Using Fractal Dimensions in Modeling Complex Systems in Engineering

Abstract

The article is devoted to the development and implementation of elements of express methods for designing heterogeneous objects. The method “of express-selection from the results of reverse calculation on the direct model - RCDM” is proposed. It allows you to dramatically speed up the creation of a direct computer model of an object, testing it and making a decision on its compliance with the specified operating conditions of the object. In the case of a negative answer, the original direct model is corrected, followed by a retest. The method consists in using the fractal dimension when modeling complex systems. Heterogeneous objects consist of at least two elements, between which there is a boundary. This boundary has a fractal dimension, and deliberate distortion (crumpling) of the original object leads to a change in the fractal dimension of the boundaries. The latter makes it possible to bring the distortion of the object to the extent that the boundaries reach the surface of the object and to numerically estimate the fractal dimension of the boundaries after crushing on the model. As a result, we get a number that allows us to measure the initial fractal dimension of this boundary, and therefore, to measure its state.