Distributed Point Source Method for Modeling Wave Propagation in Anisotropic Media

Abstract

Distributed Point Source Method (DPSM) is a modeling technique for solving various engineering problems including ultrasonic and electromagnetic wave propagation problems. The DPSM is extended to analyze anisotropic materials in this dissertation. The DPSM requires evaluation of elasto-dynamic Green's function between many pairs of source and observation or target points. For homogeneous and isotropic media, the Green's functions are available as closed form analytical expressions. However, for anisotropic solids, the evaluation of Green's function is more complicated and needs to be done numerically. Nevertheless, important applications, such as defect detection in composite materials, require anisotropic analysis. The Green's function for anisotropic solids consists of two integrals. One of them contains singular terms while the other one contains non-singular or regular terms. The regular part, being in the form of a 2D surface integral, is responsible for the majority of the computational time. For transversely isotropic materials, the integration domain of the regular part can be reduced from a hemi-sphere to a quarter sphere. This reduction of integration domain is utilized in this dissertation. In addition, a technique called ”windowing” is suggested which makes use of the regular pattern of relative position of the source and target points in DPSM, in order to avoid repetitive evaluation of the Green's function. As another attempt to further reduce the computational time, a calibration strategy is suggested in this dissertation which is based on an equivalent isotropic stiffness tensor, and results in a multi-resolution integration technique which sets automatically an optimum number of integration points for a finite number of distance intervals between the source and the target points. The developed DPSM model equipped with windowing technique and multi-resolution numerical integration is then applied to solve a number of example problems, and its applicability and effectiveness for simulating ultrasonic wave propagation in anisotropic media is examined.