Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation

@article{Berkolaiko2022ThreedimensionalEB,
  title={Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation},
  author={Gregory Berkolaiko and Mahmood Ettehad},
  journal={Studies in Applied Mathematics},
  year={2022},
  volume={148},
  pages={1586 - 1623}
}
We consider three‐dimensional elastic frames constructed out of Euler–Bernoulli beams and describe a simple process of generating joint conditions out of the geometric description of the frame. The corresponding differential operator is shown to be self‐adjoint. In the special case of planar frames, the operator decomposes into a direct sum of two operators, one coupling out‐of‐plane displacement to angular (torsional) displacement and the other coupling in‐plane displacement with axial… 
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