Transformation of systems under influence of loads on the basis of static-geometric method

Abstract

The possibility of approximation of shells by folded transformed systems of granular modular elements is investigated. The options of parqueting the template with facets are given and the models of approximate approximation of surfaces by a modular element are presented. The paper deals with the folding surfaces in the formation of architectural shells and other types of structures that are often used. In some cases, it is caused by the architectonics of structures, which often have repetitive parts (folding in this case). In other cases, this is due to the need to approximate the folded surface, which consists of compartments of simpler surfaces, which make it easier to solve geometric problems in the design and construction. The comparison line is purposefully considered as an element of the set, which makes it possible to study the properties of such sets and methods of separating among them many kinds of folded surfaces (faces in this case). This gives reason to consider the technique of constructing comparable surfaces as the only scheme for constructing linear and non-linear surfaces. A generalized polygon is called a comparative line, which generally has curvilinear links that intersect or collide with each other at vertices, with a prominent joining order. A folding structure is a structure made up of folded elements, flat or spatial, by means of a method of module layout, transformation or profile sectioning of a surface. Generalized polyline lines of general form having zero order of joining in the vertices are formed by the method of joining the links in the vertices without matching tangents to the links. Methods of geometric shaping of modern buildings and newest forms, types of structures are being intensively developed, and sometimes they are subject to structural improvement. Geometric design, based on the principles of the combination of standard elements, seriality, manufacturability, meets the requirements of industrial production and mass application.