Unformatted text preview: XB } + [K FFB ]{ XF }) + ([K FFS ]{ XF } + [K FS ]{ X S ) = {0}
(5)
by:
(6)
Then, the second parenthesis must be:
(7)
where, {F} denotes "Interaction
Force Vector" between B and S
region, and is applied on the
interface F. {F} Joining Eq.(11):
(1) with Eq.(6) :
(6)
gives:
(8) Also, joining Eq.(7) :
(7)
with Eq.(13) :
(1) leads to:
(9) All entries in the dynamic stiffness matrix of Eq.(8) :
(8)
can be determined by the material constants of B region,
while that of Eq.(9):
(9)
by S region. You can see that Eq.(1):
(1)
is separated into Eq.(8) :
(8)
and Eq.(9):
(9)
Eq.(8) and Eq.(9) are jointed by the interaction force
vector {F} on the interface F. The mechanics for Eq.(8) :
(8)
can be expressed by Fig.3:
which governs the B region including the F region. And also, the mechanics of Eq.(9) :
(9)
is illustrated by Fig.4: The equation governs the S region including the F region
with a void.
The void indicates the soil part which is excavated. In Eq.(9):
(9)
the external force term vector can be decomposed into:
(10)
The corresponding displacement vector are defined by:
(11)
The first vector {{XFf} {{XSf}}T in the right hand side is due
to the interaction force vector {{F} {0}}T,
while the second {{XFq} {{XSq}}T to the earthquake
disturbance vector {{0} {Q}}T. That is, the fir...
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 Summer '14
 DrGRD
 Force, Euclidean vector, Eq., KFF, SSI Analysis

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