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I am trying to develop a program in Python that runs a few different basic analyses for optimization like minimizing compliance and buckling. I want to use machine learning to try to develop a fast (once programmed) multi-objective optimizer. To do this I need a way to calculate the critical buckling load of whatever arbitrary geometry it is optimizing, so that the agent can learn to minimize this value.

I have searched what feels like everywhere and cannot find any method of calculating the critical buckling load that is not just using a massive prebuilt software like Abaqus or Fusion 360. The problem with using scripting for those services is that in order to run this computationally intensive program and train the machine learning model, I need to use cloud computing and cannot use a service like Microsoft Azure with another commercial program like Abaqus (as far as my understanding goes).

Does anyone know if it is currently possible and reasonable to program an FEA to determine the critical buckling load of an arbitrarily shaped object?

I currently represent the object as a 3D grid of voxels, and expect to run it at a resolution of roughly 30x30x30 for now.

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Representing the geometry using voxels seems very inefficient to me. Although voxels could be translated to solid brick elements in FEA, buckling analysis is usually more important for thin shell and beam structures, so you would need a way to extract shell and beam elements from the voxels.

Critical buckling load is very sensitive to small changes to geometry and calculating it precisely can be very difficult. The most precise analysis involves initial imperfections of the geometry, large deformations and nonlinear material model, which is quite a challenge even for professional FEA packages.

Maybe you could use just the simplest analysis, the eigen buckling in combination with static analysis (which is not very precise) and focus only on frame structures (represented using beams instead of voxels of course).

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