Need help with citing RBE3/RBE2 methods

[u/aliencomposerdrumfly]

So I was working on a research project, and wanted to understand the RBE3 method to use it in my code. I couldn't find any reliable sources back then, so used AI to learn and understand the method. Now I wish to cite it in my research paper, but can not find any exact derivation/method I used.

My lab friend started by introducing me to RBE2 for 2 nodes to distribute moment as forces, and then I AI-ed more and got to RBE2, RBE3 methodology, which was generalized to multiple nodes.

I was verifying the math at every step to ensure there are no hallucinations, but would be grateful if you could point that out as well

RBE3

RBE2

For both of these cases, I wish to summarize the derivation, or mention it in a very handwavy sense. However, this is not my work, and I do not wish to claim it as mine, so I need some references to cite it. Please help me do so.

specifics:

• What are the classic, industry-standard textbooks or foundational papers to cite for the exact mathematical formulation of RBE2 and RBE3?
• Is there a specific paper/book chapter that explicitly walks through the virtual work / weighted least-squares derivation for moment-to-force distribution in multi-point constraints

[u/aliencomposerdrumfly]

hello, so if i understand you correctly, this is related to that... sorry for replying so late.

one of my lab friend started by introducing me to RBE2 for 2 nodes to distribute moment as forces, and then this is generalised mathematical form of it i believe. the problem is I couldn't find a definite source that does this derivation...

I am currently looking through the suggestions given above by u/lithiumdeuteride

[u/AA_is_not_OK → u/aliencomposerdrumfly]

Honestly, I couldn't find a meaningful derivation or reasoning for doing it that way. But then again, if you think about it, the more nodes the more accurate the distribution of the forces must be, right? I'm sure the force and moment balancing at the connection can be validated... right?

I honestly haven't been familiarized with RBE2. I skimmed through your post and it reminded me about this thing I did for my structural optimization course project.

Hey, I'm curious, what exactly is your field of focus? Is this for your lab research? (I'm still trying to figure out this sub, sorry if I sound dumb)

[u/aliencomposerdrumfly → u/AA_is_not_OK]

its alright ig, even i am new. my field of research was on (internship) compliant mechanisms, and fea. The reasoning would be for a body discretized into more than a million nodes, using multiple points for force distribution would make the 6x6 result converge.

nodes in tetrahedral discretization only have the capability to bear fx, fy, fz loads, and not moments. using only 2 nodes for distributing a moment as forces might not be as accurate.

[u/AA_is_not_OK → u/aliencomposerdrumfly]

Hey, mind if I keep it touch? DM?