Definition of the stiffness matrix of a hierarchical structure by using virtual testing and artificial neural networks

In this paper, we consider structures characterized by a definite geometrical hierarchy, such as multilayer wire ropes. We investigate the mechanical behavior, namely, the influence of the hierarchical helix geometry on the stiffness of the cable. It is shown how the stiffness matrix of these structures is different from the usual stiffness matrix of Euler-Bernoulli beams. Furthermore, the dependence of the stiffness coefficients on the twist pitches of the multilevel helixes is also analyzed. A hybrid finite element-artificial neural network approach (ANN-FE) is proposed, suggesting that suitably trained ANNs can replace the module that usually provides the stiffness matrix in an FE code. Finally, a comparison is shown, where results obtained via the FE method are compared with those calculated by an ANN-FE procedure.