Civil Engineering Reference
In-Depth Information
Form and factorise the global stiffness matrix
For all load (displacement) increments
Read applied load increment
For all iterations
Solve equations to give displacement increments
Set converged to .TRUE. if displacements hardly changed
from last iteration
For all elements
For all Gauss points
Compute elastic strain increments
Compute elastic stress increments and add to
stresses left over from last load increment
Failure criterion exceeded?
Yes No
Accumulate viscoplastic strains Go to next
Form integrals for element bodyloads Gauss point
Assemble global bodyloads
Convergence?
Yes, converged=.TRUE. No, converged=.FALSE.
Update element stresses Iterate again
ready for next load step
Update and print displacements.
Figure 6.8
Structure chart for viscoplastic algorithm
E
and
v
. Theoretically, bearing failure in this problem occurs when
q
reaches the “Prandtl”
load given by
q
ult
=
(
2
+
π)c
u
(6.38)
Apart from the variables,
type 2d='plane'
,
element='quadrilateral'
,
nod=8
and
dir='y'
, which are built into the program, the data follows the familiar
pattern established in Chapter 5. The “loads” in this case are the nodal forces which would
deliver a uniform stress of 1 kN/m
2
across the footing semi-width of 2 m (Appendix A).
These “weightings” are then increased proportionally by the load increment values held
in the vector
qinc
. In order to capture failure in a load-controlled problem such as this,
the increments need to made smaller as failure is approached. This may involve some trial
