The finite element method: its fundamentals and applications in engineering
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific Publ.
2011
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 326 S. graph. Darst. |
| ISBN: | 9789814350570 9789814350563 9814350567 9814350575 |
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MARC
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| 100 | 1 | |a Chen, Zhangxin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The finite element method |b its fundamentals and applications in engineering |c Zhangxin Chen |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific Publ. |c 2011 | |
| 300 | |a XXI, 326 S. |b 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 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-024672296 | ||
Record in the Search Index
| _version_ | 1804148743069499392 |
|---|---|
| adam_text | Contents
Preface
vii
List of Figures
xvii
List of Tables
xxi
1.
One-Dimensional Model Problems
1
1.1.
Examples of one-dimensional problems
........... 1
1.2.
The finite element method
.................. 4
1.2.1.
Basis (shape) functions
............... 6
1.2.2.
Linear systems
.................... 7
1.3.
Boundary conditions
..................... 9
1.3.1.
Nonhomogeneous Dirichlet boundary
conditions
....................... 10
1.3.2.
General boundary conditions
............ 11
1.4.
Local coordinate formulation
................. 12
1.4.1.
Element matrices
................... 12
1.4.2.
Local coordinate transformation
.......... 13
1.5.
Computer programming considerations
........... 15
1.6.
Equivalence and error estimates
............... 18
1.7.
Exercises
............................ 21
2.
Two-Dimensional Model Problems
27
2.1.
Two-dimensional differential problems
........... 27
2.2.
The finite element method
.................. 30
2.2.1.
Green s formula
................... 30
2.2.2.
Variational formulation
............... 31
2.2.3.
Basis (shape) functions
............... 33
2.2.4.
Linear systems
.................... 35
xi
x¡¡
The Finite Element Methods
2.3.
Extensions to general boundary conditions
......... 38
2.3.1.
Nonhomogeneous Dirichlet boundary
conditions
....................... 38
2.3.2.
General boundary conditions
............ 40
2.4.
Local coordinate formulations
................ 42
2.4.1.
Local element matrices
............... 42
2.4.2.
Construction of
triangulations
........... 43
2.4.3.
Assembly of stiffness matrices
............ 45
2.4.4.
Local coordinate transformation
.......... 46
2.5.
Programming considerations
................. 48
2.5.1.
Numbering of nodes
................. 49
2.5.2.
Matrix storage
.................... 51
2.5.3.
Computer program
.................. 51
2.6.
Error estimates
........................ 58
2.7.
Exercises
............................ 60
3.
General Variational Formulation
69
3.1.
Continuous variational formulation
............. 69
3.2.
The finite element method
.................. 70
3.3.
Examples
........................... 71
3.4.
Exercises
............................ 79
4.
One-Dimensional Elements and their Properties
81
4.1.
Element classification
..................... 82
4.2.
Different approaches for deriving basis functions
...... 82
4.2.1.
Global coordinate approach
............. 82
4.2.2.
Local coordinate transformation approach
..... 84
4.2.3.
Interpolation function approach
.......... 85
4.3.
Lagrangian elements
..................... 85
4.4.
Hermitian elements
...................... 86
4.5.
Exercises
............................ 87
5.
Two-Dimensional Elements and their Properties
89
5.1.
Rectangular and quadrilateral elements
........... 89
5.1.1.
Lagrangian rectangular elements
.......... 90
5.1.2.
Serendipity elements
................. 93
5.1.3.
Hermitian rectangular elements
........... 94
5.1.4.
Quadrilateral elements
................ 96
5.2.
Triangular elements
...................... 97
5.2.1.
Natural coordinates in two dimensions
....... 98
5.2.2.
Lagrangian triangular elements
........... 100
Contents xiii
5.2.3. Hermitian
triangular
elements
........... 104
5.3.
Exercises
............................ 109
6.
Three-Dimensional Elements and their Properties 111
6.1.
Hexahedral elements
.....................
Ill
6.1.1.
Lagrangian hexahedral elements
.......... 112
6.1.2.
Serendipity elements
................. 113
6.2.
Tetrahedral elements
..................... 114
6.2.1.
Natural coordinates in three dimensions
...... 115
6.2.2.
Natural coordinates in
cř-dimensions
........ 117
6.2.3.
Lagrangian tetrahedral elements
.......... 118
6.2.4.
Hermitian tetrahedral elements
........... 119
6.3.
Pentahedral elements
..................... 120
6.4.
Isoparametric elements
.................... 122
6.5.
Choice of an element
..................... 124
6.6.
General domains
....................... 124
6.7.
Quadrature rules
....................... 128
6.7.1.
One dimension
.................... 128
6.7.2.
Rectangles and bricks
................ 129
6.7.3.
Triangles and tetrahedra
.............. 130
6.8.
Exercises
............................ 132
7.
Finite Elements for Transient and Nonlinear
Problems
135
7.1.
Finite elements for transient problems
........... 135
7.1.1.
A one-dimensional model problem
......... 136
7.1.2.
A semi discrete scheme in space
.......... 138
7.1.3.
Fully discrete schemes
................ 140
7.2.
Finite elements for nonlinear problems
........... 144
7.2.1.
Linearization approach
............... 145
7.2.2.
Extrapolation time approach
............ 146
7.2.3.
Implicit time approximation
............ 148
7.2.4.
Explicit time approximation
............ 149
7.3.
Exercises
............................ 150
8.
Application to Solid Mechanics
151
8.1.
Plane stress and plane strain
................. 151
8.1.1.
Kinematics
...................... 152
8.1.2.
Equilibrium
...................... 153
8.1.3.
Material laws
..................... 154
8.1.4.
Boundary conditions
................. 157
8.1.5.
The finite element method
............. 158
xiv
The Finite Element Methods
8.2.
Three-dimensional solids
................... 161
8.3.
Axisymmetric solids
...................... 165
8.3.1. Anisotropie
material
................. 167
8.3.2. Isotropie
material
.................. 167
8.4.
Exercises
............................ 169
9.
Application to Fluid Mechanics
171
9.1.
Equations of fluid dynamics
................. 172
9.2.
A characteristic-based splitting method
........... 174
9.2.1.
An explicit characteristic-based method
...... 175
9.2.2.
Application to fluid mechanics
........... 178
9.2.3.
Solution schemes in time
.............. 184
9.2.4.
Remarks on the splitting method
.......... 185
9.3.
The finite element method
.................. 187
9.4.
The nonconforming finite element method
......... 189
9.5.
The mixed finite element method
.............. 191
9.6.
The Navier-Stokes equations
................. 194
9.7.
Exercises
............................ 195
10.
Application to Porous Media Flow
197
10.1.
Single-phase flow
....................... 197
10.1.1.
Basic differential equations
............. 197
10.1.2.
Units
......................... 198
10.1.3.
Different forms of flow equations
.......... 199
10.1.4.
Boundary and initial conditions
.......... 203
10.2.
Two-phase flow
........................ 204
10.2.1.
Basic differential equations
............. 204
10.2.2.
Alternative differential equations
.......... 205
10.2.3.
Boundary conditions
................. 210
10.3.
Finite element solution of single-phase flow
......... 212
10.3.1.
Treatment of initial conditions
........... 213
10.3.2.
The finite element method
............. 213
10.3.3.
Practical issues
.................... 217
10.4.
Exercises
............................ 220
11.
Other Finite Element Methods
221
11.1.
The CVFE method
...................... 221
11.1.1.
The basic CVFE method
.............. 222
11.1.2.
Positive transmissibilities
.............. 225
11.1.3.
The CVFE grid construction
............ 226
11.1.4.
Flux continuity
.................... 228
Contents xv
11.2.
Multipoint flux approximations
............... 230
11.2.1.
Definition of MPFA
................. 230
11.2.2.
А
-orthogonal grids
.................. 233
11.3.
The nonconforming finite element method
......... 235
11.3.1.
Second-order partial differential problems
..... 236
11.3.2.
Nonconforming finite elements on triangles
.... 236
11.4.
The mixed finite element method
.............. 240
11.4.1.
A one-dimensional model problem
......... 241
11.4.2.
A two-dimensional model problem
......... 247
11.4.3.
Extension to boundary conditions
of other kinds
..................... 250
11.4.4.
Mixed finite element spaces
............. 253
11.5.
The discontinuous finite element method
.......... 258
11.5.1.
DG methods
..................... 258
11.5.2.
Stabilized DG methods
............... 263
11.6.
The characteristic finite element method
.......... 264
11.6.1.
The modified method of characteristics
...... 266
11.6.2.
The Eulerian- Lagrangian localized
adjoint method
.................... 274
11.7.
The adaptive finite element method
............. 278
11.7.1.
Local grid refinement in space
........... 279
11.7.2.
Data structures
.................... 284
11.7.3
A posteriori error estimates
............. 285
11.8.
The multiscale finite element method
............ 293
11.8.1.
The multiscale finite element method
....... 294
11.8.2.
Boundary conditions of basis functions
....... 295
11.9.
Exercises
............................ 296
Bibliography
309
Index
319
|
| any_adam_object | 1 |
| author | Chen, Zhangxin |
| author_facet | Chen, Zhangxin |
| author_role | aut |
| author_sort | Chen, Zhangxin |
| author_variant | z c zc |
| building | Verbundindex |
| bvnumber | BV039812007 |
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| dewey-full | 620.00151825 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.00151825 |
| dewey-search | 620.00151825 |
| dewey-sort | 3620.00151825 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Maschinenbau / Maschinenwesen Mathematik |
| format | Book |
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| id | DE-604.BV039812007 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:11:59Z |
| institution | BVB |
| isbn | 9789814350570 9789814350563 9814350567 9814350575 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024672296 |
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| open_access_boolean | |
| owner | DE-1050 DE-703 DE-29T DE-83 |
| owner_facet | DE-1050 DE-703 DE-29T DE-83 |
| physical | XXI, 326 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific Publ. |
| record_format | marc |
| spelling | Chen, Zhangxin Verfasser aut The finite element method its fundamentals and applications in engineering Zhangxin Chen Singapore [u.a.] World Scientific Publ. 2011 XXI, 326 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf 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=024672296&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Zhangxin The finite element method its fundamentals and applications in engineering Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4017233-8 |
| title | The finite element method its fundamentals and applications in engineering |
| title_auth | The finite element method its fundamentals and applications in engineering |
| title_exact_search | The finite element method its fundamentals and applications in engineering |
| title_full | The finite element method its fundamentals and applications in engineering Zhangxin Chen |
| title_fullStr | The finite element method its fundamentals and applications in engineering Zhangxin Chen |
| title_full_unstemmed | The finite element method its fundamentals and applications in engineering Zhangxin Chen |
| title_short | The finite element method |
| title_sort | the finite element method its fundamentals and applications in engineering |
| title_sub | its fundamentals and applications in engineering |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024672296&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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