Civil Engineering Reference
In-Depth Information
Read data
Allocate arrays
Find problem size
Null global array
For all elements
Find nodal coordinates and steering vector
Null element [k
m
] [k
c
] and [c] matrices
For all integrating points
Compute shape functions and derivatives in
local coordinates
Convert from local to global coordinates
Form stiffness contribution [km] using
8-node elements
Form conductivity and coupling contributions
[k
c
] and [c] using 4-node shape functions funf
Form element [k
e
] matrix and assemble
into global symmetric band matrix kv
Factorise the left-hand-side
For all the time steps
Form the right-hand-side from
applied loads and fluid 'loads'
Complete the equation solution
Update the displacements and pore pressures
For all elements
Calculate and print effective stresses
Figure 9.7 Structure chart for incremental form of Biot analysis with global matrix assem-
bly in Program 9.3
time stepping parameter is set to
theta=0.5
. Displacement and pore pressure output is
requested at node
nres=21
at every tenth time step
npri=10
. The nodal freedom data
comes next, fixing the pore pressures at the top of the mesh to zero (drained) and also
the
x
-displacements at each side of the mesh to zero (smooth). This implies “oedometer”
conditions, with drainage at the top only. As with Programs 9.1 and 9.2, no pressures are
computed at the mid-side nodes, so the third freedom at all mid-side nodes is removed from
the analysis. The next data provide the load weightings corresponding to a unit pressure
(Appendix A) applied to the 3 nodes at the top of the mesh. The final data define the
load-time function to be applied at the top of the mesh. The bilinear function described in
Figure 9.9 is defined by just three coordinates and is interpolated linearly at each calculation
time step. The example given in Figure 9.8 is for a ramp load that reaches its maximum
value of 1.0 after
t
o
=
0
.
5 seconds.
