Boundary element methods for engineers and scientists:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2003
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XV, 488 S. Ill., graph. Darst. |
| ISBN: | 3540004637 |
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MARC
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| 245 | 1 | 0 | |a Boundary element methods for engineers and scientists |c Lothar Gaul, Martin Kögl, Marcus Wagner |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2003 | |
| 300 | |a XV, 488 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Includes bibliographical references and index | ||
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Titel: Boundary element methods for engineers and scientists
Autor: Gaul, Lothar
Jahr: 2003
Contents
Part I. The Direct Boundary Element Method
1. Introduction.3
1.1 Numerical Solution of Engineering Problems.3
1.2 Historic Development of Boundary Element Method.G
1.3 The Method of Weighted Residuals.7
1.3.1 Collocation Method.8
1.3.2 Method of Moments.9
1.3.3 Galerkin's Method.9
1.3.4 Collocation by Subregions.9
1.3.5 Least Squares.10
1.3.6 Summary.11
1.4 Boundary Elements vs. Finite Elements.11
1.4.1 General Features.12
1.4.2 Comparison of FE and BE Formulations.13
1.5 Boundary Integral Method for 1-D Differential Equation.10
1.6 General Boundary Element Approach.20
2. Mathematical Preliminaries.23
2.1 Notation.23
2.1.1 Vector Notation and Matrix Representation of Vectors 23
2.1.2 Index Notation.25
2.2 Theory of Distributions .2G
2.2.1 Definition and Rules.27
2.2.2 Dirac Distribution and Heaviside Function.27
2.3 Integral Theorems.29
2.4 Time-Harmonic Motion .30
2.5 Introduction to the Calculus of Variations.31
3. Continuum Physics.35
3.1 Introduction.35
3.1.1 Continuous Media.35
3.1.2 Variables and Equations of State.3G
3.1.3 Crystal Structure of a Continuous Medium.37
3.2 Elastodynamics.38
X
Contents
39
3.2.1 Kinematics.
3.2.2 Kinetics.
3.2.3 Conservation of Mass - The Continuity Equation.44
3.2.4 Conservation of Linear Momentum.413
3.2.5 Conservation of Angular Momentum.47
3.2.G Conservation of Energy.48
3.2.7 Constitutive Equation .o0
3.2.8 Field Equations and Boundary Conditions.53
3.2.9 Elastodynamic Wave Equations.
3.2.10 Waves in Anisotropic Materials .5G
3.3 Heat Conduction.60
3.3.1 First Law of Thermodynamics.60
3.3.2 Second Law of Thermodynamics .61
3.3.3 Field Equations of Heat Conduction.63
3.3.4 Boundary and Initial Conditions.64
3.4 Electrodynamics.6o
3.4.1 Maxwell's Equations in Vacuum.65
3.4.2 Electromagnetic Wave Equations.67
3.4.3 Electrostatic Field in Macroscopic Media.68
3.4.4 Field Equation for Dielectrics.68
3.4.5 Electric Jump Conditions at Interfaces.70
3.4.6 Electric Boundary Conditions for an Ideal Conductor . 70
3.5 Thcrmoelasticity.71
3.5.1 First Law of Thermodynamics.71
3.5.2 Second Law of Thermodynamics .72
3.5.3 Constitutive Equations.73
3.5.4 Field Equations of Thcrmoelasticity.7G
3.5.5 Simplified Thermoclastic Theories.77
3.G Acoustics.79
3.G.1 The Acoustic Wave Equation.80
3.G.2 Constitutive Equations.81
3.6.3 The Velocity Potential.8G
3.G.4 Boundary Conditions in Acoustics.8G
3.6.5 Radiation Condition in Infinite Domains.87
3.7 Piezoelectricity.89
3.7.1 Polarisation in Piezoelectrics.90
3.7.2 Energy Balance and Thermodynamic Potentials.91
3.7.3 Constitutive Equations.92
3.7.4 Field Equations of Piezoelectricity.93
4. Boundary Element Method for Potential Problems.95
4.1 Introduction.95
4.2 BE Formulation of Laplace's Equation.96
4.2.1 Inverse Formulation of Differential Equation.96
4.2.2 Green's Representation Formula.98
Contents XI
4.2.3 Fundamental Solutions. 99
4.2.4 Boundary Integral Equation of the 2-D Problem. 99
4.2.5 Discretisation of the Boundary.104
4.2.G The Collocation Method .107
4.2.7 Modelling of Discontinuous Fluxes.110
4.3 Example: Steady-State Heat Conduction .114
4.3.1 Calculation of System Matrices .114
4.3.2 Assembly and Solution of Equations.120
4.3.3 The Analytical Solution.121
4.4 Calculation of Solution in the Domain.122
4.4.1 Potential in the Domain.122
4.4.2 Flux in the Domain.123
4.5 Poisson's Equation - Treatment of Source Terms.123
4.5.1 Calculation of Domain Integral by Cell Integration . 124
4.5.2 Calculation of Domain Integral by Transformation to
a Boundary Integral.127
4.5.3 Calculation of the Unknown Boundary Variables.130
4.6 Indirect Calculation of Diagonal Entries of if.131
4.7 Concentrated Sources.131
4.8 Subdoinains .132
4.9 Orthotropic Heat Conduction.134
4.10 Example: Coupling of Orthotropic and Isotropic Subdomains 136
4.10.1 Calculation of Matrix Elements and .138
4.10.2 Analytical Solution.140
5. Boundary Element Method for Elastic Continua.141
5.1 Integral Formulation of Equation of Motion.141
5.1.1 Method of Weighted Residuals.141
5.1.2 Inverse Statement.142
5.1.3 Reciprocal Work Principle.145
5.1.4 Somigliana's Identity .146
5.2 Derivation of Boundary Integral Equation.149
5.2.1 Boundary Extension Around Load Point.149
5.2.2 Integration over Boundary Extension re.151
5.2.3 Boundary Integral Equation.152
5.3 Numerical Implementation.152
5.3.1 Discretisation with Boundary Elements.153
5.3.2 Approximation of Boundary Variables.156
5.3.3 Matrix Assembly.157
5.4 Implementation of Anisotropic Fundamental Solutions .160
5.4.1 Fundamental Solutions in Elastostatics.160
5.4.2 Interpolation Scheme for Anisotropic Fundamental So-
lution .161
5.4.3 Evaluation of Anisotropic Fundamental Solution .165
5.5 Static Piezoelectricity.168
XII Contents
5.5
.1 Contracted Notation
5.5
1G8
170
2 Boundary Element Formulation
r ^ • .1 _.1/1
u.0.3 Numerical Example
0. Numerical Integration.17a
G.l Regular Integration in 1-D.176
6.1.1 Simpson's Rule.1"G
6.1.2 Gaussian Quadrature.179
G.2 Regular Integration in 2-D and 3-D.183
G.2.1 Multidimensional Gaussian Quadrature.183
0.2.2 Numerical Integration over Boundary Elements .184
G.3 Weakly Singular Integration.187
C.3.1 Weak Singularity in 2-D BEM .187
G.3.2 Weak Singularity in 3-D BEM.188
C.4 Strongly Singular Integration.193
6.4.1 Strong Singularity in 2-D BEM .193
G.4.2 Strong Singularity in 3-D BEM .199
Part II. The Dual Reciprocity Method
7. DRM for Potential Problems and Elastodynamics.207
7.1 Introduction.
7.2 Dual Reciprocity Formulation for Poisson's Equation.209
7.2.1 Dual Representation Formula.209
7.2.2 Boundary Integral Equation and Discretisation.211
7.2.3 Coefficients a and System of Equations.213
7.2.4 Calculation of Interior Values.214
7.3 The Wave Equation.214
7-4 The Hehnholtz Equation.217
7.5 Transient Heat Conduction.218
7.G Anisotropic Elastodynamics.219
7.6.1 Representation Formula.220
7.G.2 Dual Reciprocity Formulation.220
7.G.3 Boundary Integral Equation and System of Equations . 222
7.7 Particular Solutions.223
7.7.1 Types of Interpolation Functions.223
7.7.2 Interpolation Functions in Anisotropic Analysis.225
8. Solution of the Equations of Motion.227
8.1 System of Equations.227
8.2 The Elliptic Problem: Static and Time-Harmonic Analysis . . 228
8.2.1 Solution of the Equations.228
8.2.2 Numerical Example.229
8.3 The Eigenprohlem: Free Vibration Analysis.231
Contents XIII
8.3.1 Solution of the Eigenvalue Problem.231
8.3.2 Numerical Example.232
8.4 The Hyperbolic Problem: Transient Analysis.237
8.4.1 Direct Analysis .238
8.4.2 Modal Superposition.240
8.4.3 Instabilities in Time Integration.243
8.4.4 Numerical Example.250
8.5 The Parabolic Problem: Transient Heat Conduction.253
9. Dynamic Piezoelectricity.255
9.1 Dual Reciprocity Formulation.255
9.2 Coefficients oc and System of Equations.257
9.3 Solution of Piezoelectric Equations .258
9.4 Numerical Example.260
10. Coupled Thermoelasticity .263
10.1 Representation Formulae.263
10.1.1 Elastic Representation Formula.264
10.1.2 Thermal Representation Formula.265
10.1.3 Thermoelastic Representation Formula.265
10.2 Dual Reciprocity Formulation.267
10.3 The Coefficients ot .269
10.4 System of Equations.271
10.5 Solution of Thermoelastic Equations.272
10.5.1 Stationary Thermoelasticity.273
10.5.2 Uncoupled Quasi-Static Thermoelasticity.273
10.5.3 Theory of Thermal Stresses.273
10.5.4 Coupled Quasi-Static Thermoelasticity.274
10.5.5 Fully Coupled Thermoelasticity.275
10.6 Numerical Examples.275
10.6.1 Stationary Thermoelasticity.275
10.6.2 Quasi-Static Thermoelasticity.278
Part III. Hybrid Boundary Element Methods
11. Variational Principles of Continuum Mechanics.283
11.1 Virtual Quantities in Continuum Mechanics.283
11.1.1 Virtual Work.284
11.1.2 Strain Energy.285
11.1.3 Complementary Strain Energy.286
11.2 Single-Field Principles .287
11.2.1 Elastostatics.287
11.2.2 Elastodynamics.289
11.3 Generalised Principles.292
XIV Contents
292
11.3.1 Elastostatics.
11.3.2 Elastodynamics.
12. The Hybrid Displacement Method.29^
12.1 Introduction with Laplace's Equation.
12.2 Discretisation of the First Variation.299
12.2.1 Boundary Approximation .309
12.2.2 Domain Approximation.300
12.2.3 Domain Modification .302
12.3 Matrix Formulation for Potential Problems.303
12.3.1 Example for Laplace's Equation .
12.4 The HDBEM for Elastodynamics.310
12.4.1 Transformation to the Frequency Domain .313
12.4.2 Discretisation of the First Variation.315
12.4.3 Matrix Formulation in Elastodynamics.317
12.4.4 Computation of Field Points.319
12.5 Numerical Implementation.319
12.5.1 The L Matrix .319
12.5.2 The Vector of Equivalent Nodal Loads.320
12.5.3 The F Matrix.321
12.5.4 Efficient Calculation of the F Matrix.332
12.G The Concept of Rigid Body Motion in Elastostatics.33G
12.7 Harmonic Bending Waves of Beams.338
12.7.1 Hybrid Integral Formulation for the Beam.341
12.7.2 Example: Viscoelastic Beam Element.348
13. The Hybrid Stress Method for Acoustics.351
13.1 Hellinger-Reissner Principle for Acoustics.351
13.2 Matrix Formulation.354
13.2.1 Efficient Field Point Computation.356
13.3 Numerical Implementation for Acoustics.360
13.4 Orthogonality Properties of the HSBEM .3G2
13.4.1 Coordinate Sets and Transformation Relations.3G2
13.4.2 Finite Domains .304
13.4.3 Determination of the Fundamental Solution Matrix 0O 3G7
13.4.4 Infinite Domains.373
13.5 Applications in Acoustics.375
13.5.1 Interior Problems.37G
13.5.2 An Exterior Problem.378
13.G Fluid-Structure Interaction in the Frequency Domain .381
13.G.1 Model of Acoustic Fluid-Structure Interaction.381
13.G.2 Coupled Multi-Field Problem.385
13.G.3 Sound Radiation by Bending Waves.390
Contents XV
14. The Hybrid Boundary Element Method in Time Domain . 399
14.1 Time-domain Formulation for Elastodynamics.400
14.1.1 Non-Singular Formulation of the HDBEM.401
14.1.2 Positioning of the Load Points.404
14.1.3 Transformation of the Mass Matrix to the Boundary . 405
14.1.4 Numerical Examples.40G
14.2 Time-domain Formulation for Acoustics.413
14.2.1 Hybrid Boundary Element Formulation for the Fluid. 414
14.2.2 Approximation of Domain and Boundary Variables . 415
14.2.3 Boundary Integral Formulation.416
14.2.4 System of Discretised Equations.417
14.2.5 Numerical Examples.419
14.3 Fluid-Structure Interaction in the Time Domain.421
Part IV. Appendices
A. Properties of Elastic Materials.431
B. Fundamental Solutions .433
B.l Potential Problems.433
B.l.l Laplace's Equation.433
B.1.2 The Hehnholtz Equation.437
B.1.3 Anisotropic Form of Laplace's equation .440
B.2 Elastomechanics.442
B.2.1 Isotropic Elastostatics.442
B.2.2 Anisotropic Elastostatics.445
B.2.3 Isotropic Time-Harmonic Elastodynamics .448
B.2.4 Anisotropic Elastodynamics .451
B.3 Piezoelectricity.451
B.3.1 Static Piezoelectricity.452
B.3.2 Dynamic Piezoelectricity.453
C. Particular Solutions .455
C.l Poisson's Equation .455
C.2 Anisotropic Heat Conduction .457
C.3 Isotropic Elastostatics.457
C.4 Anisotropic Elastostatics.459
C.5 Piezoelectricity.459
D. The Bott-Duffin Inverse.461
References.463
Index
477 |
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| isbn | 3540004637 |
| language | English |
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| physical | XV, 488 S. Ill., graph. Darst. |
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| spelling | Gaul, Lothar 1945-2018 Verfasser (DE-588)108829316 aut Boundary element methods for engineers and scientists Lothar Gaul, Martin Kögl, Marcus Wagner Berlin [u.a.] Springer 2003 XV, 488 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Randelemente-Methode (DE-588)4076508-8 gnd rswk-swf Randelemente-Methode (DE-588)4076508-8 s DE-604 Kögl, Martin Sonstige oth Wagner, Marcus Sonstige (DE-588)115097656X oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010185698&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gaul, Lothar 1945-2018 Boundary element methods for engineers and scientists Randelemente-Methode (DE-588)4076508-8 gnd |
| subject_GND | (DE-588)4076508-8 |
| title | Boundary element methods for engineers and scientists |
| title_auth | Boundary element methods for engineers and scientists |
| title_exact_search | Boundary element methods for engineers and scientists |
| title_full | Boundary element methods for engineers and scientists Lothar Gaul, Martin Kögl, Marcus Wagner |
| title_fullStr | Boundary element methods for engineers and scientists Lothar Gaul, Martin Kögl, Marcus Wagner |
| title_full_unstemmed | Boundary element methods for engineers and scientists Lothar Gaul, Martin Kögl, Marcus Wagner |
| title_short | Boundary element methods for engineers and scientists |
| title_sort | boundary element methods for engineers and scientists |
| topic | Randelemente-Methode (DE-588)4076508-8 gnd |
| topic_facet | Randelemente-Methode |
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