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CALCULATING THE DYNAMIC STIFFNESS MATRIX OF 2‐D FOUNDATIONS BY DISCRETE WAVE NUMBER INDIRECT BOUNDARY ELEMENT METHODS
Author(s) -
ZHAO J. X.,
CARR A. J.,
MOSS P. J.
Publication year - 1997
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(199701)26:1<115::aid-eqe626>3.0.co;2-0
Subject(s) - boundary element method , stiffness matrix , boundary (topology) , matrix (chemical analysis) , damping matrix , stiffness , boundary value problem , finite element method , mathematical analysis , direct stiffness method , mathematics , engineering , structural engineering , materials science , composite material
Apart from some special cases, calculating the dynamic stiffness matrix of foundations on a layered half‐space, especially for embedded foundations, is computationally expensive. An efficient method for two‐dimensional foundations in a horizontally layered soil media is presented in this paper. This method is based on indirect boundary element methods and uses discrete wave number solution methods for calculating Green's functions for displacements and analytical methods for the integrations over the boundary. For surface foundations, the present method applies at all frequencies. For embedded foundations or for constructing energy transmitting boundaries, because the free‐field part is modelled by boundary elements and the excavated part is modelled by finite elements, the present method applies only at low frequencies for the spring coefficients (the real parts of the dynamic stiffness matrix) but applies at all frequencies for the damping coefficients (the imaginary part of the dynamic stiffness matrix) for undamped sites. The novelty of the method can be used for three‐dimensional foundations. © 1997 by John Wiley & Sons, Ltd.