An investigation was made of the loss of stability of polymer rods exposed to disturbances in the form of camber of the rod and eccentricity of load application. At present, polymeric materials are being used not only as fencing constructions and as constructions of 'secondary' value but also as bearing elements. Polymer rods for the strengthening of suspended constructions are an example. These rods undergo both elongation and compression.

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.

Abstract. In the article the derivation of the resolving equations for the calculation of a three-layer plate taking into account the creep of the middle layer by the finite element method is given. Rectangular finite elements are used. The problem reduces to a system of linear algebraic equations. An example of calculating a three-layer plate hinged on the contour and loaded with a uniformly distributed load is considered. A comparison of the results with the solution based on the finite difference method is presented.