Beam elements with neural shape functions

Object. Variable-stiffness beam elements whose shape functions, stiffness matrix and fixed-end forces are obtained with physics-informed neural networks. The network error is measured against Molina-Villegas's closed-form solution for non-uniform Euler-Bernoulli beams and frames.

Method. Four phases. In each one the network is trained, checked against the reference solution and tested on frames outside the training set, with an engineering tolerance set before the results are evaluated.

Status. Phases 1 to 3 closed with internal verification; phase 4 under way. The manuscript for external evaluation is prepared when phase 4 closes.