Fast reduced model of non-linear dynamic Euler–Bernoulli beam behaviour

This paper introduces a new way to obtain the dynamical response of Euler–Bernoulli beams under large deflections. They are simulated with parsimonious models based on a two integrated neural networks. Our article proves that neural network based-reduced modelling allows mechanical simulations to benefit shorter time processing without a great loss of accuracy. Our model reduction technique ensures a good error-speed compromise. It rapidly leads to algebraic generic model matching interactive simulation or high-realistic multi-sensorial virtual protoyping requirements. The originality of our solution consists in the linking of two neural networks. They are integrated in a conditional loop. First, the article presents a systematic numerical technique that enables users to efficiently build an optimal neural network. This approach is based on the handling of discrete optimization evolutionary technique. Our optimization process is applied to the construction of the two neural networks. From an exhaustive learning base created from non-linear finite element analysis series, we secondly clearly describe our two neural network-based reduced models. The first neural network that enables nodal displacements to be determined from boundary conditions is linked to the second one that aims to set boundary conditions from a deformation state. The new relationship is finally analysed for justifying the successes of our proposal. The article completely details a new numerical process supervising the making of an integrated neural network loop being a new from of model for beam non-linear behaviour representation.