Contents
1 Introduction 1
1.1 The role of simulation methods for SHM . . . 10
2 Aim and the scope of the thesis 13 2.1 Aim . . . 13
2.2 Scope . . . 18
3 Modelling methods 21 3.1 Modelling methods . . . 22
3.1.1 Finite Difference Method . . . 22
3.1.2 Finite Element Method . . . 24
3.1.2.1 Solution approaches . . . 25
3.1.3 Spectral Element Method . . . 27
3.1.3.1 Dynamic Stiffness Method . . . 28
3.1.3.2 Spectral Analysis Method . . . 28
3.1.3.3 Spectral Element Method . . . 29
3.1.4 Boundary Element Method . . . 30
3.1.5 Finite Volume Method . . . 31
3.1.6 Other numerical methods . . . 32
3.1.7 Time discretisation . . . 36
3.1.7.1 Direct integration . . . 36
3.1.7.2 Mode superposition . . . 38
3.2 Wave propagation modelling . . . 39
3.3 Hybrid and Multiscale modelling . . . 40
3.4 Damage modelling . . . 42
CONTENTS
4 The Local Interaction Simulation Approach 47
4.1 The LISA algorithm . . . 47
4.2 GPU implementation . . . 52
4.2.1 Modular Solver . . . 53
4.2.2 Object Data Architecture . . . 53
4.2.3 Parallel Processing . . . 55
4.3 Developed LISA software package . . . 57
4.3.1 Analysis definition strategy . . . 58
4.3.2 Geometry reader . . . 60
4.3.3 Sensors and actuators . . . 66
4.3.4 Tables . . . 68
4.3.5 Auxiliary section . . . 68
4.3.6 Analysis management . . . 68
4.3.7 Postprocessing tools . . . 69
4.3.8 cuLISA3D solver-based programs . . . 70
4.3.8.1 PASP3D . . . 70
4.3.8.2 General Purpose Graphical User Interface . . . 72
4.3.9 Damage models in the LISA method . . . 73
4.3.10 Integration with hardware . . . 74
5 Absorbing boundary conditions for the LISA method 77 5.1 The Perfectly Matched Layers for the LISA . . . 79
5.1.1 The PML for the LISA method - derivation . . . 81
6 Hybrid approach for wave propagation modelling 91 6.1 Coupling . . . 94
6.1.1 Theoretical background . . . 95
6.1.2 Implementation of the hybrid method . . . 98
6.2 Stability issues . . . 110
6.2.1 Stability analysis of the hybrid method . . . 115 6.2.2 Stability analysis for LISA with absorbing boundary conditions . 116
CONTENTS
7 Applications 121
7.1 The cuLISA3D solver’s performance . . . 122
7.2 Lamb-Wave Dispersion Characteristics identification and damage detection126 7.3 Coupled Wave Propagation and Transducer Modelling for the LISA method133 7.4 Damage Detection with Lamb Waves . . . 136
7.5 Temperature field influence on the Lamb waves propagation . . . 138
7.6 Nonlinear acoustics for damage detection . . . 140
7.7 Model-based probability of detection analysis . . . 141
7.8 Application of absorbing boundary conditions for ultrasonic wave prop-agation . . . 143
7.9 Hybrid FE-LISA modelling . . . 145
8 Discussion 147
References 151
