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I would like to create a spreadsheet as a "proof-of-concept" for clarifying the relationships and equations involved in doing the structural analysis of a geodesic dome. I then plan to translate that logic into C source code to tackle the real problem, namely half-sphere geodesic dome having "frequency" 2+.

To keep the "proof-of-concept" as simple and straightforward as possible, I am focusing on the analysis of force/load application/transmission thru the structure whose struts form a simple, regular tetrahedron. This choice is deliberate to offer a maximum of symmetry, allowing me to incorporate logic that would identify, and take advantage of, any and all symmetry existing in the structure.

My issue is that I am so removed, time-wise and memory-wise, from the knowledge of doing that from my university days, that I can't seem to get it straight, after having looked at a number of books.

So I hope someone could itemize for me the complete set of force and moment equations that I need to apply to my defined proof-of-concept problem. If someone could do that fully for node/vertex #4, I believe I could figure it out for all the rest. I am hoping to publish the results for common usage in Google's Geodesic Help Group.

From what I have read, a "stiffness" matrix may be involved, but I have never been introduced to that concept before, let alone actually used one.

I understand I need a set of equations for both force/moment balance (i.e. =0) at all joints/supports. I just can't visualize how that becomes

  • separate but interacting problems (joint-specific), or
  • a single, all-encompassing matrix that covers all the joints, where the values interract during the "solution" of the matrix.

Thank you in advance for your assistance.

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LibreOffice .ods File:

Proof-of-Concept Model - Load Propagation Structural Analysis

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