FE-PML Modeling of Guided Elastic Waves and its Applications to Ultrasonic NDE
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Date
2010-09-10T22:33:36Z
Authors
Mahmoud, Abdel-Rahman
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Abstract
This thesis investigates the use of a combined finite element and perfectly matched layer approach in modeling guided elastic wave motion in infinite plates and cylinders and its potential applications to non-destructive evaluation. Underlying principles of the per-fectly-matched, absorbing layer are demonstrated on one-dimensional wave propagation in a semi-infinite elastic rod.
Feasibility of using the perfectly matched layer as absorbing boundary condition in the finite-element modeling of guided elastic wave propagation and scattering is studied for the canonical problem of shear horizontal wave motion in isotropic plates. Numerical re-sults in this study are validated against exact analytical solutions. Excellent agreement has motivated the endeavour to take the technique to the next level of pressure, shear-vertical wave motion in isotropic and transversely isotropic plates.
Time-domain, finite-element formulation of the perfectly matched layer for pressure, shear-vertical wave motion was validated through comparisons with semi-analytical lit-erature data and reciprocity checks. Numerical implementation of the model was em-ployed in studying the effect of crack presence on the time of arrival in a pitch-catch, non-destructive inspection arrangement. Predictions made confirmed previously-reported experimental findings.
Extensions into three-dimensional, Cartesian and cylindrical spaces were validated against reported data. Practical examples of wave scattering in damaged concrete beams, oil and gas pipelines, and composite shells demonstrated the potential use of the proposed model in simulating elastic-wave based non-destructive inspection. Up to 80 % of the computational time needed to run an extended-mesh, finite-element model can be saved by introducing the perfectly-matched, absorbing layer to the finite-element model as the current thesis proposes. This significant saving in computational time by the proposed FE-PML model can accelerate the production of artificial neural network training data or help tackle complicated non-destructive testing applications.
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Keywords
Elastic Waves, PML, FEM, Plates, Pipes, NDE
Citation
Mahmoud, A and Luo, Y. (2009). Application of Perfectly Matched Layer Boundary Condition to Finite Element Modeling of Elastic Wave Scattering in Cracked Plates, Advances in Theoretical and Applied Mechanics 2(1-4): 75-92.
Mahmoud, Abdel-Rahman; Rattanawangcharoen, Nipon; Luo, Yunhua; and Wang, Quan (2010). FE-PML Modeling of 3D Scattering of Transient Elastic waves in Cracked Plate with Rectangular Cross Section, International Journal of Structural Stability and Dynamics (to appear)
Mahmoud, Abdel-Rahman; Rattanawangcharoen, Nipon; Luo, Yunhua; and Wang, Quan (2010). FE-PML Modeling of 3D Scattering of Transient Elastic waves in Cracked Plate with Rectangular Cross Section, International Journal of Structural Stability and Dynamics (to appear)