Finite Element Analysis of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 519

either automatic ( direct ) time incrementation or user-specified fixed time incrementa-
tion to control the solution. Automatic time incrementation is a built-in
incrementation scheme that allows the software to judge the increment
needed based on equilibrium requirements. On the other hand, user-
specified fixed time incrementation forces the software to use a specified
fixed increment, which in many cases may be large or small or need updating
during the step. This results in the analysis to be stopped and readjusted.
Therefore, automatic incrementation is recommended for most cases.
The methods for selecting automatic or direct incrementation are always
prescribed by all general-purpose software to help modelers. In nonlinear
analyses, most general-purpose computer programs will use increment
and iterate as necessary to analyze a step, depending on the severity of the
nonlinearity. Iterations conducted within an increment can be classified as
regular equilibrium iterations and severe discontinuity iterations . In regular equilib-
rium iterations, the solution varies smoothly, while in severe discontinuity
iterations, abrupt changes in stiffness occur. The analysis will continue to
iterate until the severe discontinuities are sufficiently small (or no severe dis-
continuities occur) and the equilibrium tolerances are satisfied. Modelers can
provide parameters to indicate a level of accuracy in the time integration,
and the software will choose the time increments to achieve this accuracy.
Direct user control is provided because it can sometimes save computational
cost in cases where modelers are familiar with the problem and know a suit-
able incrementation scheme. Modelers can define the upper limit to the
number of increments in an analysis. The analysis will stop if this maximum
is exceeded before the complete solution for the step has been obtained. To
reach a solution, it is often necessary to increase the number of increments
allowed by defining a new upper limit.
In nonlinear analyses, general-purpose software uses extrapolation to
speed up the solution. Extrapolation refers to the method used to determine
the first guess to the incremental solution. The guess is determined by the
size of the current time increment and by whether linear , parabolic ,orno
extrapolation of the previously attained history of each solution variable is
chosen. Linear extrapolation is commonly used with 100% extrapolation
of the previous incremental solution being used at the start of each increment
to begin the nonlinear equation solution for the next increment. No extrap-
olation is used in the first increment of a step. Parabolic extrapolation uses
two previous incremental solutions to obtain the first guess to the current
incremental solution. This type of extrapolation is useful in situations when
the local variation of the solution with respect to the time scale of the