My intent is to build a program dedicated to analysis of geodesic structures.
My proof-of-concept spreadsheet is intended to help me clarify the interactions at each node, so that when I approach the coding of a C program, I will know the path for the workflow required for force balancing throughout the structure.
My simplified model is a basic icosahedron, truncated at the lower pentagon for a flat base.
I am using this simplified model to help visualize the maximum recognition of symmetry, and to apply those simplifications for the compute model.
The model is starting to get more realistic. Hoop stresses in the upper pentagon are clearly shown to be greater than those for the bottom pentagon, as one would expect. That bit of sanity check confirms I am on the right track.
In the region of CY55, I am trying to resolve the force balance equations for node 11 (point K), but something is not working out and I don't understand why. I think I am doing it right, the magnitude of the force on struts are as expected based on the balance at node 10, but the projections along each axis are not nullifying in this case (DE62:DE63).
I would appreciate it if someone could point out what it is that I have misunderstood/misapplied.
Thank you in advance for your reviewing and providing feedback.
LibreOffice .ods File: