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Hydrodynamic‐stiffness matrix based on boundary elements for time‐domain dam‐reservoir‐soil analysis
Author(s) -
Wepf Dieter H.,
Wolf John P.,
Bachmann H.
Publication year - 1988
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.4290160309
Subject(s) - displacement (psychology) , mathematical analysis , boundary element method , matrix (chemical analysis) , mathematics , boundary (topology) , stiffness matrix , time domain , boundary value problem , frequency domain , free surface , geometry , stiffness , finite element method , mechanics , physics , engineering , structural engineering , computer science , materials science , psychology , computer vision , composite material , psychotherapist
For a reservoir with an arbitrary shape of the upstream dam face and of the bottom including an adjacent regular part of constant depth extending to infinity, the hydrodynamic‐stiffness matrix in the frequency domain for a displacement formulation is derived using the boundary‐element method. The fundamental solution takes the boundary condition at the free surface into account. The analytical solution of the semi‐infinite reservoir is used to improve the accuracy. To be able to transform the hydrodynamic‐stiffness matrix from the frequency to the time domain, the singular part consisting of its asymptotic value of ω ∞ is split off. It consists of an imaginary linear term in ω which can be interpreted as a damper with a coefficient per unit area equal to the product of the mass density and the wave velocity. This also applies for a reservoir bottom of arbitrary shape. The remaining regular part of the stiffness matrix is transformed numerically. The corresponding interaction force‐displacement relationship involves convolution integrals. This boundary‐element solution agrees well with analytical results and with those of other numerical procedures based on a time‐stepping method. The method is also applied to an actual earthquake acting on a reservoir with an irregular part with an inclined bottom and a regular part extending to infinity. The results of the analysis in the time domain coincide with those determined in the frequency domain.