Wave Propagation in Infinite Domains: With Applications..: Wave Propagation in Infinite Domains With Applications.rar

Wave Propagation in Infinite Domains: With Applications to Structure Interaction (Lecture Notes in Applied and Computational Mechanics)
By Lutz Lehmann


Publisher: Springer
Number Of Pages: 185
Publication Date: 2007-06-11
ISBN-10 / ASIN: 3540711082
ISBN-13 / EAN: 9783540711087
Binding: Hardcover


Wave propagation in infinite or unbounded domains is often encountered in scientific and engineering applications. Theoretical fundamentals and applications of a new numerical model which has the ability to simulate such wave propagation are presented. Attention is focused on linear waves in ideal fluids and elastic domains. Wave propagation based on scalar and vector wave equations, as well as fluid-structure interaction and soil-structure interaction is numerical simulated. The model is based on a coupled finite element/scaled boundary finite element method (FEM/SBFEM). While the FEM maps the near-field, under the immense variety of non-reflecting boundary conditions the SBFEM, developed by Wolf and Song, was chosen. It has some unique features: reduction of the spatial dimension by one without requiring a fundamental solution, no discretisation of free and fixed boundaries and interfaces between different materials, and influence of the infinite far-field could be stored in the form of matrices for further simulations (e.g., different load cases). Benchmark examples show the efficiency and accuracy of the proposed algorithm. Finally, covered fields of applications are: acoustics, dynamic behaviour of offshore wind turbines, and seismic analysis of buildings including soil-structure interaction.

Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Part I Theory
1 Finite element method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.1 Strain-displacement relationship . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.2 Constitutive equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.3 Dynamic equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Virtual work formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Approximative solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Time integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.1 Newmark algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.2 Hilber-Hughes-Taylor-αmethod . . . . . . . . . . . . . . . . . . . . . . . 13
2 Boundary element method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Integral formulation for elastodynamics . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Numerical implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Time domain boundary element formulation . . . . . . . . . . . . . . . . . . . . 22
3 Scaled boundary finite element method . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1 Scaled boundary transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Governing equations in scaled boundary coordinates . . . . . . . . . . . . . 27
3.3 Derivation of SBFE equation in displacements (frequency domain) . 31
3.4 Derivation of SBFE equation in dynamic stiffness (frequency
domain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Derivation of the acceleration unit-impulse response matrix (time
domain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5.1 Time discretisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6 Numerical implementation (near-field/far-field coupling) . . . . . . . . . 44
3.7 Improvement of efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.7.1 Convolution (reduction of non-locality in time) . . . . . . . . . . . 46
VIII Contents
3.7.2 Influence Matrices (reduction of non-locality in space) . . . . . 48
3.8 Application of hierarchicalmatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.8.1 Low rankmatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.8.2 Hierarchical partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.8.3 Approximationwith low rankmatrices . . . . . . . . . . . . . . . . . . 54
3.8.4 Matrix vector multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4 Benchmark examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1 Two-dimensional benchmark examples of soil-structure interaction
in the time domain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.1 Semi-infinite rectangular domain with vertical load . . . . . . . . 59
4.1.2 Response of an elastic half-space . . . . . . . . . . . . . . . . . . . . . . . 63
4.1.3 Road-tunnel traffic system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 Three-dimensional benchmark example of soil-structure interaction
in the time domain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Part II Applications
5 Wave propagation in fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.1.1 Sound propagation in unbounded fluids . . . . . . . . . . . . . . . . . . 82
5.1.2 Vibration of thin plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1.3 Finite elementmethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1.4 Scaled boundary finite element method . . . . . . . . . . . . . . . . . . 85
5.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2.1 Scaled boundary finite element method in the frequency
domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2.2 Scaled boundary finite element method in the time domain . 86
5.2.3 Boundary element method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.3 Coupling of fluid and structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.3.1 FE/FE coupling of elastic structure and interior fluid. . . . . . . 87
5.3.2 FE/SBFE coupling of elastic structure and exterior fluid . . . . 88
5.3.3 FE/BE coupling of elastic structure and exterior fluid . . . . . . 89
5.4 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.4.1 Fluid-structure-fluid interaction (frequency domain analysis) 90
5.4.2 Sound insulating wall (frequency and time domain analysis) 91
5.4.3 Waveguide (time domain analysis) . . . . . . . . . . . . . . . . . . . . . . 103
5.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6 Offshore wind energy conversion systems . . . . . . . . . . . . . . . . . . . . . . . . 109
6.1 Short history of wind conversion systems . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Wind loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2.1 Wind speed distribution andwind profile . . . . . . . . . . . . . . . . 111
Contents IX
6.2.2 Atmospheric turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.2.3 Spectral characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.3 Wave- and sea ice loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.3.1 Deterministic description of waves with the linear wave
theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.3.2 Statistical description of offshore waves . . . . . . . . . . . . . . . . . 119
6.3.3 Fluid-induced forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.3.4 Correlation of wind andwave loading . . . . . . . . . . . . . . . . . . . 129
6.3.5 Sea ice loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.4 Subsoil in the North Sea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.5 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.5.1 Foundation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.5.2 Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.5.3 Nacelle and wind turbine rotor . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.6 Numerical example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.6.1 Offshore environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.6.2 Discretisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7 Earthquake excited building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.1 Seismic waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.2 Ground response analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.3 Numerical example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7.3.1 Kobe earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7.3.2 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.3.3 Discretisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
A Recorded horizontal accelerations, velocities . . . . . . . . . . . . . . . . . . . . . . 167
B Calculated displacements of earthquake excited building . . . . . . . . . . . 171
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Wave Propagation in Infinite Domains With Applications to Structure Interaction

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