Abstract
In engineering fields there have recently been a number of studies that have applied the finite-difference time-domain (FDTD) numerical method to elastodynamic problems. These studies include those of ultrasonic transducers and electro-mechanical devices. In FDTD formulations, the first-order set of partial differential equations given by the constitutive equations are discretized using a leap-frog finite-difference scheme. When a high-contrast discontinuity, especially a free surface, is present, some difficulties arise due to the spatially staggered nature of the grid of the FDTD approach, with neither all the velocity variables nor all the stress variables appearing on the same grid lines. The present study considers the following modifications to the FDTD approach: a standard staggered grid for anisotropic elastic wave fields is rotated so that the diagonal directions of the standard grid lie parallel to the axes of the analysis region. This configuration, called the diagonally staggered grid (DSG), improves the accuracy of the implementation of free boundaries without requiring virtual grids in a vacuum area. The effectiveness of DSG was verified by applying this method to model problems of isotropic and anisotropic solid materials.