Application of cellular neural networks in stress analysis of prismatic bars subjected to torsion

Abstract

In the most general case the finding of the shear stress distribution on the cross section of prismatic bar subjected to torsion is a specific problem that can be solved in two steps. The first of them consists in finding the so-called stress function, and the second one in finding the shear stresses on the basis of the formerly found stress function. The stress function is the solution of Poisson's partial differential equation for given conditions of unambiguity that in the elasticity theory describes the torsion of prismatic bars in terms of stresses. Modeling by means of electrical networks is one of a few possible ways to find the stress function. This paper describes how Chua and Yang's cellular neural networks can be used as an analogous model to find the stress function of a twisted prismatic bar, which serves to calculate the shear stress distribution. Effectiveness of the presented method is illustrated by the solutions of two problems. The method can be applied in mechanical and civil engineering.