Civil Engineering Reference
In-Depth Information
New dynamic real arrays:
bdylds pp
distributed body loads vector
bload
element body loads
increment of viscoplastic strain
devp
accumulating element body loads
eload
viscoplastic strain rate
erate
viscoplastic strains
evp
distributed total viscoplastic strains
evpt pp
viscoplastic flow
flow
distributed loads vector
loads pp
plastic potential derivatives matrix
m1
plastic potential derivatives matrix
m2
plastic potential derivatives matrix
m3
previous distributed displacements
oldis pp
vector of load increment terms
qinc
distributed stored element stiffness matrices
storkm pp
stress vector
stress
distributed stresses
tensor pp
distributed total displacements
totd pp
updated distributed pcg vector
xnew pp
This program follows naturally from the previous one by extending the material
behaviour beyond the elastic range. The post elastic region is perfectly plastic governed by
the Mohr-Coulomb yield criterion that was first introduced in Program 6.3 and applied in
three-dimensional analyses in Program 6.11. The same geometric restrictions apply as in the
previous program-only cuboidal meshes are allowed with the central loaded patch a vertical
uniformly distributed load extending to one-fifth of the surface in the
x
and
y
directions
(
is vertical). Thus only multiples of 5 should be used for
nxe
in this simple case.
After
INTEGER
and
REAL
data have been read and broadcast, load increment array
qinc
(See Programs 6.1 and 6.2) is read and needs to be broadcast to all other pro-
cessors using
MPI_BCAST
. The loop labelled
elements_1
can be compared with the
same loop in Program 6.11. In parallel,
geometry_20bxz
is used in place of the serial
geom_rect
but the basic process of finding
coord
,
num
and
g
for each element is clearly
equivalent.
Similarly loop labelled
elements_2
with its embedded integration loop
gauss_pts_
1
carries over essentially unaltered from serial to parallel versions.
In Program 6.11 each set of conjugate gradient iterations begins with a starting
x
value
of zero. In large non-linear problems it is beneficial to use the value of
x
computed in
the previous step as the starting
x
for a new step. Typically this halves the number of
pcg iterations in subsequent steps, and this procedure is used in this program (see loop
elements_2a
).
Loops labelled
conjugate_gradients
,
elements_3
,and
elements_4
with its
embedded
gauss_points_2
are equivalent in serial and parallelised versions.
The problem analysed as shown in Figure 12.1 with data in Figure 12.14, deals with
the bearing capacity of a square uniformly loaded punch at the surface of an elasto-plastic
z
