Abstract. The problem of optimization of building structures is considered in architectural bionic modeling on the bionic principle basis. It is possible to get a reliable and durable constructions by studying the structure and the laws of organization of natural objects. Modern architects have created unique buildings using the bionic approach. There are such properties as symmetry, asymmetry, self-similarity and fractality used in the modern architecture. Using the methods of fractal geometry in the design of architectural forms allows finding a variety of constructive solutions.

In the paper, questions of form-building in architecture on the basis of fractal analysis in the design of unique structures are considered. The properties of the fractal and the principles resulting from these properties are studied. Examples of architectural elements with various fractals and their influence on the shape and structure of buildings are given. In this study, consideration is given to the organization of space in the complex of structures.

The article shows the presence of proportional correspondence of the parts and the whole using the principles of fractal geometry in the natural objects and phenomena beauty concept formation. The objects of the artificial environment are studied for the formation of images using the mathematical models’ example for calculating natural objects with fractal properties.

One of the work cycles of reinforced concrete structures is the state of repair and reconstruction, including the steps of strengthening elements. The traditional types of strengthening of reinforced concrete which are steel and concrete collars and shirts - now are receding into the background. New methods of strengthening with modern materials such as lamellae are increasingly being used. The article deals with the issues related to strengthening the structures made of high-strength concrete using composite polymeric materials.