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CONSISTENT INFINITESIMAL FINITE‐ELEMENT CELL METHOD IN FREQUENCY DOMAIN
Author(s) -
WOLF J. P.,
SONG C.
Publication year - 1996
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/(sici)1096-9845(199611)25:11<1307::aid-eqe613>3.0.co;2-0
Subject(s) - finite element method , mathematical analysis , infinitesimal , mathematics , stiffness matrix , mixed finite element method , extended finite element method , boundary knot method , boundary value problem , discretization , smoothed finite element method , geometry , boundary (topology) , boundary element method , physics , thermodynamics
To calculate the dynamic‐stiffness matrix at the structure–medium interface of an unbounded medium for the range of frequencies of interest, the consistent infinitesimal finite‐element cell method based on finite elements is developed. The derivation makes use of similarity and finite‐element assemblage, yielding a non‐linear first‐order ordinary differential equation in frequency. The asymptotic expansion for high frequency yields the boundary condition satisfying the radiation condition. In an application only the structure–medium interface is discretized resulting in a reduction of the spatial dimension by one. The boundary condition on the free surface is satisfied automatically. The consistent infinitesimal finite‐element cell method is exact in the radial direction and converges to the exact solution in the finite‐element sense in the circumferential directions. Excellent accuracy results.