A Neuro - Mechanical Shape Memory Device

1. Abstract In this paper we present what we call a Neuro-Mechanical Shape Memory Device (NMSMD), together with a method for configuration of such devices. This work builds on previous efforts dealing with the concept of Neuro-Mechanical Networks, and a NMSMD is here defined as a Neuro-Mechanical Network (NMN) which has the ability to take on certain predefined shapes when subject to external (mechanical or other) stimuli. From a mathematical point of view, the NMSMD is described by a coupled system of equations governing the behavior of an active truss with a neural network superimposed onto it. It is shown that with certain restrictions on the model parameters and an appropriate neuro-mechanical coupling term, a Liapunov function for the complete system can be found. In order to configure a NMSMD, we begin by setting up a ground structure and introducing a set of stimuli vectors, load cases, and associated shapes to be taken on by the device. We then solve an optimization problem with the objective of minimizing a measure of the sum of deviations from the desired shapes. As design variables we use the element volumes and the neural network weights. The problem is solved using the MMA algorithm, and some numerical examples to illustrate the idea are provided in the paper. 2.