Boundary Element Topics: Proceedings of the Final Conference of the Priority Research Programme Boundary Element Methods 1989–1995 of the German Research Foundation October 2–4, 1995 in Stuttgart

505 Pages·1997·15.345 MB·English

by  Prof Dr.-Ing. Wolfgang L. Wendland (auth.), Prof Dr.-Ing. Wolfgang L. Wendland (eds.)

Boundary Element Topics
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Wolfgang L. Wendland (Editor)
Boundary Element Topics
Proceedings of the Final Conference
of the Priority Research Programme
Boundary Element Methods 1989-1995
of the German Research Foundation
October 2-4, 1995 in Stuttgart
With 151 Figures
, Springer
Prof. Dr.-Ing. Wolfgang L. Wendland
UniversiUit Stuttgart
Mathematisches Institut A
Pfaffenwaldring 57
0-70569 Stuttgart / Germany
ISBN-13: 978-3-642-64554-9 e-ISBN-13: 978-3-642-60791-2
DOl: 10.1007/978-3-642-60791-2
CIP data appl ied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Boundary element topics: proceedings of the Final Conference of
the Priority Research Programme Boundary Element Methods 1989 -
1995 of the German Research Foundation. October 2 -4, 1995 in
Stuttgart / Wolfgang L. Wendland (ed.). - Berlin; Heidelberg; New
York; Barcelona; Budapest; Hong Kong; London; Milan; Paris;
Santa Gara ; Singapur ; Tokyo: Springer, 1998
ISBN-13: 978-3-642-64554-9
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List of Contributors
Dr. H. Andra
Karlsruhe University, Institute of Solid Mechanics, Kaiserstrai3e 12, Box 6980,
76131 Karlsruhe, Germany.
Prof. Dr. H. Antes
Technical University of Brunswick, Institute for Applied Mechanics,
Spielmannstr. 11, 38106 Brunswick, Germany.
Dr. D. Berthold
Technical University of Chemnitz-Zwickau, Faculty of Mathematics,
09107 Chemnitz, Germany.
Dipl.-Math. U. Brink
University of Hanover, Institute for Structural and Computational
Mechanics, Appelstr. 9A, 30167 Hanover, Germany.
Prof. Dr. W. Dahmen
RWTH Aachen, Institute of Geometry and Practical Mathematics,
Templergraben 55, 52062 Aachen, Germany.
Prof. Dr.-Ing. L. Gaul
University of Stuttgart, Institute A of Mechanics, Pfaffenwaldring 9,
70550 Stuttgart, Germany.
Dr.-Ing. C. Haack
Technical University Hamburg-Harburg, Ocean Engineering Section II,
Eii3endorfer Str. 42,21073 Hamburg, Germany.
Dr. G. Haase
Johannes Kepler University Linz, Institute of Mathematics,
Altenberger Str. 69, A 4040 Linz, Austria.
Prof. Dr. W. Hackbusch
Christian-Albrechts-University of Kiel, Lehrstuhl fUr Praktische Mathematik,
Mathematisches Seminar, 24098 Kiel, Germany.
Dr. T. Hartmann
University of Hanover, Institute for Applied Mathematics, Welfengarten 1,
30167 Hanover, Germany.
Dr. B. Heise
Johannes Kepler University Linz, Institute of Mathematics,
Altenberger Str. 69, A 4040 Linz, Austria.
VI List of Contributors
Dr. R. Hinder
TH Darmstadt, Department of Mathematics, SchloBgartenstr. 7,
64289 Darmstadt, Germany.
Dr. M. Jager
Technical University of Brunswick, Institute for Applied Mechanics,
Spielmannstr. 11, 38106 Brunswick, Germany.
Prof. Dr. L. Jentsch
Technical University of Chemnitz-Zwickau, Faculty of Mathematics,
09107 Chemnitz, Germany.
Prof. Dr. K. Kalik
University of Stuttgart, Mathematical Institute A, Pfaffenwaldring 57,
70569 Stuttgart, Germany.
Dipl.-Math. B. Kleemann
Berlin Institute of Optics (BIFO), Rudower Chaussee 5,
12484 Berlin, Germany.
Dr. M. Kreienmeyer
University of Hanover, Institute for Structural and Computational
Mechanics, Appelstr. 9A, 30167 Hanover, Germany.
Prof. Dr.-Ing. G. Kuhn
University of Erlangen-Niirnberg, Lehrstuhl fUr Technische Mechanik,
Box 3429, 91022 Erlangen, Germany.
Dipl.-Math. M. Kuhn
Johannes Kepler University Linz, Institute of Mathematics,
Altenberger Str. 69, A 4040 Linz, Austria.
Dr. C. Lage
Christian-Albrechts-University of Kiel, Lehrstuhl fUr Praktische Mathematik,
Mathematisches Seminar, 24098 Kiel, Germany.
Prof. Dr. U. Langer
Johannes Kepler University Linz, Institute of Mathematics,
Altenberger Str. 69, A 4040 Linz, Austria.
o.
Prof. Dr.-Ing. Mahrenholtz
Technical University Hamburg-Harburg, Ocean Engineering Section II,
EiBendorfer Str. 42, 21073 Hamburg, Germany.
Dr. M. Maischak
University of Hanover, Institute for Applied Mathematics, Welfengarten 1,
30167 Hanover, Germany.
Prof. Dr. E. Meister
TH Darmstadt, Department of Mathematics, SchloBgartenstr. 7,
64289 Darmstadt, Germany.
List of Contributors VII
Dr. D. Mirschinka
Technical University of Chemnitz-Zwickau, Faculty of Mathematics,
09107 Chemnitz, Germany.
Dipl.-Ing. P. Partheymiiller
University of Erlangen-Nurnberg, Lehrstuhl fUr Technische Mechanik,
Box 3429, 91022 Erlangen, Germany.
Prof. Dr. S. ProBdorf
Weierstrass Institute of Applied Analysis and Stochastics (WIAS),
Mohrenstr. 39, 10117 Berlin, Germany.
Dipl.-Math. R. Quatember
University of Stuttgart, Mathematical Institute A, Pfaffenwaldring 57,
70569 Stuttgart, Germany.
Dr. A. Rottgermann
University of Stuttgart, Institut of Aerodynamics and Gasdynamics,
Pfaffenwaldring 21, 70569 Stuttgart, Germany.
Prof. Dr. A.-M. Sandig
University of Stuttgart, Mathematical Institute A, Pfaffenwaldring 57,
70569 Stuttgart, Germany.
Dr. S. Sauter
Christian-Albrechts-University of Kiel, Lehrstuhl fur Praktische Mathematik,
Mathematisches Seminar, 24098 Kiel, Germany.
Dr.-Ing. M. Schanz
Technical University of Brunswick, Institute for Applied Mechanics,
Spielmannstr. 11, 38106 Brunswick, Germany.
Dr.-Ing. V. Schlegel
Technical University Hamburg-Harburg, Ocean Engineering Section II,
Eif3endorfer Str. 42, 21073 Hamburg, Germany.
Prof. Dr. E. Schnack
Karlsruhe University, Institute of Solid Mechanics, Kaiserstrafie 12, Box 6980,
76131 Karlsruhe, Germany.
Dr. R. Schneider
TH Darmstadt, Department of Mathematics, SchloBgartenstr. 7,
64289 Darmstadt, Germany.
Dr. H. Schulz
University of Stuttgart, Mathematical Institute A, Pfaffenwaldring 57,
70569 Stuttgart, Germany.
Prof. Dr. B. Silbermann
Technical University of Chemnitz-Zwickau, Faculty of Mathematics,
09107 Chemnitz, Germany.
VIII List of Contributors
Prof. Dr. E. Stein
University of Hanover, Institute for Structural and Computational
Mechanics, Appelstr. 9A, 30167 Hanover, Germany.
Dr. O. Steinbach
University of Stuttgart, Mathematical Institute A, Pfaffenwaldring 57,
70569 Stuttgart, Germany.
Prof. Dr. E. P. Stephan
University of Hanover, Institute for Applied Mathematics, Welfengarten 1,
30167 Hanover, Germany.
Dr. Sz. Szikrai
Karlsruhe University, Institute of Solid Mechanics, KaiserstraBe 12, Box 6980,
76131 Karlsruhe, Germany.
Dr. G. Trondle
Technical University of Brunswick, Institute for Applied Mechanics,
Spielmannstr. 11, 38106 Brunswick, Germany.
Dr. K. Tiirke
Karlsruhe University, Institute of Solid Mechanics, KaiserstraBe 12, Box 6980,
76131 Karlsruhe, Germany.
Prof. Dr. S. Wagner
University of Stuttgart, Institut of Aerodynamics and Gasdynamics,
Pfaffenwaldring 21, 70569 Stuttgart, Germany.
Prof. Dr. W. L. Wendland
University of Stuttgart, Mathematical Institute A, Pfaffenwaldring 57,
70569 Stuttgart, Germany.
Dipl.-Ing. W. Wenzel
University of Stuttgart, Institute A of Mechanics, Pf(iffenwaldring 9,
70550 Stuttgart, Germany.
Prof. Dr. B. Zastrau
University of Wuppertal, Institute of Mechanics, Pauluskirchstr. 7,
42285 Wuppertal, Germany.
Table of Contents
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Efficient Calculation of Acoustic Fields by Boundary
Element Method
G. Trondle, M. Jager, and H. Antes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1 Introduction................................................. 9
2 Acoustic problems in frequency domain. . . . . . . . . . . . . . . . . . . . . . . .. 10
3 Multigrid solver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11
3.1 Operator splitting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13
4 Adaptive mesh refinement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17
4.1 Error indicator .......................................... 18
4.2 Refinement strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
5 Acoustic problems in time domain ............................. 21
6 Analysis of different boundary element methodologies. . . . . . . . . . . .. 22
6.1 Comparison of Point Collocation and Galerkin Method. . . . . .. 23
6.2 New BE realizations of Morino's modified Kirchhoff's equation 25
7 Adaptive meshes for moving noise sources. . . . . . . . . . . . . . . . . . . . . .. 26
7.1 An Effective but Simple Local Error Indicator. . . . . . . . . . . . . .. 27
7.2 Strategy For Refining and Re-Coarsening Grids Creating a
"Moving" Mesh. . . . . .. . . . . . . . . . . .. . . .. . . . . . . . . . . . . . . . . . .. 27
8 Conclusion.................................................. 28
A Boundary Element Formulation for Generalized
Viscoelastic Solids in Time Domain
M. Schanz, L. Gaul, W. Wenzel, and B. Zastrau . . . . . . . . . . . . . . . . . . .. 31
1 Introduction................................................. 31
2 Constitutive equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32
3 Elastic BE-formulation ....................................... 35
4 Viscoelastic BE-formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38
5 Numerical example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39
5.1 3-d pressure bar ......................................... 40
5.2 Foundation slab on soil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43
6 Stability and numerical damping of the elastic solution ........... 44
7 Conclusions................................................. 49
X Table of Contents
On the Efficient Realization of Sparse Matrix Techniques for
Integral Equations with Focus on Panel Clustering,
Cubature and Software Design Aspects
W. Hackbusch, C. Lage, and S.A. Sauter. . . . . . . . . . . . . . . . . . . . . . . . . .. 51
1 Introduction................................................. 51
2 Setting and Preliminaries .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52
3 Cubature Techniques for the Approximation of Singular and Nearly
Singular Surface Integrals Arising in BEM ...................... 55
3.1 Cubature Techniques for the Collocation Method. . . . . . . . . . .. 57
3.2 Cubature Techniques for the Galerkin Method. . . . . . . . . . . . . .. 58
4 The Panel Clustering Method ................................. 62
4.1 Kernel Expansions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62
4.2 The Algorithm .......................................... 65
5 Error Analysis of the Panel Clustering Method .................. 66
5.1 Complexity of the Panel Clustering Algorithm. . . . . . . . . . . . . .. 67
6 Software Design Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69
Bimetal Problems
L. Jentsch and D. Mirschinka. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77
1 Introduction................................................. 77
2 Two-dimensional Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79
3 Three-dimensional Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 82
4 Boundary integral operators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 86
5 Meshes and Spline spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94
6 Stability and error estimates for the Galerkin method ............ 95
Analysis of 3D Elastoplastic Notch and Crack Problems
using Boundary Element Method
G. Kuhn and P. Partheymiiller ................................... 99
1 Introduction................................................. 99
2 Basics of Continuum Mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.1 Elasticity Theory ........................................ 100
2.2 Plasticity Theory ........................................ 101
3 Basics of Fracture Mechanics .................................. 102
3.1 Linear Elastic Fracture Mechanics .......................... 102
3.2 Nonlinear Fracture Mechanics ............................. 104
4 Boundary Element Method in Elastoplasticity ................... 104
4.1 Boundary Integral Formulations ........................... 104
4.2 Elastoplastic Solution .................................... 107
5 Crack Problems and Boundary Element Method ................. 109
5.1 Crack Modelling in the Boundary Element Method ........... 109
5.2 Evaluation of Fracture Mechanics Parameters ................ 115
6 Conclusion .................................................. 116