Civil Engineering Reference
In-Depth Information
The final program in this chapter repeats the analysis of Program 6.10, using a pre-
conditioned conjugate gradient solver involving no mesh assembly. The rather crude mesh
demonstrated in the previous example still required 1,538,004 locations in the vector
kv
in
order to store the stiffness matrix using a skyline strategy. Even quite modest 3D meshes
require arrays with millions of locations in order to store the global matrices.
The “mesh-free” approach made possible with preconditioned conjugate gradient (pcg)
solvers, enables large 3D analyses to be performed on computers with modest core memory
availability. Furthermore, the pcg approach is highly amenable to exploitation on computers
with parallel architecture as will be demonstrated in detail in Chapter 12.
Program 6.11 (data shown in Figure 6.49) involves no new variables and can be con-
sidered an extension of Program 6.2, in which the pcg technique was first introduced in a
plasticity analysis.
w1 s1 w2 h1 h2 d1
20.0 20.0 20.0 10.0 5.0 40.0
nx1 nx2 ny1 ny2 nze
5 3 5 3 5
ifix cg_tol cg_limit np_types
2 0.0001 500 5
prop(phi,c,psi,gamma,e,v)
0.0 60.0 0.0 20.0 1.0e5 0.3
0.0 55.0 0.0 20.0 1.0e5 0.3
0.0 50.0 0.0 20.0 1.0e5 0.3
0.0 45.0 0.0 20.0 1.0e5 0.3
0.0 40.0 0.0 20.0 1.0e5 0.3
etype(i),i=1,nels (x then y then z)
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
tol limit
0.0001 1000
nsrf,(srf(i),i=1,nsrf)
6
1.0 1.4 1.5 1.55 1.58 1.60
Figure 6.49
Data for Program 6.11 example
There are 2972 equations
srf max disp iters cg iters/plastic iter
1.00 0.2264E-01 17 107.88
1.40 0.3119E-01 78 110.40
1.50 0.3918E-01 206 110.41
1.55 0.4959E-01 379 110.11
1.58 0.6377E-01 723 110.04
1.60 0.9431E-01 1000 110.03
Figure 6.50
Results from Program 6.11 example
