Civil Engineering Reference
In-Depth Information
Figure 9.13
Mixed procedure
faster convergence rate but only at the expense of having to re-assemble and
solve a new system of linear equations at each iteration.
9.15.3
Mixed procedure
In practice, usually both the incremental and iterative procedures are used
together. The total load will be divided into a number of load increments.
At every increment of load, iterative procedure is applied until
convergence is obtained under that load increment. The accumulated load,
displacement, stress and strain arrived at up to that stage are stored and
become the starting values for the next load increment and the same
procedure is repeated till the full load has been applied. For non-linear
analysis of reinforced concrete structures, experience seems to indicate
that relatively small load increments with fairly frequent updating of the
stiffness for just a few iteration steps are required to produce the best
results. The mixed procedure is illustrated in Figure 9.13.
9.15.4
Flow chart of the non-linear analysis procedure
In short, the non-linear analysis procedure in fact consists of a series of
linear solutions in an iterative process which is based on the initial stiffness
method or Newton-Raphson (tangential stiffness) method and the residual
force concept. It also requires the use of constitutive laws describing the
