A Sierpiński triangle geometric algorithm for generating stronger structures

Abstract

In the twenty-first century, in the era of 3D printers and advanced technologies for the production of complex parts, it becomes possible to create objects that have a fractal structure. This gives relevance to the attempts of applying the knowledge of fractal geometry. This paper presents effectiveness confirmation and feasibility studies of using a fractal algorithm for making stronger structures. The algorithm is based on the Sierpiński fractal. The essence of the algorithm is to increase the buckling strength of the rods by fixing their midpoints. This principle makes it possible to create complex flat and three-dimensional structures, as well as to solve some engineering problems. Analytical strength calculations were run in Wolfram Mathematica, whilst Solid Works, a CAD and CAE program, were used to compute the strength.