Boundary element plate formulations for dynamic fracture and ultrasonic guided-wave structural health monitoring

Abstract

In this thesis, new boundary element formulations based on first-order plate theories are developed for dynamic fracture problems and Lamb-wave based structural health monitoring. The boundary integral equations are formulated in the complex frequency domain (Laplace-transform domain), which avoids domain integrals due to the inertial terms. In these plate formulations, only line elements are required for the discretization of membrane and bending problems. The dual boundary element method (DBEM) provides a general and computationally efficient way to model cracks. A new boundary element formulation for the Kane-Mindlin theory, a first-order theory for extensional motion of plates, is proposed for modelling the fundamental symmetric (S0) Lamb wave mode. The formulation is demonstrated to enable efficient and accurate modelling of the S0 mode over a wide frequency range. New fundamental solutions for such formulation are derived for the first time. The above-mentioned formulation is extended to a dual boundary element formulation to solve dynamic crack problems. The traction boundary integral equation utilized for this dual formulation is derived for the first time as well as their corresponding fundamental solutions. An out-of-plane fracture mode and the influence of plate thickness on dynamic stress intensity factors are analysed using such formulation, and the studies of the S0-mode wave scattering by a crack are also carried out. The cracked plate structures subjected to dynamic bending loads are investigated using a new Laplace-transform dual boundary element formulation which is developed for the Mindlin theory, a first-order shear deformable plate theory. The singular behaviours of the Laplace-transform fundamental solutions are re-examined and corrected. The dynamic fracture analysis of Mindlin plates is carried out using this formulation, which also allows to analyse the interaction between the fundamental antisymmetric Lamb wave (A0 mode) and the crack. The original fundamental solutions are modified slightly to represent the dispersion characteristic of the A0 mode more accurately. Piezoelectric actuators and sensors are incorporated into the above-mentioned boundary element plate formulations to simulate the Lamb wave excitation and sensing respectively, which provides an alternative numerical tool for the Lamb-wave based structural health monitoring (SHM). A new actuator model, called an equivalent pin-force model, is proposed, which makes the numerical implementation efficient and simple. This BEM model is able to provide data accurately and efficiently as input for damage detection algorithms to localize crack in a plate. Three-dimensional finite element simulation and experiments are carried out to validate the BEM-simulated results. Finally, spectral elements are introduced into a two-dimensional Laplace-transform BEM to solve high-frequency elastodynamic problems. It is shown that the computational efficiency can be improved significantly using the spectral elements, which indicates that it is well worth introducing the spectral elements into the proposed boundary element plate formulations for ultrasonic guided-wave SHM applications in the future.