Manolis / Polyzos Recent Advances in Boundary Element Methods

A Volume to Honor Professor Dimitri Beskos
1. Auflage 2009
ISBN: 978-1-4020-9710-2
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 467 Seiten

This volume, dedicated to Professor Dimitri Beskos, contains contributions from leading researchers in Europe, the USA, Japan and elsewhere, and addresses the needs of the computational mechanics research community in terms of timely information on boundary integral equation-based methods and techniques applied to a variety of fields. The contributors are well-known scientists, who also happen to be friends, collaborators as past students of Dimitri Beskos. Dimitri is one the BEM pioneers who started his career at the University of Minnesota in Minneapolis, USA, in the 1970s and is now with the University of Patras in Patras, Greece. The book is essentially a collection of both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the newer Mesh Reduction Methods (MRM), covering a variety of research topics. Close to forty contributions compose an over-500 page volume that is rich in detail and wide in terms of breadth of coverage of the subject of integral equation formulations and solutions in both solid and fluid mechanics.

Autoren/Hrsg.

Manolis, George

Polyzos, Demosthenes

Inhaltsverzeichnis

1;Editorial;6
2;Contents;8
3;Contributors;11
4;Biography of Dimitri Beskos;16
4.1;Personal Information;17
4.2;Address;17
4.3;Distinctions and Honours;17
4.4;Administrative Positions;18
4.5;Societies;18
4.6;Academic Positions;19
4.7;Publication Record;19
4.8;List of Publications – Books;20
4.9;List of Publications – Guest Editorials;21
4.10;List of Publications – Book Chapters;21
4.11;List of Publications – Journal Papers;23
4.12;Doctoral Students – University of Minnesota;32
4.13;Doctoral Students – University of Patras;33
5;Stability Analysis of Plates;35
5.1;1 Introduction;35
5.2;2 Basic Concepts;36
5.3;3 Shear Deformable Plate Boundary Integral Equations;39
5.4;4 Classical Plate Boundary Integral Equations;41
5.5;5 Approximation of Domain Integrals;42
5.6;6 Matrix Equations;43
5.7;7 Numerical Results;44
5.8;8 Conclusions;46
5.9;References;47
6;Multi-Level Fast Multipole BEM for 3- D Elastodynamics;49
6.1;1 Introduction;49
6.2;2 Elastodynamic Boundary Element Method;50
6.3;3 Elastodynamic Fast Multipole Method;51
6.4;4 Numerical Examples;56
6.5;5 Conclusions;60
6.6;References;61
7;A Semi-Analytical Approach for Boundary Value Problems with Circular Boundaries;62
7.1;1 Introduction;62
7.2;2 Methods of Solution;64
7.3;3 Illustrative Examples;71
7.4;4 Conclusions;74
7.5;References;75
8;The Singular Function Boundary Integral Method for Elliptic Problems with Boundary Singularities;76
8.1;1 Introduction;76
8.2;2 The Singular Function Boundary Integral Method;77
8.3;3 Convergence Analysis;80
8.4;4 Numerical Results for Laplacian Problems;82
8.5;5 The SFBIM for Biharmonic Problems;84
8.6;6 Conclusions;89
8.7;References;89
9;Fast Multipole BEM and Genetic Algorithms for the Design of Foams with Functional- Graded Thermal Conductivity;90
9.1;1 Introduction;90
9.2;2 The Fast Multipole Boundary Element Method and Modeling Considerations;91
9.3;3 The Representative Volume Element;93
9.4;4 Genetic Algorithms;95
9.5;5 Examples;97
9.6;6 Conclusions;102
9.7;References;103
10;An Integral Equation Formulation of Three- Dimensional Inhomogeneity Problems;104
10.1;1 Introduction;104
10.2;2 Basic Formulation;105
10.3;3 Numerical Examples;107
10.4;4 Conclusions;112
10.5;References;112
11;Energy Flux Across a Corrugated Interface of a Basin Subjected to a Plane Harmonic SH Wave;114
11.1;1 Introduction;114
11.2;2 Statement of Problem;115
11.3;3 Numerical Results;117
11.4;4 Summary and Conclusions;124
11.5;References;124
12;Boundary Integral Equations and Fluid- Structure Interaction at the Micro Scale;126
12.1;1 Introduction;126
12.2;2 Quasi-Static Stokes Flow with Slip Boundary Conditions;128
12.3;3 Gas Structure Interaction in the Free Molecule Regime;134
12.4;4 Numerical Application;138
12.5;5 Conclusions;142
12.6;References;142
13;A 2D Time-Domain BEM for Dynamic Crack Problems in Anisotropic Solids;145
13.1;1 Introduction;145
13.2;2 Problem Statement and BIEs;147
13.3;3 Numerical Solution Procedure;148
13.4;4 Numerical Examples;153
13.5;5 Conclusions;159
13.6;References;160
14;Simulation of Elastic Scattering with a Coupled FMBE- FE Approach;162
14.1;1 Introduction;162
14.2;2 FE Formulation for the Structural Domain;163
14.3;3 BE Formulation for the Fluid Domain;165
14.4;4 Coupled FMBE/FE Formulation;171
14.5;5 The Spherical Scatterer;172
14.6;6 Conclusion;175
14.7;References;175
15;An Application of the BEM Numerical Green’s Function Procedure to Study Cracks in Reissner’s Plates;177
15.1;1 Introduction;177
15.2;2 The BEM Applied to Reissner’s Plate Theory;178
15.3;3 Numerical Green’s Function Approach;179
15.4;4 Implementation Features;183
15.5;5 Stress Intensity Factors;185
15.6;6 Examples;185
15.7;7 Conclusion;190
15.8;References;191
16;General Approaches on Formulating Weakly- Singular BIES for PDES;192
16.1;1 Introduction;192
16.2;2 Part I: Weakly-Singular BIEs for Elasticity;196
16.3;3 Part II: Weakly-Singular BIEs for Acoustics;209
16.4;References;219
17;Dynamic Inelastic Analysis with BEM: Results and Needs;221
17.1;1 Introduction;221
17.2;2 Dynamic Inelastic Analysis with Boundary Elements;222
17.3;3 Numerical Examples;229
17.4;4 Conclusions and General Criticism;233
17.5;References;234
18;Quantifier-Free Formulae for Inequality Constraints Inside Boundary Elements;237
18.1;1 Introduction;237
18.2;2 Quantifier Elimination for the Quadratic Polynomial;240
18.3;3 Quantifier Elimination for the Cubic Polynomial;244
18.4;4 Conclusions;250
18.5;References;250
19;Matrix Decomposition Algorithms Related to the MFS for Axisymmetric Problems;251
19.1;1 Introduction;251
19.2;2 Axisymmetric Potential Problems;252
19.3;3 Axisymmetric Elasticity Problems;257
19.4;4 Numerical Results;261
19.5;5 Concluding Remarks;263
19.6;Appendix;263
19.7;References;264
20;Boundary Element Analysis of Gradient Elastic Problems;266
20.1;1 Introduction;266
20.2;2 Simplified Gradient Elastic Model, Integral Representation of the Problem;268
20.3;3 BEM Procedure;271
20.4;4 Numerical Results;273
20.5;5 Conclusions;277
20.6;References;278
21;The Fractional Diffusion-Wave Equation in Bounded Inhomogeneous Anisotropic Media. An AEM Solution;281
21.1;1 Introduction;281
21.2;2 The Initial Boundary Value Problem;282
21.3;3 The AEM Solution;284
21.4;4 Solution of the Semi-Discretised Equations;287
21.5;5 Examples;293
21.6;6 Conclusions;300
21.7;Appendix Approximation of Dac u(0);300
21.8;References;302
22;Efficient Solution for Composites Reinforced by Particles;303
22.1;1 Introduction;303
22.2;2 Description of the Model;305
22.3;3 Examples and Discussion;309
22.4;4 Conclusions;311
22.5;References;311
23;Development of the Fast Multipole Boundary Element Method for Acoustic Wave Problems;313
23.1;1 Introduction;313
23.2;2 Basic Equations for Acoustic Wave Problems;314
23.3;3 BIE Formulations;315
23.4;4 Fast Multipole Formulation for 2-D Acoustic Wave Problems;317
23.5;5 Fast Multipole Formulation for 3-D Acoustic Wave Problems;320
23.6;6 Numerical Examples;321
23.7;7 Conclusions;326
23.8;References;327
24;Some Issues on Formulations for Inhomogeneous Poroelastic Media;330
24.1;1 Introduction;330
24.2;2 Basic Poroelastic Formulation;332
24.3;3 Governing Equations for Inhomogeneous Poroelastic Media;333
24.4;4 The Laplace Transform;335
24.5;5 Exponential-Type Inhomogeneity;336
24.6;6 Poroelasticity Versus Themoelasticity;338
24.7;7 Conclusions;340
24.8;Appendix 1. The Algebraic Transformation;341
24.9;Appendix 2. Matrix Differential Equation for Exponential Case;341
24.10;References;343
25;Axisymmetric Acoustic Modelling by Time- Domain Boundary Element Techniques;344
25.1;1 Introduction;344
25.2;2 Basic Concepts;345
25.3;3 Time Integration;347
25.4;4 Space Integration;353
25.5;5 Time-Marching Scheme;357
25.6;6 Numerical Application;357
25.7;7 Conclusions;360
25.8;Appendix: Analytical Expressions for Time Integrals;360
25.9;References;362
26;Fluid-Structure Interaction by a Duhamel- BEM / FEM Coupling;363
26.1;1 Introduction;363
26.2;2 Fluid Modeling by the Duhamel-BEM Approach;364
26.3;3 Structure Modeling by the Newmark-FEM Approach;370
26.4;4 Fluid-Structure Coupling Procedure;371
26.5;5 Numerical Results;374
26.6;6 Conclusions;376
26.7;References;377
27;BEM Solution of Creep Fracture Problems Using Strain Energy Density Rate Concept;379
27.1;1 Introduction;379
27.2;2 Asymptotic Crack-Tip Fields in a Creeping Material;381
27.3;3 Boundary Integral Equations;382
27.4;4 Special Boundary Element Implementation and Solution Procedure;383
27.5;5 The Strain Energy Rate Definition;385
27.6;6 Numerical Examples;385
27.7;7 Conclusions;388
27.8;References;389
28;MFS with RBF for Thin Plate Bending Problems on Elastic Foundation;391
28.1;1 Introduction;391
28.2;2 Basic Equations of Thin Plate Bending;393
28.3;3 Formulation;394
28.4;4 Numerical Examples;398
28.5;5 Remarks and Conclusions;401
28.6;References;401
29;Time Domain B-Spline BEM Methods forWave Propagation in 3- D Solids and Fluids Including Dynamic Interaction Effects of Coupled Media;403
29.1;1 Introduction;403
29.2;2 Fundamentals;405
29.3;3 B-Spline BEM Formulations;407
29.4;4 Solution Procedures;410
29.5;5 Demonstrative Examples;417
29.6;References;419
30;A BEM Solution to the Nonlinear Inelastic Uniform Torsion Problem of Composite Bars;422
30.1;1 Introduction;422
30.2;2 Statement of the Problem;424
30.3;3 Incremental – Iterative Solution Algorithm;434
30.4;4 Integral Representations for the PrimaryWarping Function;434
30.5;5 Numerical Example;435
30.6;6 Conclusions;437
30.7;References;437
31;Time Domain BEM: Numerical Aspects of Collocation and Galerkin Formulations;438
31.1;1 Introduction;438
31.2;2 Time Domain Boundary Integral Equations;440
31.3;3 Boundary Element Formulations;445
31.4;4 Numerical Results;449
31.5;5 Conclusions;454
31.6;References;454
32;Some Investigations of Fast Multipole BEM in Solid Mechanics;456
32.1;1 Introduction;456
32.2;2 Application of FMBEM on Simulation of Composite Materials;457
32.3;3 Large-Scale Parallel Computation of FMBEM;460
32.4;4 Simulation of CNT Composites Using FMBEM;462
32.5;5 Simulation of Crack and Crack Growth Using FMBEM;464
32.6;6 FMBEM for 2D Elasto-Plasticity Problems;469
32.7;7 Concluding Remarks;471
32.8;References;471
33;Thermomechanical Interfacial Crack Closure: A BEM Approach;473
33.1;1 Introduction;473
33.2;2 Boundary Element Analysis of Thermoelastic Crack Closure;474
33.3;3 Fracture Characterization;477
33.4;4 Numerical Results;479
33.5;5 Conclusions;485
33.6;References;485
34;Author Index;487
35;Subject Index;489