Unit-impulse response matrix of unbounded medium by infinitesimal finite-element cell method Original Research Article

To calculate the unit-impulse response matrix of the unbounded medium, the infinitesimal finite-element cell method based solely on the finite-element formulation and working exclusively in the time domain is developed. A formulation can be derived for acceleration, velocity and displacement unit-impulse response matrices. Starting from the acceleration unit-impulse impulse response matrix those of the velocity and displacement are constructed. The algorithm to determine the acceleration unit-impulse response matrix and its application are simpler than the other two alternatives. As in the cloning algorithm, the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the infinitesimal finite-element cell. The derivation is performed exclusively in the time domain. At each time station a linear system of equations is solved. The consistent-boundary method to analyse a layered medium in the frequency domain and the viscous-dashpot boundary method are special cases of the infinitesimal finite-element cell method. The error is governed by the finite-element discretization in the circumferential direction, as the width of the finite-element cell in the radial direction is infinitesimal. The infinitesimal finite-element cell method is thus “exact in the finite-element sense”. The method leads to highly accurate results for a vast class of problems, ranging from a one-dimensional spherical cavity to a rectangular foundation embedded in a half-plane.