DYNAMIC-STIFFNESS MATRIX IN TIME-DOMAIN OF UNBOUNDED MEDIUM BY INFINITESIMAL FINITE-ELEMENT CELL METHOD

To calculate the dynamic-stiffness matrix in the time domain (unit-imp ulse response functions) of the unbounded medium, the infinitesimal fi nite element cell method based solely on the finite element formulatio n and working exclusively in the time domain is developed. As in the c loning algorithm, the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the in finitesimal finite element cell. The derivation can be performed exclu sively in the time domain, or alternatively in the frequency domain. A t each time station a linear system of equations is solved. The consis tent-boundary method to analyse a layered medium in the frequency doma in and the viscous-dashpot boundary method are special cases of the in finitesimal finite element cell method. The error is governed by the f inite element discretization in the circumferential direction, as the width of the finite-element cell in the radial direction is infinitesi mal. The infinitesimal finite element cell method is thus 'exact in th e finite-element sense'. This 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.