Civil Engineering Reference
In-Depth Information
The example presented here uses lumped mass (
consistent = .FALSE.
), but the
program can also handle consistent mass if required, in which case the element mass
matrix is formed by subroutine
ecmat
. It should be noted that “exact” integration is
needed to integrate the consistent mass matrix of a general 8-node quadrilateral element.
In this example therefore, 9 integrating points (
nip=9
) have been used for all the element
integrations. If, as is often the case, “reduced” (
nip=4
) integration is preferred in the
generation of the stiffness matrix, two separate integration loops would be required, one
for the (consistent) mass, and one for the stiffness.
Up to the section headed “global stiffness and mass matrix assembly” the program's
task is the familiar one of generating the global stiffness and mass matrices, stored as usual
as skyline vectors
kv
and
mv
respectively. The matrix arising on the left-hand side of
(3.139) is then created, called (
f1
) and factorised using subroutine
sparin
.
In the time-stepping loop, the matrix-by-vector multiplications and vector additions
specified on the right-hand side of (3.139) are carried out and equation solution is completed
4.0
16
1
4
1.0
2
17
18
5
3
E=1 kN/m
2
n
=0.3
r
=1 t/m
3
F=cos
w
t
nxe nye
3 1
np_types
1
prop(e,v,rho)
1.0 0.3 1.0
etype (not needed)
x_coords, y_coords
0.0 1.33333 2.66667 4.0
0.0 -1.0
dtim nstep theta npri nres fm fk
1.0 20 0.5 1 18 0.005 0.272
nr,(k,nf(:,k),i=1,nr)
3
1 0 0 2 0 0 3 0 0
loaded_nodes,(node(i),val(i,:),i=1,loaded_nodes)
1
18 0.0 1.0
Figure 11.9
Mesh and data for Program 11.3 example
