On self-learning finite element codes based on monitored response of structures

In this paper, a strategy for developing self-learning finite element codes is presented. At the heart of these codes is a neural network based constitutive model (NNCM). In contrast to the normal practice of training neural networks for constitutive models with the data from homogenous material tests, training is accomplished here with stresses and strains at certain calibrating points in tests on structures where the stress/strain states are not homogenous. This strategy has a distinct advantage since a considerable effort is devoted by the experimentalists to achieve as homogenous state of stress/strain as possible. In many situations this is impractical for many reasons such as the samples being too small, precious or may require expensive methods of preparation. The methodology of self-learning finite element codes is illustrated by the solution of two heuristic boundary value problems. The first is a two-bar structure in which one of the bars is made of an ideally plastic or a strain softening material whilst the second bar is linear elastic. Computed load-deformation data of the structure are used for training of the neural network based constitutive model (NNCM) for the non-linear bar. It is shown that NNCM is capable of simulating the ideal plastic as well as the strain softening behaviour. The second problem simulates a plane stress panel of linear elastic material subjected to a concentrated vertical load at the top. The displacements at a number of monitoring points are used to train a NNCM. It is shown that the choice of the position of monitoring points affects the training programme and consequently the convergence of the NNCM predictions to standard solutions. The position of the load is then changed to demonstrate that the NNCM has been adequately trained to be able to perform analysis of any boundary value problem in which the material law corresponds to the trained NNCM. It is believed that the proposed technique of self-learning finite element codes will make a crucial impact on the methodology of engineering analyses and condition monitoring of structures. (C) 2000 Elsevier Science Ltd. All rights reserved.