constitutive equation
..................... 159
11.6
Boundary conditions
...................... 161
11.6.1
Example: concrete dam
................ 161
11.6.2
Example: rigid punch
................. 162
11.6.3
Formal definition of the boundary conditions
.... 163
11.6.4
Inadmissible concentrated boundary conditions
. 164
11.6.5
Symmetry and anti-symmetry
............ 166
11.6.6
Example: a pure-traction problem
.......... 168
11.6.7
Example: shaft under torsion
............. 170
11.6.8
Example: overspecified boundary conditions
.... 172
11.7
Initial conditions
........................ 172
12.
Galerkin Formulation for Elastodynamics
175
12.1
Manipulation of the residuals
................. 175
12.1.1
The first two steps
................... 175
12.1.2
Step
3:
Preliminaries
................. 176
12.1.3
Step
3:
The glorious conclusion
............ 177
12.2
Method of weighted residuals as the principle of
virtual work
.......................... 179
12.3
Discretizing
........................... 179
12.3.1
The trial function
................... 179
12.3.2
The test function
................... 181
12.3.3
Producing the requisite equations
.......... 182
12.4
The discrete equations: system of ODE s
.......... 184
12.4.1
Inerţial
term: Mass matrix
.............. 185
12.4.2
Body loads and traction loads
............ 186
12.4.3
Resisting forces: Stiffness matrix
........... 186
12.4.4
Summary of the elastodynamics ODE s
....... 187
12.5
Constitutive equations of linearly elastic materials
..... 188
12.5.1
General anisotropic material
............. 188
12.5.2
Orthotropic material
.................. 188
12.5.3
Transversely
isotropie
material
............ 189
12.5.4
Isotropie
material
................... 190
12.6
Imposed (thermal) strains
................... 191
12.7
Strain-displacement matrix
.................. 193
12.7.1
Transformation of basis
................ 194
12.8
Stiffness matrix
........................ 197
Contents xi
12.9 Pure-
traction
problems and singular stiffness
........ 199
Exercises
............................... 200
13.
Finite Elements for True
3-D
Problems
201
13.1
Modal analysis with the tetrahedron T4: the drum
..... 201
13.2
Modal analysis with the tetrahedron T4:
the composite rod
....................... 204
13.3
Tetrahedron T10
........................ 207
13.3.1
Example: the drum revisited
............. 208
13.4
The composite rod with the tetrahedron T10
........ 209
13.5
Static analysis with hexahedra H8 and H20
......... 210
13.5.1
Hexahedron H8
.................... 210
13.5.2
Dilatational locking
.................. 211
13.5.3
Shear locking
...................... 214
13.5.4
Thin clamped square plate with concentrated load
. 215
13.5.5
Quadratic element H20
................ 216
13.5.6
Quadratic element Q8
................. 220
13.5.7
Pinched cylinder
.................... 221
13.5.8
Pinched sphere
..................... 222
13.5.9
Beam deflection revisited
............... 223
13.6
Errors, validation, and verification
.............. 224
13.6.1
Verification and Prediction
.............. 226
13.6.2
Validation
....................... 227
13.6.3
Errors
.......................... 227
13.6.4
Using modeling to make predictions
......... 227
13.6.5
Using benchmarks
................... 228
Exercises
............................... 230
14.
Analyzing the Stresses
231
14.1
Singularities
.......................... 231
14.2
Interpretation of stresses
................... 234
14.3
Stress concentrations
..................... 235
15.
Plane Strain, Plane Stress, and Axisymmetric Models
237
15.1
Plane strain model reduction
................. 237
15.2
Plane stress model reduction
................. 240
15.3
Model reduction for axial symmetry
............. 242
15.4
Material stiffness for two-dimensional models
........ 245
xii
A Pragmatic Introduction to the Finite Element Method
15.5
Strain-displacement matrices for two-dimensional
models
............................. 246
15.6
Integration for two-dimensional models
........... 247
15.7
Thermal strains in two-dimensional models
......... 249
15.8
Examples
............................ 250
15.8.1
Thermal strains in a bimetallic assembly
...... 250
15.8.2
Orthotropic balloon
.................. 254
15.9
Transient dynamic analysis
.................. 257
15.9.1
Centered difference time stepping
.......... 257
15.9.2
Example: stress wave propagation
.......... 259
Exercises
............................... 263
16.
Consistency -f Stability
=
Convergence
265
16.1
Consistency
........................... 265
16.1.1
Completeness
...................... 265
16.1.2
Compatibility
..................... 267
16.2
Stability
............................ 268
16.2.1
Conclusion
....................... 269
Exercises
............................... 270
Bibliography
271
Index
273
This textbook provides an accessible and
self-contained description of the
Galerkin finite element method for the
two important models of continuum
mechanics, transient heat conduction
and eiastodynamics, from formulation A Pragmatic Introduction to
of the governing equations to
the Finite Element Method for
implementation in
Matlab.
Thermal and Stress Analysis
The coverage follows an intuitive
approach: the salient features of each
initial boundary value problem are
reviewed, including a thorough
description of the boundary conditions;
the method of weighted residuals is
applied to derive the discrete equations;
and clear examples are introduced to
illustrate the method.
|
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| author | Krysl, Petr |
| author_facet | Krysl, Petr |
| author_role | aut |
| author_sort | Krysl, Petr |
| author_variant | p k pk |
| building | Verbundindex |
| bvnumber | BV023801361 |
| classification_rvk | SK 910 |
| ctrlnum | (OCoLC)255583183 (DE-599)BVBBV023801361 |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV023801361 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:37:06Z |
| institution | BVB |
| isbn | 9812704116 981256876X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017443560 |
| oclc_num | 255583183 |
| open_access_boolean | |
| owner | DE-634 DE-703 |
| owner_facet | DE-634 DE-703 |
| physical | XII, 278 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Krysl, Petr Verfasser aut A pragmatic introduction to the finite element method for thermal and stress analysis with the Matlab Toolkit SOFEA Petr Krysl Singapore [u.a.] World Scientific 2006 XII, 278 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Elastodynamik (DE-588)4151692-8 gnd rswk-swf Wärmeleitung (DE-588)4064192-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Finite-Elemente-Methode (DE-588)4017233-8 s Kontinuumsmechanik (DE-588)4032296-8 s Wärmeleitung (DE-588)4064192-2 s Elastodynamik (DE-588)4151692-8 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017443560&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017443560&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Krysl, Petr A pragmatic introduction to the finite element method for thermal and stress analysis with the Matlab Toolkit SOFEA Finite-Elemente-Methode (DE-588)4017233-8 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd Elastodynamik (DE-588)4151692-8 gnd Wärmeleitung (DE-588)4064192-2 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4032296-8 (DE-588)4151692-8 (DE-588)4064192-2 (DE-588)4123623-3 |
| title | A pragmatic introduction to the finite element method for thermal and stress analysis with the Matlab Toolkit SOFEA |
| title_auth | A pragmatic introduction to the finite element method for thermal and stress analysis with the Matlab Toolkit SOFEA |
| title_exact_search | A pragmatic introduction to the finite element method for thermal and stress analysis with the Matlab Toolkit SOFEA |
| title_full | A pragmatic introduction to the finite element method for thermal and stress analysis with the Matlab Toolkit SOFEA Petr Krysl |
| title_fullStr | A pragmatic introduction to the finite element method for thermal and stress analysis with the Matlab Toolkit SOFEA Petr Krysl |
| title_full_unstemmed | A pragmatic introduction to the finite element method for thermal and stress analysis with the Matlab Toolkit SOFEA Petr Krysl |
| title_short | A pragmatic introduction to the finite element method for thermal and stress analysis |
| title_sort | a pragmatic introduction to the finite element method for thermal and stress analysis with the matlab toolkit sofea |
| title_sub | with the Matlab Toolkit SOFEA |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd Elastodynamik (DE-588)4151692-8 gnd Wärmeleitung (DE-588)4064192-2 gnd |
| topic_facet | Finite-Elemente-Methode Kontinuumsmechanik Elastodynamik Wärmeleitung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017443560&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017443560&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kryslpetr apragmaticintroductiontothefiniteelementmethodforthermalandstressanalysiswiththematlabtoolkitsofea |