This thesis develops a computational framework based on the Scaled Boundary Finite Element Method (SBFEM) to simulate ultrasonic guided waves for non-destructive testing (NDT) and structural health monitoring (SHM). Guided waves are well-suited for inspecting large structures with minimal sensor deployment, yet their modelling remains challenging due to dispersion, multimodal behaviour, and short wavelengths at high frequencies. Traditional finite element methods (FEM) often struggle to address these complexities efficiently.

This work aims to establish an SBFEM-based framework to advance the simulation of ultrasonic guided waves. The approach is motivated by the distinct advantages of SBFEM, offering potential solutions to challenges encountered with conventional numerical methods. Several techniques are introduced, analysed, and validated through numerical experiments and benchmark studies.

First, the feasibility of image-based modelling is examined for 2D guided wave simulations in plates. This study is then extended to 3D plate structures, requiring the implementation and validation of high-order transition shape functions within the classical SBFEM formulation. Benchmark tests confirm the applicability of this approach.

Next, the formulation of unbounded domains for 3D plates is investigated. Non-reflective boundaries are crucial in ultrasonic guided wave simulations, and the semi-analytical nature of SBFEM provides a distinct advantage in this context. However, its application to unbounded 3D plate structures remains largely unexplored. This work evaluates a modified version of the SBFEM using benchmark cases, demonstrating its performance relative to conventional methods.

Additionally, a domain decoupling strategy based on the mortar finite element method is introduced by taking advantage of the compatibility of the SBFEM with it. This method enables the independent treatment of near field and far field models. Several examples assess the effectiveness of this domain decoupling strategy, confirming its suitability for guided wave simulations.

Finally, the developed techniques are integrated with boundary integral formulations to analyse far field scattering of guided waves. The resulting framework facilitates a modal-based approach to wave-defect interaction analysis, providing an efficient and accurate means to simulate scattering phenomena.

In summary, this research establishes the SBFEM as a robust tool for guided wave problems, addressing key challenges in meshing, unbounded domain modelling, and defect interactions. The main contributions include non-conventional meshing, SBFEM for unbounded 3D plates, integration with the mortar finite element method for domain decoupling, and an approach for far field scattering analysis. These advancements position the SBFEM as an efficient alternative for guided wave simulations, with significant potential for broader applications in NDT and SHM.