Overview of Geometric Ways to Increase the Constructions’ Specific Strength: Topological Optimization and Fractal Structures

The paper is an overview of geometric methods for increasing the specific strength of parts and constructions. In the making of engineering knowledge it had been deduced by theoretical and empirical ways a number of rules for specifying the shape of bodies withstanding the loads applied to them. So, in construction, they prefer to use an I-beam instead of a beam with rectangular section, since the first one is able to withstand a large load with a similar mass and the same material, that is, with a certain loading scheme, the I-beam has a greater specific strength due to the features of its geometry. The basic principles of creating such a geometry have been considered in this paper. With the development of the theory of strength of materials, as well as methods for automatization of design and strength calculations, it became possible to create the shape of parts optimized for specific loads. Computer generation of such a form is called topological optimization. A lot of modern research has been devoted to the development and improvement of algorithms for topological optimization (TO). In this paper have been described some of TO algorithms, and has been presented a general analysis of optimized forms, demonstrating their similarity to fractals. Despite the rapid development of topological optimization, it has constraints, some of which can be circumvented by using fractal structures. In this study a new classification of fractals is presented, and the possibility of their use to create parts and constructions of increased specific strength is considered. Examples for successful application of fractal geometry in practice are also presented. The combination of principles for designing strong parts and fractal shaping algorithms will make it possible in the future to develop the structure of strong elements applicable to increase the constructions’ specific strength. Further research will be devoted to this.