Application of the Koch Curve to Increase the Strength of Aircraft Parts

Abstract

Fractals are formed by iterative repetition of the construction algorithm at different scale levels. The use of such an algorithm, which increases the strength properties during the construction of the structure, will strengthen these properties with each iteration. The Koch curve principle is applied in the article. Replacing the compressible plate with four new ones connected at angles increases the stability of the structure.
 This article theoretically confirms the increase in the stability of the Koch plate both at the level of individual plates and at the level of fractal segments and the structure as a whole (general stability). Regularities of stability changes at different scale levels with an increase in the number of iterations are established. A comparison of variants of Koch plates with different similarity coefficients is also carried out.
 The theoretical results were confirmed using simulations in the CAE system Solid-Works - a finite element analysis of the stability of computer models of the Koch plates was carried out. The graphs constructed from the obtained data correspond to the theoretical predictions of the dependence of stability on the geometric parameters of the Koch plate.
 As an illustration of the applicability of this kind of fractal structures in the design of aircraft parts, a fractal modification of a typical part, the slat rail, has been developed. The proposed modification of the rail was also investigated using computer simulations. A comparison of the strength properties of a standard-shaped part and its analogue with a fractal structure included showed the advantage of the latter: with certain values of mass and loading scheme, the fractal modification showed twice as much stability. This reduces the weight of the standard slat rail by 5% without loss of strength properties.