A Transmitting Boundary for Finite-Difference Analysis of Wave Propagation in Solids

The object of this study is to develop a transmitting boundary suitable for use in numerical solution of wave propagation problems. The detailed analysis refers to two-dimensional problems in plane strain. The medium near the transmitting boundaries must be linear, but inelastic action is permitted within the region. The method consists first of splitting the field near the boundaries into its irrotational (P) and equivoluminal (S) components by finding potentials for the motion near the boundaries. Transmitting boundaries are then developed which pass P and S waves with no interaction. Two types of transmitting boundary have been devised. In the first, the disturbances are taken as locally plane near the boundary in each time interval. A more refined approximation is also obtained in which the disturbances are taken as locally cylindrical. Numerical comparisons have been carried out which indicate that these transmitting boundaries actually perform well and are suitable for practical computation. In addition, other boundary conditions are examined by the use of potentials, especially the boundary between two elastic layers with different properties. Calculations show that the numerical solutions in the vicinity of such a boundary are stable, unlike the results obtained in some earlier work which did not use potentials.National Science Foundation Contract GK 24294Office of Naval Research. Department of the Navy: Contract No. N00014-75-C-0164; Project No. NR 064-18