I am trying to model nonlinear, cyclic behaviour of a cantilever beam, I wish to apply a cyclic load at the free end. And I want the midpoint of the beam to be displacement controlled (ie. reverse loading direction once the displacement at midspan reaches predetermined values).
How can I do this?
Hi Barry,
At a minimum you will need to split your cantilevered beam into two elements at the mid-span. After that, the process is straight forward. Apply the load at the cantilever tip, and use the DisplacementControl integrator:
integrator DisplacementControl $node $dof $dy
$node must be the integer for the node as defined at the midspan. $dof must be 2 if you wish to control the vertical displacement in a 2D model space. $dy is your displacement increment. If you wish to model a cyclic load, you must put this inside a loop:
analysis Static;
foreach peak $peaks {
set steps 100
set dy [expr $peak/$nsteps[]
integrator DisplacementControl $node $dof $dy
analyze $steps;
}
analysis Static;
foreach peak $peaks {
set steps 100
set dy [expr $peak/$nsteps[]
integrator DisplacementControl $node $dof $dy
analyze $steps;
}
The code above takes a list of displacement peaks, and for each peak, it performs 100 static analysis steps until the peak displacement is reached. Define a list of peaks accordingly based on what cyclic displacement you want to base your analysis on. For example, if you wish to go back and force between 2 in of vertical displacement, peaks should be:
set $peaks [list 2 -4 4 -4 4]
The first 100 steps will be to 2 inches in 0.02 inch increments, then to -2 inches in 0.04 inch increments (assuming your units are in inches, kip, ksi for example).
You could also define a displacement time series and perform a dynamic analysis, but this tends to be less stable than the simple displacement-controlled static analysis and it also depends on the time step (you will get dynamic effects for a fast loading and a close-to-static response for slow loading, whereas the static analysis does not include any dynamics in the system of equations).
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