Modeling and detection of delaminations in laminated plates

Abstract

The main topic of this thesis is the analysis and detection of delaminations in plate-like structural systems, such as concrete walls, large diameter pipes, slabs and decks. The first three chapters deal primarily with the numerical 2D modeling of delaminated plates. In the first chapter, we present the Traction Boundary Element Method (TBEM) that is the tool we use to model scattering of waves by cracks in elastic media. A critical step in the TBEM is the evaluation of integrals with hypersingular kernels; we propose a novel approach to evaluate analytically these integrals for the plane-strain cases (antiplane and in-plane). Finally, to test the TBEM and the analytical integrals, we study the 2-D scattering of plane waves by a single crack in an unbounded elastic medium; results compare nicely with previous pseudo-analytical solutions. The second and third chapters deal with the computation of Green's functions (singular solutions) for homogeneous and laminated plates, to be used in combination with the TBEM. In the second chapter, we present some classical modal solutions for anti-plane waves in a homogeneous plate and in two-layer plate, and in-plane waves in a homogeneous plate with mixed boundary conditions. In the third chapter, we present the Thin Layer Method (TLM), which is a powerful numerical tool for the computation of singular solutions in layered plates. Inasmuch the TLM has already been the subject of comprehensive studies, we focus here in its performance to model the near field and stresses for line loads and dipoles; areas of significant interest for the combination of the TLM and the TBEM that have been yet been explored. We carry out convergence analyses of the method for these cases of interest. The second part of the thesis focuses on the detection of delaminations. The combination of the TBEM and the TLM gives us a powerful tool to predict the response of plates with known properties and delaminations (the so-called forward model). We use this tool to model numerous configurations and study how the size and location of a delamination do affect the response of the plate. The fourth chapter addresses the standard indirect Non Destructive Evaluation techniques, namely the Impact-echo Method and the Sounding Method. We carry out parametric analyses for how the size and depth of a delamination affect the frequency response of the plate. We draw conclusions as to the limits of these methods in detecting delaminations and estimating their sizes and locations. In the fifth chapter, we use array-processing techniques, widely used in other areas such as seismology and telecommunications, to unravel the wave field of delaminated plates. We demonstrate that delaminations have a significant impact in the wave field, and that the decomposition of the propagating field into wave-guide modes can be used for the detection and chara