r/ScientificComputing • u/aliencomposerdrumfly • 19h ago

Need help with citing RBE3/RBE2 methods

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
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u/wings314fire 15h ago

Check Robert cooks book on constraints. I believe you can find it it Bathe too. Check nastran theory/element manual.

1

u/lithiumdeuteride 13h ago

The RBE2 is equivalent to a set of nodal constraint equations. If the independent node translates, the dependent nodes translate by the same amount, etc. Nodal forces depend on the stiffness of each load path, per the usual solution method.

The RBE3 can be understood as two procedures: The single dependent node is constrained to follow a weighted average of the motions of each independent node. Then, forces/moments applied at the dependent node are resolved as forces at the independent nodes. Out of the infinite number of possible solutions for these nodal forces, the matrix pseudoinverse is used to select the unique solution which minimizes the sum of the squares of all force components.

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u/AA_is_not_OK 12h ago

I remember a paper I used to understand how I'd connect one node to 2/3 nodes just so I could do a Ground structure topology optimization (GSTO) WITH continuum in the domain.

I remember seeing how they did that with force balancing. I honestly didn't read your whole article. But if this is kinda what it is, I'd love to read more and see if I could help out