Date of Award

Fall 2019

Document Type

Open Access Dissertation


Mechanical Engineering

First Advisor

Sourav Banerjee


In this thesis, a meshless semi-analytical computational method is presented to compute the ultrasonic wave field in generalized anisotropic material while understanding the physics of wave propagation in detail. To understand the wave-damage interaction in an anisotropic material, it is neither feasible nor cost-effective to perform multiple experiments in the laboratory. Hence, recently the computational nondestructive evaluation (CNDE) received much attention to performing the NDE experiments in a virtual environment. In this thesis, a fundamental framework is constructed to perform the CNDE experiment of a thick composite specimen in a Pulse-Echo (PE) and through-transmission mode. To achieve the target, the following processes were proposed. The solution of the elastodynamic Green’s function at a spatial point in an anisotropic media was first obtained by solving the fundamental elastodynamic equation using Radon transform and Fourier transform. Next, the basic concepts of wave propagation behavior in a generalized material and the visualization of the anisotropic bulk wave modes were accomplished by solving the Christoffel’s Equation in 3D. Moreover, the displacement and stress Green’s functions in a generalized anisotropic material were calculated in the frequency domain. Frequency domain Green’s functions were achieved by superposing the effect of propagating eigen wave modes that were obtained from the Christoffel’s solution and integrated over the all possible directions of wave propagation by discretizing a sphere. MATLAB and C++ codes were developed to compute the displacement and stress Green's functions numerically. The generated Green’s function is verified with the existing methodologies reported in the literature. Further, the numerically calculated Green’s functions were implemented and integrated with the meshless Distributed Point Source Method (DPSM). DPSM technique was used to virtually simulate NDE experiments of half-space, 1-layer plate, and multilayered plate anisotropic material for both pristine and damage state scenarios, inspected by a circular transducer immersed in fluid. The ultrasonic wave fields were calculated using DPSM after applying the boundary conditions and solving the unknown source strengths. A method named sequential mapping of poly-crepitus Green’s function was introduced and executed along with discretization angle optimization for the time- efficient computation of the wave fields. The full displacements and stress wave fields in transversely isotropic, fully orthotropic and monoclinic materials are presented in this thesis on different planes of the material. The time domain signal was generated for 1-ply plate at any given point for transversely isotropic, fully orthotropic and monoclinic materials. Finally, the wave field is presented for structures with damage scenarios such as material degradation and delamination and compared with pristine counterparts to visualize and understand the effect of damages/defect in material state.


© 2019, Sajan Shrestha