Unformatted text preview: XS} S F
{XF} {Q} That is, the index B refers to the BuildingFoundation, F
to the interface and S to the soil. The stiffness matrix in Eq.(1) includes
[ 0 ] matrix, (1) which means that the B region does
not touch directly the S region but
touches the S region through the F
region. Dynamic stiffness matrix [KIJ] , which includes the mass,
the damping and stiffness, is expressed by: (2) where, [kIJ] , [mIJ] and [cIJ] are stiffness, mass and
damping matrix. And δIJ=1 when I is equals to J, while
δIJ=0 when I is not equal to J. Because the index F indicates the interface between B
and S region,
the dynamic stiffness
matrix [KFF] consists of
the dynamic stiffness
[KFFB] for B region and
[KFFS] for S region as
shown in Fig.2. That is:
(3) In Eq.(1) :
(1) The second equation in Eq.(1) (expressed by Eq.(12)) is:
(4)
Substituting Eq.(3) : (3) into Eq.(4) gives:
[K FB ]{ XB } + ([K FFB ] + [K FFS ]){ XF } + [K FS ]{ X S } = {0}
∴ ([K FB ]{ XB } + [K FFB ]{ XF }) + ([K FFS ]{ XF } + [K FS ]{ X S ) = {0}
(5) Expressing the first parenthesis in Eq.(5):
∴ ([K FB ]{...
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This note was uploaded on 03/14/2014 for the course CE 5680 taught by Professor Drgrd during the Summer '14 term at Indian Institute of Technology, Chennai.
 Summer '14
 DrGRD

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