Hi,

I'm studying a difficult non-linear problem where I need a very smooth load/unload curve (displacement vs time).

There are several instabilities in the solution, therefore loading/unloading should occur very slow.

I tought about using a Gaussian function, it almost does the job, altough you need to adjust it in the beginning and at the end.

Do you have any suggestions of possible mathemathical functions that can be good for a slow loading/unloading ?

I'm attaching the Excel spreadsheet I've used to build a load/unload curve where total time is 2 seconds, loading starts at o sec and ends at 1 sec. Unloading is from 1 sec to 2 sec

It would be nice to know if this is a NL static or dynamic study. Assuming it is a static study and you are trying to capture instabilities the best approach, if your problem has no contact in it, is to use the arc length method for control. No time curve is required and it is a method built for problems that undergo a complete loss of stiffness. If that doesn't fit as you are either doing a contact of NL dynamic problem then not landing on an instability is the probably more what needs to be done that having any concern for smoothness in the loading curve in a force controlled solution. It will be very challenging indeed to get a NL static solution with contact to post buckle. You best option would be to try it as a dynamic analysis and hope that the inertial terms help sort out the sequence of what buckles when. Matching the real expected rates of loading here would be key. Either way, it will likely be challenging but that is what I would try not really knowing what it is you are trying to pull off.