Two new inclined boundary conditions are developed which constrain a homogeneous elastic isotropic half-plane into a limited space in the near-field of a structure. The solution to the two-dimensional boundary-value problem of the phenomenon of seismic wave propagation in the elastic medium is obtained by converting the boundary conditions into a finite difference form and then applying the finite element method for the core region in the near-field. The two mutually perpendicular boundaries inclined to the horizontal free surface are capable of limiting the reflections from these boundaries. Both transient and steady-state situations are considered. The resulting boundary conditions are applicable in the time domain, and therefore can be applied to non-linear analysis. © 2001 Elsevier Science Ltd. All rights reserved.
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