Dear Community,
While I have been using iVABS for structural optimization for a while, I have not derived the VABS formulation myself. Recently we are facing a scalability issue in optimization, and wanted to revisit the formulation to see if any simplification/acceleration could be done. I figured maybe the experts here can help.
To pose the question, let’s consider a composite beam with a rectangular cross-section (CS) and rounded corners. The goal is to design the CS to match some target properties - for simplicity, let’s consider EI in one direction. Say there are 50 plies, and we are optimizing the materials and the orientation (only 0, +/-45, 90) of each ply - so there are 100 variables. We are already able to do this in iVABS, but it is very time-consuming - as one could imagine - one VABS analysis per iteration over the CS resolved at the ply level.
Then here comes the question on additivity. Suppose for each individual, standalone ply, we do VABS to get the EI of that particular ply, and then add the EI’s of all plies up. How would this sum compare to the actual EI of the entire CS computed by VABS? In classical theory, I believe the two would equal, but for VABS as a nonlinear theory I’d wonder how different it would be?
We are doing some numerical experiments to explore, but wanted to ask from the theoretical aspect as well.
Even if the additivity is approximate, we could solve a linear programing problem first (very cheap) and warm start iVABS with much better initial guesses.
Thank you in advance.