# Artificial Neural Networks

## Overview

As an alternative to modelling approaches using continuum or structural mechanics, artificial intelligence opens up new ways of mapping structural deformations. As a result of a self-learning algorithm, it is possible to simulate deformations, which originate from experiments or simulations, by means of artificial neural networks (KNN). In contrast to mechanical laws, this approach is based on empirical values with which the KNN is trained. Depending on the existing data structure, a functional approximation of the real system is created.

As an example, the deformation of a metal plate under impulse-like load in a shock wave tube is considered.

The circular test plate has a diameter of 553 mm and is 2 mm thick. It is loaded with the pressure in Figure 2 and leads to viscoplastic deformations within milliseconds.

With trained measurement data, the KNN can simulate the deformations and vibrations as shown in Figure 4. The neural network, Figure 3, consists of neurons that contain measured values, such as pressures and shock wave velocities, in the input layer. The output layer contains the deformation as a single neuron.

One or more hidden layers can be used in between. This leads to a deep learning algorithm. The layers are connected by synapses. More information about the mathematical design of the weightings, transfer functions and activation functions can be found in [1].

The use of the KNN in the example shown does not mean that simulation methods such as the Finite Element Method (FEM) are not needed, but that FEM and KNN can be combined efficiently. For example, parts of a finite element can be replaced by a KNN. This leads to the development of intelligent finite elements. In the present case [1], a material law is replaced by a KNN that was previously trained with material data. As a result, one can benefit from a more efficient calculation in finite element simulation, because a complicated material model is replaced by an algebraic system of equations.

[1] Stoffel M., Bamer F., Markert B., Artificial neural networks and intelligent finite elements in non-linear structural mechanics, Thin-Walled Structures, 131, 102-106, 2018.