4 - Memorial University of Newfoundland DAI

From tho ~tatic dispiaeemont muita, the master flexibility matrix, [om,].
and the slave flexibility matrix, [a,], wen formed. Similarly, the master
mau matrix, [m,], and rlsvc maas matrix, [m..[, were also computed.
By applying equation (3.61), the condensed master stiffness matrix, [K]..
and lmm oquation (3.62), the transformation matrix, [TI, wen determined.
Thcn thecondensed mass matrix, [My, was obtained (i.e., [MI. = [m.,]+
[71r[m..][Tj I). Likewiac, knowing the forces at the various slave and master
DOF, thecondensod mater force vector,P, is computed with theexprunion
P = f+, + [TITL(t). Since tho resulting mass matrix, [MY, is a. urnaiatent
matrix, it was diiqgonaiized to form the stick model, uring the method re*
ommended by Cmk rcfcrcnced earlier in Appendix A. Thus, equation (3.64)
wns established.
Natural frequencies of the system were solved (i.e., setting &(t) = Q) us-
ing CLolos4y's pmccdure and the response was computed using the Houbolt
algorithm relcreneed earlier in Appendix A. The wave force vector at each
tnastcr node was ~pneraled with the same program used to ~olve the 3-D
struelure discwed in the precious section.
Damage Simulation: Structural damage or kilute in the 3-D and stick
model was simulated by making tile member(.) inactivein the analyses. This
was accompliahetl by removing the member(a) and the wociated pmpertiea
from lho computations. Sin- the flexibility matrix used togenerate ths stick
mod01 was obtained lrom the 3-D model program, the influence of member
mmoval was present in the flexibility analysis attained fmm the ulrit Iwd(s)
static diaplacnnent analyses. (A aummary of the computer aalyre. is pre-
salted in flow chart form in Piyre 3.13.)