Civil Engineering Reference
In-Depth Information
There are 30 equations and the skyline storage is 285
Result at node 18
time load x-disp y-disp
0.0000E+00 0.1000E+01 0.0000E+00 0.0000E+00
0.1000E+01 0.9553E+00 0.7363E+00 0.2167E+01
0.2000E+01 0.8253E+00 0.2231E+01 0.5226E+01
0.3000E+01 0.6216E+00 0.3252E+01 0.7398E+01
0.4000E+01 0.3624E+00 0.3987E+01 0.1046E+02
0.5000E+01 0.7074E-01 0.4832E+01 0.1398E+02
0.6000E+01 -0.2272E+00 0.5272E+01 0.1678E+02
0.7000E+01 -0.5048E+00 0.5086E+01 0.1839E+02
0.8000E+01 -0.7374E+00 0.4370E+01 0.1894E+02
0.9000E+01 -0.9041E+00 0.3255E+01 0.1834E+02
0.1000E+02 -0.9900E+00 0.1789E+01 0.1650E+02
0.1100E+02 -0.9875E+00 0.8872E-01 0.1349E+02
0.1200E+02 -0.8968E+00 -0.1674E+01 0.9574E+01
0.1300E+02 -0.7259E+00 -0.3372E+01 0.5082E+01
0.1400E+02 -0.4903E+00 -0.4915E+01 0.3726E+00
0.1500E+02 -0.2108E+00 -0.6150E+01 -0.4128E+01
0.1600E+02 0.8750E-01 -0.6858E+01 -0.7908E+01
0.1700E+02 0.3780E+00 -0.6839E+01 -0.1050E+02
0.1800E+02 0.6347E+00 -0.5986E+01 -0.1157E+02
0.1900E+02 0.8347E+00 -0.4304E+01 -0.1096E+02
0.2000E+02 0.9602E+00 -0.1902E+01 -0.8708E+01
Figure 11.10
Results from Program 11.3 example
by subroutine
spabac
. It then remains only to compute the new velocities and accelerations
using (3.140) and (3.141).
The problem layout and data are given in Figure 11.9. Following the usual data relating
to element numbers, properties and coordinates, the time stepping data calls for
nstep=20
steps of time step
dtim=1.0
with the output at node
nres=18
printed every
npri=1
time steps. The beam is damped using Rayleigh damping constants
f
m
=
0
.
005 and
f
k
=
0
close to 0.05 (see
equation (3.120)) for the first three natural frequencies. The results are listed as Figure 11.10
and plotted in Figure 11.7. The displacements are seen to be considerably disturbed by the
initial condition “transients”, but once the response has settled down, the average amplitude
agrees closely with that obtained by Modal Superposition, with a phase shift of about 90
◦
relative to the loading function.
.
272 (read as
fm
and
fk
respectively) giving a damping ratio
ζ
Program 11.4 Forced vibration analysis of an elastic solid in plane strain using rect-
angular 8-node quadrilaterals. Lumped or consistent mass. Mesh numbered in
x
-or
y
-direction. Implicit time integration using Wilson's method.
PROGRAM p114
!-------------------------------------------------------------------------
! Program 11.4 Forced vibration analysis of an elastic solid in plane
! strain using rectangular 8-node quadrilaterals. Lumped or
! consistent mass. Mesh numbered in x- or y-direction.
! Implicit time integration using Wilson's method.
!-------------------------------------------------------------------------
USE main; USE geom; IMPLICIT NONE
INTEGER,PARAMETER::iwp=SELECTED_REAL_KIND(15)
INTEGER::i,j,iel,k,loaded_nodes,ndim=2,ndof=16,nels,neq,nip=9,nn,nod=8, &
nodof=2,npri,nprops=3,np_types,nr,nres,nst=3,nstep,nxe,nye
