Premium
Dynamic‐stiffness matrix in time domain of unbounded medium by infinitesimal finite element cell method
Author(s) -
Wolf John P.,
Song Chongmin
Publication year - 1994
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290231103
Subject(s) - finite element method , mathematical analysis , infinitesimal , mixed finite element method , extended finite element method , boundary knot method , stiffness matrix , mathematics , boundary (topology) , geometry , boundary element method , physics , thermodynamics
To calculate the dynamic‐stiffness matrix in the time domain (unit‐impulse response functions) 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. 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 can be performed exclusively in the time domain, or alternatively in the frequency 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’. 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.