Influence of the geometrical researches of surfaces of revolution and translation surfaces on design of unique structures

Abstract

Aims of research. The use, design and analysis of architectural and building structures in the form of smooth and composite surfaces have become relevant and in demand lately, which determined the purpose of this article - to analyze the use of analytical surfaces given vector, parametric or explicit equations in real structures. Methods. The relationship between studies on the geometry of surfaces of revolution and transport and the creation of new forms of thin-walled structures and buildings is determined. An example of a real structure is given on each surface. The article does not consider composite, multifaceted, fractal surfaces, as well as surfaces that are not defined analytically. Results. It turned out that only a small number of considered surfaces of these two classes have found application in the world. At the end of the article, a bibliography is presented, which sets out the mathematical side of the design of analytical surfaces, their computer modeling, more detailed information about real structures in the form of the surfaces under consideration.

Analytical surfaces for architecture and engineering

“…This hinders their application [23]. There is a well-known velaroidal shell for covering an industrial workshop, designed by M. Mihailescu [24], a sloping reinforced concrete velaroidal shell erected over the Nekrasovsky market in St. Petersburg in 1960 (Figure 2) and a fragment of the covering of the Cultural Center in Muscat (Oman) [25]. The group "Velaroidal surfaces" is often included in the class of transfer surfaces.…”